diff --git a/changelog b/changelog index 2532ed6..f8f6e9f 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,90 @@ +20081204 tpd src/input/r21bugsbig.input cleanup +20081204 tpd src/algebra/zerodim.spad cleanup +20081204 tpd src/input/void.input cleanup +20081204 tpd src/input/tutchap1.input cleanup +20081204 tpd src/input/test.input cleanup +20081204 tpd src/input/stream2.input cleanup +20081204 tpd src/algebra/si.spad cleanup +20081204 tpd src/input/sersolve.input cleanup +20081204 tpd src/input/series.input cleanup +20081204 tpd src/input/schaum9.input cleanup +20081204 tpd src/input/schaum8.input cleanup +20081204 tpd src/input/schaum7.input cleanup +20081204 tpd src/input/schaum6.input cleanup +20081204 tpd src/input/schaum5.input cleanup +20081204 tpd src/input/schaum4.input cleanup +20081204 tpd src/input/schaum3.input cleanup +20081204 tpd src/input/schaum34.input cleanup +20081204 tpd src/input/schaum33.input cleanup +20081204 tpd src/input/schaum32.input cleanup +20081204 tpd src/input/schaum31.input cleanup +20081204 tpd src/input/schaum30.input cleanup +20081204 tpd src/input/schaum2.input cleanup +20081204 tpd src/input/schaum29.input cleanup +20081204 tpd src/input/schaum28.input cleanup +20081204 tpd src/input/schaum27.input cleanup +20081204 tpd src/input/schaum26.input cleanup +20081204 tpd src/input/schaum25.input cleanup +20081204 tpd src/input/schaum24.input cleanup +20081204 tpd src/input/schaum23.input cleanup +20081204 tpd src/input/schaum22.input cleanup +20081204 tpd src/input/schaum21.input cleanup +20081204 tpd src/input/schaum20.input cleanup +20081204 tpd src/input/schaum1.input cleanup +20081204 tpd src/input/schaum19.input cleanup +20081204 tpd src/input/schaum18.input cleanup +20081204 tpd src/input/schaum17.input cleanup +20081204 tpd src/input/schaum16.input cleanup +20081204 tpd src/input/schaum15.input cleanup +20081204 tpd src/input/schaum14.input cleanup +20081204 tpd src/input/schaum13.input cleanup +20081204 tpd src/input/schaum12.input cleanup +20081204 tpd src/input/schaum11.input cleanup +20081204 tpd src/input/schaum10.input cleanup +20081204 tpd src/input/reclos.input cleanup +20081204 tpd src/input/quat.input cleanup +20081204 tpd src/input/patch51.input cleanup +20081204 tpd src/input/page.input cleanup +20081204 tpd src/input/op1.input cleanup +20081204 tpd src/input/oct.input cleanup +20081204 tpd src/algebra/oct.spad cleanup +20081204 tpd src/input/nsfip.input cleanup +20081204 tpd src/input/noonburg.input cleanup +20081204 tpd src/input/ndftip.input cleanup +20081204 tpd src/input/mset2.input cleanup +20081204 tpd src/input/mpoly.input cleanup +20081204 tpd src/input/matrix.input cleanup +20081204 tpd src/input/matrix22.input cleanup +20081204 tpd src/input/mappkg1.input cleanup +20081204 tpd src/input/lupfact.input cleanup +20081204 tpd src/input/lodo.input cleanup +20081204 tpd src/input/intef2.input cleanup +20081204 tpd src/input/intbypart.input cleanup +20081204 tpd src/input/herm.input cleanup +20081204 tpd src/input/heap.input cleanup +20081204 tpd src/input/gonshor.input cleanup +20081204 tpd src/input/fr.input cleanup +20081204 tpd src/input/ffx72.input cleanup +20081204 tpd src/input/exprode.input cleanup +20081204 tpd src/input/equation2.input cleanup +20081204 tpd src/input/elfuts.input cleanup +20081204 tpd src/input/eigen.input cleanup +20081204 tpd src/input/efi.input cleanup +20081204 tpd src/input/directproduct.input cleanup +20081204 tpd src/input/danzwill2.input cleanup +20081204 tpd src/input/contfrac.input cleanup +20081204 tpd src/input/clifford.input cleanup +20081204 tpd src/input/classtalk.input cleanup +20081204 tpd src/input/ch.input cleanup +20081204 tpd src/input/calcprob.input cleanup +20081204 tpd src/input/bugs.input cleanup +20081204 tpd src/input/bini.input cleanup +20081204 tpd src/input/besselk.input cleanup +20081204 tpd src/input/assign.input cleanup +20081204 tpd src/input/array2.input cleanup +20081204 tpd src/input/alist.input cleanup +20081204 tpd src/input/algfacob.input cleanup +20081204 tpd src/input/Makefile fix self-referential input files 20081204 tpd src/axiom-website/patches.html 20081204.01.tpd.patch 20081204 tpd src/axiom-website/matrixinmatrix.jpg replace texmacs version 20081204 tpd src/axiom-website/heatequation.jpg replace texmacs version diff --git a/src/algebra/oct.spad.pamphlet b/src/algebra/oct.spad.pamphlet index 2256066..98a3da0 100644 --- a/src/algebra/oct.spad.pamphlet +++ b/src/algebra/oct.spad.pamphlet @@ -87,7 +87,7 @@ associative, since $I*(J*K) \ne (I*J)*K$. )set message test on )set message auto off )clear all ---S 1 +--S 1 of 15 oci1 := octon(1,2,3,4,5,6,7,8) --R --R @@ -95,7 +95,7 @@ oci1 := octon(1,2,3,4,5,6,7,8) --R Type: Octonion Integer --E 1 ---S 2 +--S 2 of 15 oci2 := octon(7,2,3,-4,5,6,-7,0) --R --R @@ -103,7 +103,7 @@ oci2 := octon(7,2,3,-4,5,6,-7,0) --R Type: Octonion Integer --E 2 ---S 3 +--S 3 of 15 oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R --R @@ -111,7 +111,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R Type: Octonion Integer --E 3 ---S 4 +--S 4 of 15 (oci1 * oci2) * oci3 - oci1 * (oci2 * oci3) --R --R @@ -119,7 +119,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R Type: Octonion Integer --E 4 ---S 5 +--S 5 of 15 [real oci1, imagi oci1, imagj oci1, imagk oci1, _ imagE oci1, imagI oci1, imagJ oci1, imagK oci1] --R @@ -128,7 +128,7 @@ oci3 := octon(quatern(-7,-12,3,-10), quatern(5,6,9,0)) --R Type: List PositiveInteger --E 5 ---S 6 +--S 6 of 15 q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk) --R --R @@ -136,7 +136,7 @@ q : Quaternion Polynomial Integer := quatern(q1, qi, qj, qk) --R Type: Quaternion Polynomial Integer --E 6 ---S 7 +--S 7 of 15 E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0) --R --R @@ -144,7 +144,7 @@ E : Octonion Polynomial Integer:= octon(0,0,0,0,1,0,0,0) --R Type: Octonion Polynomial Integer --E 7 ---S 8 +--S 8 of 15 q * E --R --R @@ -152,7 +152,7 @@ q * E --R Type: Octonion Polynomial Integer --E 8 ---S 9 +--S 9 of 15 E * q --R --R @@ -160,7 +160,7 @@ E * q --R Type: Octonion Polynomial Integer --E 9 ---S 10 +--S 10 of 15 q * 1$(Octonion Polynomial Integer) --R --R @@ -168,7 +168,7 @@ q * 1$(Octonion Polynomial Integer) --R Type: Octonion Polynomial Integer --E 10 ---S 11 +--S 11 of 15 1$(Octonion Polynomial Integer) * q --R --R @@ -176,7 +176,7 @@ q * 1$(Octonion Polynomial Integer) --R Type: Octonion Polynomial Integer --E 11 ---S 12 +--S 12 of 15 o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK) --R --R @@ -184,7 +184,7 @@ o : Octonion Polynomial Integer := octon(o1, oi, oj, ok, oE, oI, oJ, oK) --R Type: Octonion Polynomial Integer --E 12 ---S 13 +--S 13 of 15 norm o --R --R @@ -193,7 +193,7 @@ norm o --R Type: Polynomial Integer --E 13 ---S 14 +--S 14 of 15 p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK) --R --R @@ -201,7 +201,7 @@ p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK) --R Type: Octonion Polynomial Integer --E 14 ---S 15 +--S 15 of 15 norm(o*p)-norm(p)*norm(o) --R --R diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index 2523adf..7d63f61 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -19,7 +19,7 @@ to Codemist Common Lisp but is not defined in Common Lisp. )set message test on )set message auto off )clear all ---S 1 +--S 1 of 11 min()$SingleInteger --R --R @@ -27,7 +27,7 @@ min()$SingleInteger --R Type: SingleInteger --E 1 ---S 2 +--S 2 of 11 max()$SingleInteger --R --R @@ -35,7 +35,7 @@ max()$SingleInteger --R Type: SingleInteger --E 2 ---S 3 +--S 3 of 11 a := 1234 :: SingleInteger --R --R @@ -43,7 +43,7 @@ a := 1234 :: SingleInteger --R Type: SingleInteger --E 3 ---S 4 +--S 4 of 11 b := 124$SingleInteger --R --R @@ -51,7 +51,7 @@ b := 124$SingleInteger --R Type: SingleInteger --E 4 ---S 5 +--S 5 of 11 gcd(a,b) --R --R @@ -59,7 +59,7 @@ gcd(a,b) --R Type: SingleInteger --E 5 ---S 6 +--S 6 of 11 lcm(a,b) --R --R @@ -67,7 +67,7 @@ lcm(a,b) --R Type: SingleInteger --E 6 ---S 7 +--S 7 of 11 mulmod(5,6,13)$SingleInteger --R --R @@ -75,7 +75,7 @@ mulmod(5,6,13)$SingleInteger --R Type: SingleInteger --E 7 ---S 8 +--S 8 of 11 positiveRemainder(37,13)$SingleInteger --R --R @@ -83,7 +83,7 @@ positiveRemainder(37,13)$SingleInteger --R Type: SingleInteger --E 8 ---S 9 +--S 9 of 11 And(3,4)$SingleInteger --R --R @@ -91,7 +91,7 @@ And(3,4)$SingleInteger --R Type: SingleInteger --E 9 ---S 10 +--S 10 of 11 shift(1,4)$SingleInteger --R --R @@ -99,7 +99,7 @@ shift(1,4)$SingleInteger --R Type: SingleInteger --E 10 ---S 11 +--S 11 of 11 shift(31,-1)$SingleInteger --R --R diff --git a/src/algebra/zerodim.spad.pamphlet b/src/algebra/zerodim.spad.pamphlet index 1bd9951..5b6d499 100644 --- a/src/algebra/zerodim.spad.pamphlet +++ b/src/algebra/zerodim.spad.pamphlet @@ -5349,7 +5349,7 @@ univariateSolve(ts)$pack --RType: List Record(complexRoots: SparseUnivariatePolynomial Integer,coordinates: List Polynomial Integer) --E 23 ---S 24 +--S 24 of 28 realSolve(ts)$pack --R --R diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 0d3b6b7..032ce85 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -403,16 +403,16 @@ The input files are not removed because this parallel builds create race conditions. <>= %.output: %.input - @ echo generic 17 running test file $* using $*.input - @ echo ')set message test on' > $*.input - @ echo ')set message auto off' >> $*.input - @ echo ')read $*' >> $*.input - @ echo ')lisp (bye)' >> $*.input + @ echo generic 17 running test file $* using $*tpd.input + @ echo ')set message test on' > $*tpd.input + @ echo ')set message auto off' >> $*tpd.input + @ echo ')read $*' >> $*tpd.input + @ echo ')lisp (bye)' >> $*tpd.input @ if [ -z "${NOISE}" ] ; then \ - echo ")read $*.input" | ${TESTSYS} \ + echo ")read $*tpd.input" | ${TESTSYS} \ | egrep -v '(Timestamp|Version)' | tee $*.output ; \ else \ - echo ")read $*.input" | ${TESTSYS} \ + echo ")read $*tpd.input" | ${TESTSYS} \ | egrep -v '(Timestamp|Version)' > $*.output ; \ fi # @ rm $*.input diff --git a/src/input/algfacob.input.pamphlet b/src/input/algfacob.input.pamphlet index b49b198..59dbd8d 100644 --- a/src/input/algfacob.input.pamphlet +++ b/src/input/algfacob.input.pamphlet @@ -119,7 +119,7 @@ h := (f*g)/(g*nilFactor(2,200)) )clear all ---S 11 of 37 +--S 11 of 37 (u,v,w) : FR POLY INT --R --R Type: Void diff --git a/src/input/alist.input.pamphlet b/src/input/alist.input.pamphlet index 0f3ad98..bd21f1b 100644 --- a/src/input/alist.input.pamphlet +++ b/src/input/alist.input.pamphlet @@ -97,7 +97,7 @@ al."katie" := [23,"female"]$Data --R Type: Record(monthsOld: Integer,gender: String) --E 9 ---S 10 of 10 of 10 +--S 10 of 10 delete!(al,1) --R --R diff --git a/src/input/array2.input.pamphlet b/src/input/array2.input.pamphlet index fc9e320..ef9e74f 100644 --- a/src/input/array2.input.pamphlet +++ b/src/input/array2.input.pamphlet @@ -235,7 +235,7 @@ count(17,arr) --R Type: PositiveInteger --E 19 ---S 20 of 20 of 20 +--S 20 of 20 count(0,arr) --R --R diff --git a/src/input/assign.input.pamphlet b/src/input/assign.input.pamphlet index cb16af8..adfc652 100644 --- a/src/input/assign.input.pamphlet +++ b/src/input/assign.input.pamphlet @@ -21,7 +21,7 @@ -- This file shows the difference between assignments and rewrite -- rules. ---S 1 of 11 +--S 1 of 11 a := 1 --R --R @@ -61,7 +61,7 @@ b -- it is the value it had AT ASSIGNMENT --R Type: PositiveInteger --E 5 ---S 6 of 11 +--S 6 of 11 c == 1 -- c is a rule --R --R Type: Void diff --git a/src/input/besselk.input.pamphlet b/src/input/besselk.input.pamphlet index 7a31a2c..f0af678 100644 --- a/src/input/besselk.input.pamphlet +++ b/src/input/besselk.input.pamphlet @@ -20,7 +20,7 @@ Dover Publications, Inc. New York 1965. pp417-419 )set message auto off )clear all ---S 1 of 4 +--S 1 of 6 D(besselK(a,x),x) --R --R - besselK(a + 1,x) - besselK(a - 1,x) @@ -29,7 +29,7 @@ D(besselK(a,x),x) --R Type: Expression Integer --E 1 ---S 2 of 4 +--S 2 of 6 D(besselK(a,x),a) --R --R (2) besselK (a,x) @@ -37,25 +37,25 @@ D(besselK(a,x),a) --R Type: Expression Integer --E 2 ---S 3 of 4 +--S 3 of 6 integrate(D(besselK(a,x),a),a) --R --R (3) besselK(a,x) --R Type: Union(Expression Integer,...) --E 3 ---S 4 of 4 +--S 4 of 6 limit(D(besselK(a,x),a),a=1/2) --R --R (4) "failed" --R Type: Union("failed",...) --E 4 ---S 5 +--S 5 of 6 stegun(x)== %e^x * besselK(1,x) --E 5 ---S 6 +--S 6 of 6 [[0.1, 10.890182683 , stegun(0.1), stegun(0.1)- 10.890182683 ],_ [0.2, 5.833386037 , stegun(0.2), stegun(0.2)- 5.833386037 ],_ [0.3, 4.125157762 , stegun(0.3), stegun(0.3)- 4.125157762 ],_ diff --git a/src/input/bini.input.pamphlet b/src/input/bini.input.pamphlet index eac6e13..b03ce88 100644 --- a/src/input/bini.input.pamphlet +++ b/src/input/bini.input.pamphlet @@ -116,7 +116,7 @@ Paramaters $a,b$ and variables $x,y$) <<*>>= )clear all ---S 1 +--S 1 of 276 t1:=2*y^2*(y^2+x^2)+(b^2-3*a^2)*y^2-2*b*y^2*(x+y)+2*a^2*b*(y+x)_ -a^2*x^2+a^2*(a^2-b^2) --R @@ -126,7 +126,7 @@ t1:=2*y^2*(y^2+x^2)+(b^2-3*a^2)*y^2-2*b*y^2*(x+y)+2*a^2*b*(y+x)_ --R 2y - 2b y + (2x - 2b x + b - 3a )y + 2a b y - a x + 2a b x - a b + a --E 1 ---S 2 +--S 2 of 276 t2:=4*y^3+4*y*(y^2+x^2)-2*b*y^2-4*b*y*(y+x)+2*(b^2-3*a^2)*y+2*a^2*b --R --R @@ -134,7 +134,7 @@ t2:=4*y^3+4*y*(y^2+x^2)-2*b*y^2-4*b*y*(y+x)+2*(b^2-3*a^2)*y+2*a^2*b --R (2) 8y - 6b y + (4x - 4b x + 2b - 6a )y + 2a b --E 2 ---S 3 +--S 3 of 276 t3:=4*x*y^2-2*b*y^2-2*a^2*x+2*a^2*b --R --R @@ -148,7 +148,7 @@ Variables $x,y,z$ <<*>>= )clear all ---S 4 +--S 4 of 276 t1:=8*x^2-2*x*y-6*x*z+3*x+3*y^2-7*y*z+10*y+10*z^2-8*z-4 --R --R @@ -156,7 +156,7 @@ t1:=8*x^2-2*x*y-6*x*z+3*x+3*y^2-7*y*z+10*y+10*z^2-8*z-4 --R (1) 10z + (- 7y - 6x - 8)z + 3y + (- 2x + 10)y + 8x + 3x - 4 --E 4 ---S 5 +--S 5 of 276 t2:=10*x^2-2*x*y+6*x*z-6*x+9*y^2-y*z-4*y-2*z^2+5*z-9 --R --R @@ -164,7 +164,7 @@ t2:=10*x^2-2*x*y+6*x*z-6*x+9*y^2-y*z-4*y-2*z^2+5*z-9 --R (2) - 2z + (- y + 6x + 5)z + 9y + (- 2x - 4)y + 10x - 6x - 9 --E 5 ---S 6 +--S 6 of 276 t3:=5*x^2+8*x*y+4*x*z+8*x+9*y^2-6*y*z+2*y-z^2-7*x+5 --R --R @@ -178,7 +178,7 @@ Parameter $b$ and variables $c,d,p,q$ <<*>>= )clear all ---S 7 +--S 7 of 276 t1:=2*(b-1)^2 + 2*(q-p*q+p^2) + c^2*(q-1)^2 -2*b*q + 2*c*d*(1-q)*(q-p)_ +2*b*p*q*d*(d-c) + b^2*d^2*(1-2*p) + 2*b*d^2*(p-q) + 2*b*d*c*(p-1)_ +2*b*p*q*(c+1) + (b^2 - 2*b)*p^2*d^2 + 2*b^2*p^2 + 4*b*(1-b)*p_ @@ -202,7 +202,7 @@ t1:=2*(b-1)^2 + 2*(q-p*q+p^2) + c^2*(q-1)^2 -2*b*q + 2*c*d*(1-q)*(q-p)_ --R 2b - 4b + 2 --E 7 ---S 8 +--S 8 of 276 t2:=d*(2*p+1)*(q-p) + c*(p+2)*(1-q) + b*(b-2)*d + b*(1-2*b)*p*d_ +b*c*(q+p-p*q-1) + b*(b+1)*p^2*d --R @@ -215,7 +215,7 @@ t2:=d*(2*p+1)*(q-p) + c*(p+2)*(1-q) + b*(b-2)*d + b*(1-2*b)*p*d_ --R ((- 2b + b - 1)d + (b + 1)c)p + (b - 2b)d + (- b + 2)c --E 8 ---S 9 +--S 9 of 276 t3:=-b^2*(p-1)^2 + 2*p*(p-q) - 2*(q-1) --R --R @@ -223,7 +223,7 @@ t3:=-b^2*(p-1)^2 + 2*p*(p-q) - 2*(q-1) --R (3) (- 2p - 2)q + (- b + 2)p + 2b p - b + 2 --E 9 ---S 10 +--S 10 of 276 t4:=b^2 + 4*(p-q^2) + 3*c^2*(q-1)^2 - 3*d^2*(p-q)^2 + 3*b^2*d^2*(p-1)^2_ +b^2*p*(p-2) + 6*b*d*c*(p+q+q*p-1) --R @@ -246,7 +246,7 @@ Paramters $a,b,c,d,e,f,g,h,k$ and variables $x,y$ )clear all ---S 11 +--S 11 of 276 t1:=a*x^2+b*x*y+c*x+d*y^2+e*y+f --R --R @@ -254,7 +254,7 @@ t1:=a*x^2+b*x*y+c*x+d*y^2+e*y+f --R (1) d y + (b x + e)y + a x + c x + f --E 11 ---S 12 +--S 12 of 276 t2:=b*x^2+4*d*x*y+2*e*x+g*y^2+h*y+k --R --R @@ -268,7 +268,7 @@ Paramters $a,b,c,d,e,f,g,h,k$ and variables $x,y,z$ <<*>>= )clear all ---S 13 +--S 13 of 276 t1:=x^2+a*y*z+d*x+g --R --R @@ -276,7 +276,7 @@ t1:=x^2+a*y*z+d*x+g --R (1) a y z + x + d x + g --E 13 ---S 14 +--S 14 of 276 t2:=y^2+b*z*x+e*y+h --R --R @@ -284,7 +284,7 @@ t2:=y^2+b*z*x+e*y+h --R (2) b x z + y + e y + h --E 14 ---S 15 +--S 15 of 276 t3:=z^2+c*x*y+f*z+k --R --R @@ -298,7 +298,7 @@ Parameters $a,b$ and variables $x,A,B$ <<*>>= )clear all ---S 16 +--S 16 of 276 t1:=(x^2-A)^2 + (x^3+b*x-B)*(x^3+b*x-B-a)^2 --R --R @@ -313,7 +313,7 @@ t1:=(x^2-A)^2 + (x^3+b*x-B)*(x^3+b*x-B-a)^2 --R - B a - 2B a - B + A --E 16 ---S 17 +--S 17 of 276 t2:=4*x*(x^2-A)+(3*x^2+b)*(x^3+b*x-B-a)*(3*(x^3+b*x-B)-a) --R --R @@ -325,7 +325,7 @@ t2:=4*x*(x^2-A)+(3*x^2+b)*(x^3+b*x-B-a)*(3*(x^3+b*x-B)-a) --R (3b + 3a + 12B a + 9B )x + ((- 4a - 6B)b - 4A)x + (a + 4B a + 3B )b --E 17 ---S 18 +--S 18 of 276 t3:=12*x^2-4*A+6*x*(x^3+b*x-B-a)^2+4*(3*x^2+b)^2*(x^3+b*x-B-a)_ +2*(x^3+b*x-B)*(3*x^2+b)^2+12*x*(x^3+b*x-B)*(x^3+b*x-B-a) --R @@ -338,7 +338,7 @@ t3:=12*x^2-4*A+6*x*(x^3+b*x-B-a)^2+4*(3*x^2+b)^2*(x^3+b*x-B-a)_ --R (6b + 6a + 24B a + 18B )x + (- 4a - 6B)b - 4A --E 18 ---S 19 +--S 19 of 276 t4:=24*x+6*(x^3+b*x-B-a)^2+72*x*(x^3+b*x-B-a)*(3*x^2+b)+6*(3*x^2+b)^3_ +36*x*(x^3+b*x-B)*(3*x^2+b)+12*(x^3+b*x-B)*(x^3+b*x-B-a) --R @@ -357,7 +357,7 @@ Parameters $a,b,c$ and variables $x,y[2],z[2]$ <<*>>= )clear all ---S 20 +--S 20 of 276 t1:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1 --R --R @@ -365,7 +365,7 @@ t1:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1 --R (1) 2y1 z1 + 5y1 + 3a y1 + 2c y1 + x --E 20 ---S 21 +--S 21 of 276 t2:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2 --R --R @@ -373,7 +373,7 @@ t2:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2 --R (2) 2y2 z2 + 5y2 + 3a y2 + 2c y2 + x --E 21 ---S 22 +--S 22 of 276 t3:=2*z2+6*a*y2+20*y2^3+2*c --R --R @@ -381,7 +381,7 @@ t3:=2*z2+6*a*y2+20*y2^3+2*c --R (3) 2z2 + 20y2 + 6a y2 + 2c --E 22 ---S 23 +--S 23 of 276 t4:=3*z1^2+y1^2+b --R --R @@ -389,7 +389,7 @@ t4:=3*z1^2+y1^2+b --R (4) 3z1 + y1 + b --E 23 ---S 24 +--S 24 of 276 t5:=3*z2^2+y2^2+b --R --R @@ -403,7 +403,7 @@ Paramters $a,b,c$ and variables $x,y[3],z[3]$ <<*>>= )clear all ---S 25 +--S 25 of 276 t1:=3*z1^2+y1^2+b --R --R @@ -411,7 +411,7 @@ t1:=3*z1^2+y1^2+b --R (1) 3z1 + y1 + b --E 25 ---S 26 +--S 26 of 276 t2:=3*z1^2+y2^2+b --R --R @@ -419,7 +419,7 @@ t2:=3*z1^2+y2^2+b --R (2) 3z1 + y2 + b --E 26 ---S 27 +--S 27 of 276 t3:=3*z3^2+y3^2+b --R --R @@ -427,7 +427,7 @@ t3:=3*z3^2+y3^2+b --R (3) 3z3 + y3 + b --E 27 ---S 28 +--S 28 of 276 t4:=y1^2*z1+2*a*y1^3+4*y1^5+c*y1^2-z1^3-b*z1-y2^2*z2-2*a*y2^3_ -4*y2^5-c*y2^2+z2^3+b*z2 --R @@ -440,7 +440,7 @@ t4:=y1^2*z1+2*a*y1^3+4*y1^5+c*y1^2-z1^3-b*z1-y2^2*z2-2*a*y2^3_ --R 2a y1 + c y1 --E 28 ---S 29 +--S 29 of 276 t5:=y2^2*z2+2*a*y2^3+4*y2^5+c*y2^2-z2^3-b*z2-y3^2*z3-2*a*y3^3_ -4*y3^5-c*y3^2+z3^3+b*z3 --R @@ -453,7 +453,7 @@ t5:=y2^2*z2+2*a*y2^3+4*y2^5+c*y2^2-z2^3-b*z2-y3^2*z3-2*a*y3^3_ --R 2a y2 + c y2 --E 29 ---S 30 +--S 30 of 276 t6:=y3^2*z3+2*a*y3^3+4*y3^5+c*y3^2-z3^3-b*z3-y1^2*z1-2*a*y1^3_ -4*y1^5-c*y1^2+z1^3+b*z1 --R @@ -472,7 +472,7 @@ Paramters $a,b,c$ and variables $x,y[2],z[2]$ <<*>>= )clear all ---S 31 +--S 31 of 276 t1:=3*z1^2+y1^2+b --R --R @@ -480,7 +480,7 @@ t1:=3*z1^2+y1^2+b --R (1) 3z1 + y1 + b --E 31 ---S 32 +--S 32 of 276 t2:=3*z2^2+y2^2+b --R --R @@ -488,7 +488,7 @@ t2:=3*z2^2+y2^2+b --R (2) 3z2 + y2 + b --E 32 ---S 33 +--S 33 of 276 t3:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1 --R --R @@ -496,7 +496,7 @@ t3:=x+2*y1*z1+3*a*y1^2+5*y1^4+2*c*y1 --R (3) 2y1 z1 + 5y1 + 3a y1 + 2c y1 + x --E 33 ---S 34 +--S 34 of 276 t4:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2 --R --R @@ -504,7 +504,7 @@ t4:=x+2*y2*z2+3*a*y2^2+5*y2^4+2*c*y2 --R (4) 2y2 z2 + 5y2 + 3a y2 + 2c y2 + x --E 34 ---S 35 +--S 35 of 276 t5:=x*y1+z1^3+y1^2*z1+a*y1^3+y1^5+b*z1+c*y1^2-x*y2-z2^3-y2^2*z2_ -a*y2^3-y2^5-b*z2-c*y2^2 --R @@ -517,7 +517,7 @@ t5:=x*y1+z1^3+y1^2*z1+a*y1^3+y1^5+b*z1+c*y1^2-x*y2-z2^3-y2^2*z2_ --R y1 + a y1 + c y1 + x y1 --E 35 ---S 36 +--S 36 of 276 t6:=(6*z1^2+18*a*z1*y1+6*y1-y1^3*z1+6*c*y1^2*z1-2*y1^2)_ *(3*z2^2*y2+9*a*y2^2*z2+45*y2^4*z2-y2^3-3*x*z2+b*y2)_ -(6*z2^2+18*a*z2*y2+60*y2^3*z2+6*c*y2^2*z2-2*y2^2)_ @@ -586,98 +586,98 @@ Variables $x[16]$ <<*>>= )clear all ---S 37 +--S 37 of 276 t1:=x4*x13 + x5*x14 + x6*(1-x13-x14) --R --R --R (1) (- x14 - x13 + 1)x6 + x14 x5 + x13 x4 --E 37 ---S 38 +--S 38 of 276 t2:=x4*x15 + x5*x16 - x6*(x15+x16) --R --R --R (2) (- x16 - x15)x6 + x16 x5 + x15 x4 --E 38 ---S 39 +--S 39 of 276 t3:=x7*x13 + x8*x14 + x9*(1-x13-x14) --R --R --R (3) (- x14 - x13 + 1)x9 + x14 x8 + x13 x7 --E 39 ---S 40 +--S 40 of 276 t4:=x7*x15 + x8*x16 - x9*(x15+x16)-1 --R --R --R (4) (- x16 - x15)x9 + x16 x8 + x15 x7 - 1 --E 40 ---S 41 +--S 41 of 276 t5:=x10*x13 + x11*x14 + x12*(1-x13-x14) --R --R --R (5) (- x12 + x11)x14 + (- x12 + x10)x13 + x12 --E 41 ---S 42 +--S 42 of 276 t6:=x10*x15 + x11*x16 - x12*(x15+x16) --R --R --R (6) (- x12 + x11)x16 + (- x12 + x10)x15 --E 42 ---S 43 +--S 43 of 276 t7:=x1*x13 + x2*x14 + x3*(1-x13-x14) --R --R --R (7) (- x14 - x13 + 1)x3 + x14 x2 + x1 x13 --E 43 ---S 44 +--S 44 of 276 t8:=x1*x15 + x2*x16 - x3*(x15+x16) --R --R --R (8) (- x16 - x15)x3 + x16 x2 + x1 x15 --E 44 ---S 45 +--S 45 of 276 t9:=x1*x4*x13 + x2*x5*x14 + x3*x6*(1-x13-x14)-1 --R --R --R (9) (- x14 - x13 + 1)x3 x6 + x14 x2 x5 + x1 x13 x4 - 1 --E 45 ---S 46 +--S 46 of 276 t10:=x1*x4*x15 + x2*x5*x16 - x3*x6*(x15+x16) --R --R --R (10) (- x16 - x15)x3 x6 + x16 x2 x5 + x1 x15 x4 --E 46 ---S 47 +--S 47 of 276 t11:=x1*x7*x13 + x2*x8*x14 + x3*x9*(1-x13-x14) --R --R --R (11) (- x14 - x13 + 1)x3 x9 + x14 x2 x8 + x1 x13 x7 --E 47 ---S 48 +--S 48 of 276 t12:=x1*x7*x15 + x2*x8*x16 - x3*x9*(x15+x16) --R --R --R (12) (- x16 - x15)x3 x9 + x16 x2 x8 + x1 x15 x7 --E 48 ---S 49 +--S 49 of 276 t13:=x1*x10*x13 + x2*x11*x14 + x3*x12*(1-x13-x14) --R --R --R (13) (- x12 x14 - x12 x13 + x12)x3 + x11 x14 x2 + x1 x10 x13 --E 49 ---S 50 +--S 50 of 276 t14:=x1*x10*x15 + x2*x11*x16 - x3*x12*(x15+x16)-1 --R --R @@ -690,7 +690,7 @@ Variables $x,y,z,t$ <<*>>= )clear all ---S 51 +--S 51 of 276 t1:=2*x^2-2*y^2+2*z^2-2*t^2-1 --R --R @@ -698,7 +698,7 @@ t1:=2*x^2-2*y^2+2*z^2-2*t^2-1 --R (1) 2z - 2y + 2x - 2t - 1 --E 51 ---S 52 +--S 52 of 276 t2:=2*x^3-2*y^3+2*z^3-2*t^3-1 --R --R @@ -706,7 +706,7 @@ t2:=2*x^3-2*y^3+2*z^3-2*t^3-1 --R (2) 2z - 2y + 2x - 2t - 1 --E 52 ---S 53 +--S 53 of 276 t3:=2*x^4-2*y^4+2*z^4-2*t^4-1 --R --R @@ -714,7 +714,7 @@ t3:=2*x^4-2*y^4+2*z^4-2*t^4-1 --R (3) 2z - 2y + 2x - 2t - 1 --E 53 ---S 54 +--S 54 of 276 t4:=2*x^5-2*y^5+2*z^5-2*t^5-1 --R --R @@ -728,7 +728,7 @@ Variables $x,y,z,t,u$ <<*>>= )clear all ---S 55 +--S 55 of 276 t1:=2*x^2-2*y^2+2*z^2-2*t^2+2*u^2-1 --R --R @@ -736,7 +736,7 @@ t1:=2*x^2-2*y^2+2*z^2-2*t^2+2*u^2-1 --R (1) 2z - 2y + 2x + 2u - 2t - 1 --E 55 ---S 56 +--S 56 of 276 t2:=2*x^3-2*y^3+2*z^3-2*t^3+2*u^3-1 --R --R @@ -744,7 +744,7 @@ t2:=2*x^3-2*y^3+2*z^3-2*t^3+2*u^3-1 --R (2) 2z - 2y + 2x + 2u - 2t - 1 --E 56 ---S 57 +--S 57 of 276 t3:=2*x^4-2*y^4+2*z^4-2*t^4+2*u^4-1 --R --R @@ -752,7 +752,7 @@ t3:=2*x^4-2*y^4+2*z^4-2*t^4+2*u^4-1 --R (3) 2z - 2y + 2x + 2u - 2t - 1 --E 57 ---S 58 +--S 58 of 276 t4:=2*x^5-2*y^5+2*z^5-2*t^5+2*u^5-1 --R --R @@ -760,7 +760,7 @@ t4:=2*x^5-2*y^5+2*z^5-2*t^5+2*u^5-1 --R (4) 2z - 2y + 2x + 2u - 2t - 1 --E 58 ---S 59 +--S 59 of 276 t5:=2*x^6-2*y^6+2*z^6-2*t^6+2*u^6-1 --R --R @@ -779,7 +779,7 @@ Variables $x,y,z,t,u,v,w$ <<*>>= )clear all ---S 60 +--S 60 of 276 t1:=y*w-1/2*z*w+t*w --R --R @@ -788,7 +788,7 @@ t1:=y*w-1/2*z*w+t*w --R 2 --E 60 ---S 61 +--S 61 of 276 t2:=-2/7*u*w^2+10/7*v*w^2-20/7*w^3+t*u-5*t*v+10*t*w --R --R @@ -797,7 +797,7 @@ t2:=-2/7*u*w^2+10/7*v*w^2-20/7*w^3+t*u-5*t*v+10*t*w --R 7 7 7 --E 61 ---S 62 +--S 62 of 276 t3:=2/7*y*w^2-2/7*z*w^2+6/7*t*w^2-y*t+z*t-3*t^2 --R --R @@ -806,7 +806,7 @@ t3:=2/7*y*w^2-2/7*z*w^2+6/7*t*w^2-y*t+z*t-3*t^2 --R 7 7 7 --E 62 ---S 63 +--S 63 of 276 t4:=-2*v^3+4*u*v*w+5*v^2*w-6*u*w^2-7*v*w^2+15*w^3+42*y*v_ -14*z*v-63*y*w+21*z*w-42*t*w+147*x --R @@ -819,7 +819,7 @@ t4:=-2*v^3+4*u*v*w+5*v^2*w-6*u*w^2-7*v*w^2+15*w^3+42*y*v_ --R (5v + 4u v - 42t)w - 2v --E 63 ---S 64 +--S 64 of 276 t5:=-9/7*u*w^3+45/7*v*w^3-135/7*w^4+2*z*v^2-2*t*v^2-4*z*u*w+10*t*u*w_ -2*z*v*w-28*t*v*w+4*z*w^2+86*t*w^2-42*y*z+14*z^2+42*y*t_ -14*z*t-21*x*u+105*x*v-315*x*w @@ -837,7 +837,7 @@ t5:=-9/7*u*w^3+45/7*v*w^3-135/7*w^4+2*z*v^2-2*t*v^2-4*z*u*w+10*t*u*w_ --R (- 28t v + 10t u)w - 2t v --E 64 ---S 65 +--S 65 of 276 t6:=6/7*y*w^3-9/7*z*w^3+36/7*t*w^3-2*x*v^2-4*y*t*w+6*z*t*w_ -24*t^2*w+4*x*u*w+2*x*v*w-4*x*w^2+56*x*y-35*x*z+84*x*t --R @@ -852,7 +852,7 @@ t6:=6/7*y*w^3-9/7*z*w^3+36/7*t*w^3-2*x*v^2-4*y*t*w+6*z*t*w_ --R 7 --E 65 ---S 66 +--S 66 of 276 t7:=2*u*v*w-6*v^2*w-u*w^2+13*v*w^2-5*w^3+14*y*w-28*t*w --R --R @@ -860,7 +860,7 @@ t7:=2*u*v*w-6*v^2*w-u*w^2+13*v*w^2-5*w^3+14*y*w-28*t*w --R (7) 14w y - 5w + (13v - u)w + (- 6v + 2u v - 28t)w --E 66 ---S 67 +--S 67 of 276 t8:=u^2*w-3*u*v*w+5*u*w^2+14*y*w-28*t*w --R --R @@ -868,7 +868,7 @@ t8:=u^2*w-3*u*v*w+5*u*w^2+14*y*w-28*t*w --R (8) 14w y + 5u w + (- 3u v + u - 28t)w --E 67 ---S 68 +--S 68 of 276 t9:=-2*z*u*w-2*t*u*w+4*y*v*w+6*z*v*w-2*t*v*w-16*y*w^2_ -10*z*w^2+22*t*w^2+42*x*w --R @@ -878,7 +878,7 @@ t9:=-2*z*u*w-2*t*u*w+4*y*v*w+6*z*v*w-2*t*v*w-16*y*w^2_ --R (- 10w + (6v - 2u)w)z + (- 16w + 4v w)y + 42w x + 22t w + (- 2t v - 2t u)w --E 68 ---S 69 +--S 69 of 276 t10:=28/3*y*u*w+8/3*z*u*w-20/3*t*u*w-88/3*y*v*w-8*z*v*w_ +68/3*t*v*w+52*y*w^2+40/3*z*w^2-44*t*w^2-84*x*w --R @@ -893,7 +893,7 @@ t10:=28/3*y*u*w+8/3*z*u*w-20/3*t*u*w-88/3*y*v*w-8*z*v*w_ --R 3 3 --E 69 ---S 70 +--S 70 of 276 t11:=-4*y*z*w+10*y*t*w+8*z*t*w-20*t^2*w+12*x*u*w-30*x*v*w+15*x*w^2 --R --R @@ -901,7 +901,7 @@ t11:=-4*y*z*w+10*y*t*w+8*z*t*w-20*t^2*w+12*x*u*w-30*x*v*w+15*x*w^2 --R (11) (- 4w y + 8t w)z + 10t w y + (15w + (- 30v + 12u)w)x - 20t w --E 70 ---S 71 +--S 71 of 276 t12:=-y^2*w+1/2*y*z*w+y*t*w-z*t*w+2*t^2*w-3*x*u*w+6*x*v*w-3*x*w^2 --R --R @@ -910,7 +910,7 @@ t12:=-y^2*w+1/2*y*z*w+y*t*w-z*t*w+2*t^2*w-3*x*u*w+6*x*v*w-3*x*w^2 --R 2 --E 71 ---S 72 +--S 72 of 276 t13:=8*x*y*w-4*x*z*w+8*x*t*w --R --R @@ -923,7 +923,7 @@ Variables $x,y,z,t,u$ <<*>>= )clear all ---S 73 +--S 73 of 276 t1:=35*y^4-30*x*y^2-210*y^2*z+3*x^2+30*x*z-105*z^2+140*y*t-21*u --R --R @@ -931,7 +931,7 @@ t1:=35*y^4-30*x*y^2-210*y^2*z+3*x^2+30*x*z-105*z^2+140*y*t-21*u --R (1) - 105z + (- 210y + 30x)z + 35y - 30x y + 140t y + 3x - 21u --E 73 ---S 74 +--S 74 of 276 t2:=5*x*y^3-140*y^3*z-3*x^2*y+45*x*y*z-420*y*z^2+210*y^2*t_ -25*x*t+70*z*t+126*y*u --R @@ -949,7 +949,7 @@ Variables $x,y,z,t$ <<*>>= )clear all ---S 75 +--S 75 of 276 t1:=6*x*y^2*t-x^2*z*t-6*x*y*z*t+3*x*z^2*t-2*z^3*t-6*x*y^2+6*x*y*z-2*x*z^2 --R --R @@ -957,7 +957,7 @@ t1:=6*x*y^2*t-x^2*z*t-6*x*y*z*t+3*x*z^2*t-2*z^3*t-6*x*y^2+6*x*y*z-2*x*z^2 --R (1) - 2t z + (3t - 2)x z + ((- 6t + 6)x y - t x )z + (6t - 6)x y --E 75 ---S 76 +--S 76 of 276 t2:=-63*x*y^2*t^2+9*x^2*z*t^2+63*x*y*z*t^2+18*y^2*z*t^2-27*x*z^2*t^2_ -18*y*z^2*t^2+18*z^3*t^2+78*x*y^2*t-78*x*y*z*t-18*y^2*z*t_ +24*x*z^2*t+18*y*z^2*t-9*z^3*t-15*x*y^2+15*x*y*z-5*x*z^2 @@ -971,7 +971,7 @@ t2:=-63*x*y^2*t^2+9*x^2*z*t^2+63*x*y*z*t^2+18*y^2*z*t^2-27*x*z^2*t^2_ --R ((18t - 18t)y + (63t - 78t + 15)x y + 9t x )z + (- 63t + 78t - 15)x y --E 76 ---S 77 +--S 77 of 276 t3:=18*x^2*y^2*t-3*x^3*z*t-18*x^2*y*z*t+12*x*y^2*z*t+5*x^2*z^2*t_ -12*x*y*z^2*t+6*x*z^3*t-8*z^4*t-18*x^2*y^2+18*x^2*y*z-12*x*y^2*z_ -4*x^2*z^2+12*x*y*z^2-6*x*z^3 @@ -985,7 +985,7 @@ t3:=18*x^2*y^2*t-3*x^3*z*t-18*x^2*y*z*t+12*x*y^2*z*t+5*x^2*z^2*t_ --R ((12t - 12)x y + (- 18t + 18)x y - 3t x )z + (18t - 18)x y --E 77 ---S 78 +--S 78 of 276 t4:=-x^2*y*t+3*x*y^2*t+10*y^3*t-15*y^2*z*t+3*y*z^2*t-3*x*y^2-10*y^3+x*y*z_ +15*y^2*z-5*y*z^2 --R @@ -1001,14 +1001,14 @@ Variables $x,y,z,t,u,v,w,a,b,c$ <<*>>= )clear all ---S 79 +--S 79 of 276 t1:=y*t-y*u-u*b+u*c --R --R --R (1) (- u + t)y + (c - b)u --E 79 ---S 80 +--S 80 of 276 t2:=2*x*y^2*t-x*y^2*u-2*y^2*t*v+y^2*u*v-x*y*z*a+12*x*t^2*a-4*x*t*u*a_ -x*u^2*a+y*z*v*a-2*t*u*v*a+u^2*v*a-x*u*w*a+u*v*w*a-6*x*z*a*b --R @@ -1021,7 +1021,7 @@ t2:=2*x*y^2*t-x*y^2*u-2*y^2*t*v+y^2*u*v-x*y*z*a+12*x*t^2*a-4*x*t*u*a_ --R (- a u w - a u - 4a t u + 12a t )x + a u v w + (a u - 2a t u)v --E 80 ---S 81 +--S 81 of 276 t3:=x*y^2*z-y^2*z*v+6*x*z*t*a+x*z*u*a-z*u*v*a-2*x*y*z*b+2*y*z*v*b_ -2*x*u*w*b+2*u*v*w*b-12*x*z*b^2+x*y*z*c-y*z*v*c+x*u*w*c_ -u*v*w*c+6*x*z*b*c @@ -1038,14 +1038,14 @@ t3:=x*y^2*z-y^2*z*v+6*x*z*t*a+x*z*u*a-z*u*v*a-2*x*y*z*b+2*y*z*v*b_ --R (c - 2b)u w x + (- c + 2b)u v w --E 81 ---S 82 +--S 82 of 276 t4:=x*y*u-y*u*v+3*x*z*a+3*x*t*b+x*u*b-u*v*b --R --R --R (4) 3a x z + (u x - u v)y + (b u + 3b t)x - b u v --E 82 ---S 83 +--S 83 of 276 t5:=5*x^2*y*t-5*x^2*y*u-10*x*y*t*v+10*x*y*u*v+5*y*t*v^2-5*y*u*v^2_ -6*x^2*z*a-12*x*z*v*a+4*x^2*t*b-7*x^2*u*b+16*x*t*v*b+8*x*u*v*b_ -2*t*v^2*b-u*v^2*b+8*x^2*t*c+x^2*u*c-10*x*t*v*c-2*x*u*v*c_ @@ -1063,7 +1063,7 @@ t5:=5*x^2*y*t-5*x^2*y*u-10*x*y*t*v+10*x*y*u*v+5*y*t*v^2-5*y*u*v^2_ --R ((c - b)u + (2c - 2b)t)v --E 83 ---S 84 +--S 84 of 276 t6:=-9*x^4*t*v*c+9*x^4*u*v*c-18*x^3*t*v^2*c-9*x^3*u*v^2*c+3*x^4*y*t_ -4*x^4*y*u-9*x^3*y*t*v+10*x^3*y*u*v+9*x^2*y*t*v^2-6*x^2*y*u*v^2_ -3*x*y*t*v^3-2*x*y*u*v^3+2*y*u*v^4-6*x^4*z*a-45*x^3*z*v*a_ @@ -1093,14 +1093,14 @@ t6:=-9*x^4*t*v*c+9*x^4*u*v*c-18*x^3*t*v^2*c-9*x^3*u*v^2*c+3*x^4*y*t_ --R (- b u - 3b t)v x + b u v --E 84 ---S 85 +--S 85 of 276 t7:=w*b-t*c+u*c-w*c --R --R --R (7) (- c + b)w + c u - c t --E 85 ---S 86 +--S 86 of 276 t8:=-6*z*t*v*a+x*z*w*a-z*v*w*a-2*x*w^2*b+2*v*w^2*b+12*z*v*b^2_ +x*y*z*c-y*z*v*c+x*w^2*c-v*w^2*c-2*x*z*b*c-4*z*v*b*c+x*z*c^2-z*v*c^2 --R @@ -1113,7 +1113,7 @@ t8:=-6*z*t*v*a+x*z*w*a-z*v*w*a-2*x*w^2*b+2*v*w^2*b+12*z*v*b^2_ --R (c - 2b)w x + (- c + 2b)v w --E 86 ---S 87 +--S 87 of 276 t9:=-12*t^2*v*a+6*t*u*v*a+2*x*t*w*a-x*u*w*a-2*t*v*w*a+u*v*w*a_ -x*w^2*a+v*w^2*a+6*z*v*a*b+2*x*y*t*c-x*y*u*c-2*y*t*v*c+y*u*v*c_ -x*z*a*c+z*v*a*c @@ -1126,14 +1126,14 @@ t9:=-12*t^2*v*a+6*t*u*v*a+2*x*t*w*a-x*u*w*a-2*t*v*w*a+u*v*w*a_ --R (- a w + (- a u + 2a t)w)x + a v w + (a u - 2a t)v w + (6a t u - 12a t )v --E 87 ---S 88 +--S 88 of 276 t10:=3*z*v*a+3*t*v*b-x*t*c+t*v*c-x*w*c+v*w*c --R --R --R (10) 3a v z + (- c w - c t)x + c v w + (c + 3b)t v --E 88 ---S 89 +--S 89 of 276 t11:=-12*x*z*v*a-6*z*v^2*a-2*x^2*t*b+2*x^2*u*b+16*x*t*v*b-10*x*u*v*b_ +4*t*v^2*b+8*u*v^2*b+5*x^2*w*b-10*x*v*w*b+5*v^2*w*b-x^2*t*c_ +x^2*u*c+8*x*t*v*c-2*x*u*v*c-7*t*v^2*c+u*v^2*c-5*x^2*w*c_ @@ -1151,7 +1151,7 @@ t11:=-12*x*z*v*a-6*z*v^2*a-2*x^2*t*b+2*x^2*u*b+16*x*t*v*b-10*x*u*v*b_ --R ((c + 8b)u + (- 7c + 4b)t)v --E 89 ---S 90 +--S 90 of 276 t12:=-18*x^2*u*v^3*b-9*x*u*v^4*b-9*x^2*u*v^3*c+9*x*u*v^4*c-3*x^3*z*v*a_ -27*x^2*z*v^2*a-45*x*z*v^3*a-6*z*v^4*a-3*x^3*t*v*b_ -27*x^2*t*v^2*b-45*x*t*v^3*b-6*t*v^4*b-3*x^3*v*w*b_ @@ -1183,70 +1183,70 @@ Varables $x,y,z,t,u,v,a,A,B,C,D,E,F$ <<*>>= )clear all ---S 91 +--S 91 of 276 t1:=v*A --R --R --R (1) A v --E 91 ---S 92 +--S 92 of 276 t2:=u*A+14*B --R --R --R (2) A u + 14B --E 92 ---S 93 +--S 93 of 276 t3:=z*A --R --R --R (3) A z --E 93 ---S 94 +--S 94 of 276 t4:=u*a*A+3*z*A+2*t*A+168*B --R --R --R (4) 3A z + A a u + 2A t + 168B --E 94 ---S 95 +--S 95 of 276 t5:=y*A+5*u*B --R --R --R (5) A y + 5B u --E 95 ---S 96 +--S 96 of 276 t6:=5*v*C+21*D --R --R --R (6) 5C v + 21D --E 96 ---S 97 +--S 97 of 276 t7:=10*u*C+14*E --R --R --R (7) 10C u + 14E --E 97 ---S 98 +--S 98 of 276 t8:=-5*y*C-u*E+105*F --R --R --R (8) - 5C y - E u + 105F --E 98 ---S 99 +--S 99 of 276 t9:=5*z*C+2*u*D --R --R --R (9) 5C z + 2D u --E 99 ---S 100 +--S 100 of 276 t10:=-2/7*v^2+t-4*u-A --R --R @@ -1255,7 +1255,7 @@ t10:=-2/7*v^2+t-4*u-A --R 7 --E 100 ---S 101 +--S 101 of 276 t11:=-2/7*u^2+y-B --R --R @@ -1264,14 +1264,14 @@ t11:=-2/7*u^2+y-B --R 7 --E 101 ---S 102 +--S 102 of 276 t12:=7*u-C --R --R --R (12) 7u - C --E 102 ---S 103 +--S 103 of 276 t13:=3/7*v^3-2*t*v+6*u*v-7*z-D --R --R @@ -1280,7 +1280,7 @@ t13:=3/7*v^3-2*t*v+6*u*v-7*z-D --R 7 --E 103 ---S 104 +--S 104 of 276 t14:=9/7*u*v^2-2*t*u+16*u^2-6*z*v-42*y-E --R --R @@ -1289,7 +1289,7 @@ t14:=9/7*u*v^2-2*t*u+16*u^2-6*z*v-42*y-E --R 7 --E 104 ---S 105 +--S 105 of 276 t15:=3/7*u^3-2*y*u+7*x-F --R --R @@ -1304,7 +1304,7 @@ Variables $x,y,z,t$ <<*>>= )clear all ---S 106 +--S 106 of 276 t1:=-2*y^3*z+6*x^2*z*t-6*x*y*z*t+3*y^2*z*t-y*z*t^2-6*x^2*t+6*x*y*t-2*y^2*t --R --R @@ -1312,7 +1312,7 @@ t1:=-2*y^3*z+6*x^2*z*t-6*x*y*z*t+3*y^2*z*t-y*z*t^2-6*x^2*t+6*x*y*t-2*y^2*t --R (1) (- 2y + 3t y + (- 6t x - t )y + 6t x )z - 2t y + 6t x y - 6t x --E 106 ---S 107 +--S 107 of 276 t1:=18*x^2*y*z^2-18*x*y^2*z^2+18*y^2*z^2-63*x^2*z^2*t+63*x*y*z^2*t_ -27*y^2*z^2*t+9*y*z^2*t^2-18*x^2*y*z+18*x*y^2*z-9*y^3*z_ +78*x^2*z*t-78*x*y*z*t+24*y^2*z*t-15*x^2*t+15*x*y*t-5*y^2*t @@ -1329,7 +1329,7 @@ t1:=18*x^2*y*z^2-18*x*y^2*z^2+18*y^2*z^2-63*x^2*z^2*t+63*x*y*z^2*t_ --R - 15t x --E 107 ---S 108 +--S 108 of 276 t1:=-8*y^4*z+12*x^2*y*z*t-12*x*y^2*z*t+6*y^3*z*t+18*x^2*z*t^2_ -18*x*y*z*t^2+5*y^2*z*t^2-3*y*z*t^3-12*x^2*y*t+12*x*y^2*t_ -6*y^3*t-18*x^2*t^2+18*x*y*t^2-4*y^2*t^2 @@ -1343,7 +1343,7 @@ t1:=-8*y^4*z+12*x^2*y*z*t-12*x*y^2*z*t+6*y^3*z*t+18*x^2*z*t^2_ --R - 6t y + (12t x - 4t )y + (- 12t x + 18t x)y - 18t x --E 108 ---S 109 +--S 109 of 276 t1:=10*x^3*z-15*x^2*y*z+3*x*y^3*z+3*x^2*z*t-x*z*t^2-10*x^3+15*x^2*y_ -5*x*y^2-3*x^2*t+x*y*t --R @@ -1359,28 +1359,28 @@ Variables $a,b,c,d,e,f,g,h$ <<*>>= )clear all ---S 110 +--S 110 of 276 t1:=a-f --R --R --R (1) - f + a --E 110 ---S 111 +--S 111 of 276 t2:=b-g-h --R --R --R (2) - h - g + b --E 111 ---S 112 +--S 112 of 276 t3:=c+d+e-1 --R --R --R (3) e + d + c - 1 --E 112 ---S 113 +--S 113 of 276 t4:=b*c+a*d-1/2 --R --R @@ -1389,7 +1389,7 @@ t4:=b*c+a*d-1/2 --R 2 --E 113 ---S 114 +--S 114 of 276 t5:=b^2*c+a^2*d-1/3 --R --R @@ -1398,7 +1398,7 @@ t5:=b^2*c+a^2*d-1/3 --R 3 --E 114 ---S 115 +--S 115 of 276 t6:=a*c*g-1/6 --R --R @@ -1413,14 +1413,14 @@ Variables $a,b,c,d,e,f,g,h,i,j,k,l,m$ <<*>>= )clear all ---S 116 +--S 116 of 276 t1:=d+e+f+g-1 --R --R --R (1) g + f + e + d - 1 --E 116 ---S 117 +--S 117 of 276 t2:=c*d+b*e+a*f-1/2 --R --R @@ -1429,7 +1429,7 @@ t2:=c*d+b*e+a*f-1/2 --R 2 --E 117 ---S 118 +--S 118 of 276 t3:=c^2*d+b^2*e+a^2*f-1/3 --R --R @@ -1438,7 +1438,7 @@ t3:=c^2*d+b^2*e+a^2*f-1/3 --R 3 --E 118 ---S 119 +--S 119 of 276 t4:=a*e*i+a*d*l+b*d*m-1/6 --R --R @@ -1447,7 +1447,7 @@ t4:=a*e*i+a*d*l+b*d*m-1/6 --R 6 --E 119 ---S 120 +--S 120 of 276 t5:=c^3*d+b^3*e+a^3*f-1/4 --R --R @@ -1456,7 +1456,7 @@ t5:=c^3*d+b^3*e+a^3*f-1/4 --R 4 --E 120 ---S 121 +--S 121 of 276 t6:=a*b*e*i+a*c*d*l+b*c*d*m-1/8 --R --R @@ -1465,7 +1465,7 @@ t6:=a*b*e*i+a*c*d*l+b*c*d*m-1/8 --R 8 --E 121 ---S 122 +--S 122 of 276 t7:=a^2*e*i+a^2*d*l+b^2*d*m-1/2 --R --R @@ -1474,7 +1474,7 @@ t7:=a^2*e*i+a^2*d*l+b^2*d*m-1/2 --R 2 --E 122 ---S 123 +--S 123 of 276 t8:=a*d*i*m-1/24 --R --R @@ -1483,21 +1483,21 @@ t8:=a*d*i*m-1/24 --R 24 --E 123 ---S 124 +--S 124 of 276 t9:=a-h --R --R --R (9) - h + a --E 124 ---S 125 +--S 125 of 276 t10:=b-i-j --R --R --R (10) - j - i + b --E 125 ---S 126 +--S 126 of 276 t11:=c-k-l-m --R --R @@ -1510,7 +1510,7 @@ Variables $a,b,c,d,e,f,g,h,i,j,k,l,m,n$ <<*>>= )clear all ---S 127 +--S 127 of 276 t1:=a*e+b*f+c*g+d*h-1/2 --R --R @@ -1519,7 +1519,7 @@ t1:=a*e+b*f+c*g+d*h-1/2 --R 2 --E 127 ---S 128 +--S 128 of 276 t2:=a^2*e+b^2*f+c^2*g+d^2*h-1/3 --R --R @@ -1528,7 +1528,7 @@ t2:=a^2*e+b^2*f+c^2*g+d^2*h-1/3 --R 3 --E 128 ---S 129 +--S 129 of 276 t3:=a*f*i+a*g*j+b*g*k+a*h*l+b*h*m+c*h*n-1/6 --R --R @@ -1537,7 +1537,7 @@ t3:=a*f*i+a*g*j+b*g*k+a*h*l+b*h*m+c*h*n-1/6 --R 6 --E 129 ---S 130 +--S 130 of 276 t4:=a^3*e+b^3*f+c^3*g+d^3*h-1/4 --R --R @@ -1546,7 +1546,7 @@ t4:=a^3*e+b^3*f+c^3*g+d^3*h-1/4 --R 4 --E 130 ---S 131 +--S 131 of 276 t5:=a*b*f*i+a*c*g*j+b*c*g*k+a*d*h*l+b*d*h*m+c*d*h*n-1/8 --R --R @@ -1555,7 +1555,7 @@ t5:=a*b*f*i+a*c*g*j+b*c*g*k+a*d*h*l+b*d*h*m+c*d*h*n-1/8 --R 8 --E 131 ---S 132 +--S 132 of 276 t6:=a^2*f*i+a^2*g*j+b^2*g*k+a^2*h*l+b^2*h*m+c^2*h*n-1/12 --R --R @@ -1564,7 +1564,7 @@ t6:=a^2*f*i+a^2*g*j+b^2*g*k+a^2*h*l+b^2*h*m+c^2*h*n-1/12 --R 12 --E 132 ---S 133 +--S 133 of 276 t7:=a*g*i*k+a*h*i*m+a*h*j*n+b*h*k*n-1/24 --R --R @@ -1573,7 +1573,7 @@ t7:=a*g*i*k+a*h*i*m+a*h*j*n+b*h*k*n-1/24 --R 24 --E 133 ---S 134 +--S 134 of 276 t8:=a^4*e+b^4*f+c^4*g+d^4*h-1/5 --R --R @@ -1582,7 +1582,7 @@ t8:=a^4*e+b^4*f+c^4*g+d^4*h-1/5 --R 5 --E 134 ---S 135 +--S 135 of 276 t9:=a*b^2*f*i+a*c^2*g*j+b*c^2*g*k+ad^2*h*l+b*d^2*h*m+c*d^2*h*n-1/10 --R --R @@ -1591,7 +1591,7 @@ t9:=a*b^2*f*i+a*c^2*g*j+b*c^2*g*k+ad^2*h*l+b*d^2*h*m+c*d^2*h*n-1/10 --R 10 --E 135 ---S 136 +--S 136 of 276 t10:=a^2*b*f*i+a^2*c*g*j+b^2*c*g*k+a^3*h*l+b^2*d*h*m+c^2*d*h*n-1/15 --R --R @@ -1600,7 +1600,7 @@ t10:=a^2*b*f*i+a^2*c*g*j+b^2*c*g*k+a^3*h*l+b^2*d*h*m+c^2*d*h*n-1/15 --R 15 --E 136 ---S 137 +--S 137 of 276 t11:=a*c*g*i*k+a*d*h*i*m+a*d*h*j*n+b*d*h*k*n-1/30 --R --R @@ -1609,7 +1609,7 @@ t11:=a*c*g*i*k+a*d*h*i*m+a*d*h*j*n+b*d*h*k*n-1/30 --R 30 --E 137 ---S 138 +--S 138 of 276 t12:=a^2*f*i^2+a^2*g*j^2+2*a*b*g*j*k+b^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m +b^2*h*m^2+2*a*c*h*l*n+2*b*c*h*m*n+c^2*h*n^2-1/20 --R @@ -1623,7 +1623,7 @@ t12:=a^2*f*i^2+a^2*g*j^2+2*a*b*g*j*k+b^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m --R 20 --E 138 ---S 139 +--S 139 of 276 t13:=a^2*f*i+a^3*g*j+b^3*g*k+a^3*h*l+b^3*h*m+c^3*h*n-1/20 --R --R @@ -1632,7 +1632,7 @@ t13:=a^2*f*i+a^3*g*j+b^3*g*k+a^3*h*l+b^3*h*m+c^3*h*n-1/20 --R 20 --E 139 ---S 140 +--S 140 of 276 t14:=a*b*g*i*k+a*b*h*i*m+a*c*h*j*n+b*c*h*k*n-1/40 --R --R @@ -1641,7 +1641,7 @@ t14:=a*b*g*i*k+a*b*h*i*m+a*c*h*j*n+b*c*h*k*n-1/40 --R 40 --E 140 ---S 141 +--S 141 of 276 t15:=a^2*g*i*k+a^2*h*i*m+a^2*h*j*n+b^2*h*k*n-1/60 --R --R @@ -1650,7 +1650,7 @@ t15:=a^2*g*i*k+a^2*h*i*m+a^2*h*j*n+b^2*h*k*n-1/60 --R 60 --E 141 ---S 142 +--S 142 of 276 t16:=a*h*i*k*n-1/120 --R --R @@ -1665,7 +1665,7 @@ Variables $a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t$ <<*>>= )clear all ---S 143 +--S 143 of 276 t1:=a*f+b*g+c*h+d*i+e*j-1/2 --R --R @@ -1674,7 +1674,7 @@ t1:=a*f+b*g+c*h+d*i+e*j-1/2 --R 2 --E 143 ---S 144 +--S 144 of 276 t2:=a^2*f+b^2*g+c^2*h+d^2*i+e^2*j-1/3 --R --R @@ -1683,7 +1683,7 @@ t2:=a^2*f+b^2*g+c^2*h+d^2*i+e^2*j-1/3 --R 3 --E 144 ---S 145 +--S 145 of 276 t3:=t*d*j+a*g*k+a*h*l+b*h*m+a*i*n+b*i*o+c*i*p+a*j*q+b*j*r+c*j*s-1/6 --R --R @@ -1695,7 +1695,7 @@ t3:=t*d*j+a*g*k+a*h*l+b*h*m+a*i*n+b*i*o+c*i*p+a*j*q+b*j*r+c*j*s-1/6 --R 6 --E 145 ---S 146 +--S 146 of 276 t4:=a^3*f+b^3*g+c^3*h+d^3*i+e^3*j-1/4 --R --R @@ -1704,7 +1704,7 @@ t4:=a^3*f+b^3*g+c^3*h+d^3*i+e^3*j-1/4 --R 4 --E 146 ---S 147 +--S 147 of 276 t5:=t*d*e*j+a*b*g*k+a*c*h*l+b*c*h*m+a*d*i*n+b*d*i*o+c*d*i*p+a*e*j*q_ +b*e*j*r+c*e*j*s-1/8 --R @@ -1717,7 +1717,7 @@ t5:=t*d*e*j+a*b*g*k+a*c*h*l+b*c*h*m+a*d*i*n+b*d*i*o+c*d*i*p+a*e*j*q_ --R 8 --E 147 ---S 148 +--S 148 of 276 t6:=t*d^2*j+a^2*g*k+a^2*h*l+b^2*h*m+a^2*i*n+b^2*i*o+c^2*i*p+a^2*j*g_ +b^2*j*r+c^2*j*s-1/12 --R @@ -1731,7 +1731,7 @@ t6:=t*d^2*j+a^2*g*k+a^2*h*l+b^2*h*m+a^2*i*n+b^2*i*o+c^2*i*p+a^2*j*g_ --R 12 --E 148 ---S 149 +--S 149 of 276 t7:=a*h*k*m+t*a*j*n+t*b*j*o+a*i*k*o+t*c*j*p+a*i*l*p+b*i*m*p+a*j*k*r_ +a*j*l*s+b*j*m*s-1/24 --R @@ -1744,7 +1744,7 @@ t7:=a*h*k*m+t*a*j*n+t*b*j*o+a*i*k*o+t*c*j*p+a*i*l*p+b*i*m*p+a*j*k*r_ --R 24 --E 149 ---S 150 +--S 150 of 276 t8:=a^4*f+b^4*g+c^4*h+d^4*i+e^4*j-1/5 --R --R @@ -1753,7 +1753,7 @@ t8:=a^4*f+b^4*g+c^4*h+d^4*i+e^4*j-1/5 --R 5 --E 150 ---S 151 +--S 151 of 276 t9:=t*d*e^2*j+a*b^2*g*k+a*c^2*h*l+b*c^2*h*m+a*d^2*i*n+b*d^2*i*o_ +c*d^2*i*p+a*e^2*j*g+b*e^2*j*r+c*e^2*j*s-1/10 --R @@ -1767,7 +1767,7 @@ t9:=t*d*e^2*j+a*b^2*g*k+a*c^2*h*l+b*c^2*h*m+a*d^2*i*n+b*d^2*i*o_ --R 10 --E 151 ---S 152 +--S 152 of 276 t10:=t*d^2*e*j+a^2*b*g*k+a^2*c*h*l+b^2*c*h*m+a^2*d*i*n+b^2*d*i*o_ +c^2*d*i*p+a^2*e*j*q+b^2*e*j*r+c^2*e*j*s-1/15 --R @@ -1781,7 +1781,7 @@ t10:=t*d^2*e*j+a^2*b*g*k+a^2*c*h*l+b^2*c*h*m+a^2*d*i*n+b^2*d*i*o_ --R 15 --E 152 ---S 153 +--S 153 of 276 t11:=a*c*h*k*m+t*a*e*j*n+t*b*e*j*o+a*d*i*k*o+t*c*e*j*p+a*d*i*l*p_ +b*d*i*m*p+a*e*j*k*r+a*e*j*l*s+b*e*j*m*s-1/30 --R @@ -1794,7 +1794,7 @@ t11:=a*c*h*k*m+t*a*e*j*n+t*b*e*j*o+a*d*i*k*o+t*c*e*j*p+a*d*i*l*p_ --R 30 --E 153 ---S 154 +--S 154 of 276 t12:=t^2*d^2*j+a^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m+b^2*h*m^2+a^2*i*n^2_ +2*a*b*i*n*o+b^2*i*o^2+2*a*c*i*n*p+2*b*c*i*o*p+c^2*i*p^2_ +2*t*a*d*j*q+a^2*j*q^2+2*t*b*d*j*r+2*a*b*j*q*r+b^2*j*r^2_ @@ -1816,7 +1816,7 @@ t12:=t^2*d^2*j+a^2*g*k^2+a^2*h*l^2+2*a*b*h*l*m+b^2*h*m^2+a^2*i*n^2_ --R 20 --E 154 ---S 155 +--S 155 of 276 t13:=t*d^3*j+a^3*g*k+a^3*h*l+b^3*h*m+a^3*i*n+b^3*i*o+c^3*i*p_ +a^3*j*q+b^3*j*r+c^3*j*s-1/20 --R @@ -1830,7 +1830,7 @@ t13:=t*d^3*j+a^3*g*k+a^3*h*l+b^3*h*m+a^3*i*n+b^3*i*o+c^3*i*p_ --R 20 --E 155 ---S 156 +--S 156 of 276 t14:=a*b*h*k*m+t*a*d*j*n+t*b*d*j*o+a*b*i*k*o+t*c*d*j*p+a*c*i*l*p_ +b*c*i*m*p+a*b*j*k*r+a*c*j*l*s+b*c*j*m*s-1/40 --R @@ -1843,7 +1843,7 @@ t14:=a*b*h*k*m+t*a*d*j*n+t*b*d*j*o+a*b*i*k*o+t*c*d*j*p+a*c*i*l*p_ --R 40 --E 156 ---S 157 +--S 157 of 276 t15:=a^2*h*k*m+t*a^2*j*n+t*b^2*j*o+a^2*i*k*o+t*c^2*j*p+a^2*i*l*p_ +b^2*i*m*p+a^2*j*k*r+a^2*j*l*s+b^2*j*m*s-1/60 --R @@ -1857,7 +1857,7 @@ t15:=a^2*h*k*m+t*a^2*j*n+t*b^2*j*o+a^2*i*k*o+t*c^2*j*p+a^2*i*l*p_ --R 60 --E 157 ---S 158 +--S 158 of 276 t16:=t*a*j*k*o+t*a*j*l*p+t*b*j*m*p+a*i*k*m*p+a*j*k*m*s-1/20 --R --R @@ -1872,7 +1872,7 @@ Variables $a,c,j,l,m,n,p,v,g,h$ <<*>>= )clear all ---S 159 +--S 159 of 276 t1:=c^2*p-a*c+c*l+a-p-h --R --R @@ -1880,7 +1880,7 @@ t1:=c^2*p-a*c+c*l+a-p-h --R (1) (c - 1)p + c l - h - a c + a --E 159 ---S 160 +--S 160 of 276 t2:=a*c*h+c^2+c*n+m*h --R --R @@ -1888,7 +1888,7 @@ t2:=a*c*h+c^2+c*n+m*h --R (2) c n + h m + a c h + c --E 160 ---S 161 +--S 161 of 276 t3:=-a^2*c+a*c*l+a*c*g-c*l*h+a^2+2*c^2-a*m-a*h+l*h-2 --R --R @@ -1896,7 +1896,7 @@ t3:=-a^2*c+a*c*l+a*c*g-c*l*h+a^2+2*c^2-a*m-a*h+l*h-2 --R (3) - a m + ((- c + 1)h + a c)l - a h + a c g + 2c - a c + a - 2 --E 161 ---S 162 +--S 162 of 276 t4:=-a*c^2+a*c*j-c^2*m+a*c*n+c^2*v-c*n*h-c*m+n*h --R --R @@ -1904,42 +1904,42 @@ t4:=-a*c^2+a*c*j-c^2*m+a*c*n+c^2*v-c*n*h-c*m+n*h --R (4) c v + ((- c + 1)h + a c)n + (- c - c)m + a c j - a c --E 162 ---S 163 +--S 163 of 276 t5:=-c*l*g-a*l-j-1 --R --R --R (5) (- c g - a)l - j - 1 --E 163 ---S 164 +--S 164 of 276 t6:=-c*n*g-c*l-c*m+j*m+c*g+c*h --R --R --R (6) - c g n + (j - c)m - c l + c h + c g --E 164 ---S 165 +--S 165 of 276 t7:=-c*j*l-a*j+j*l-a*n+c*g+a-v+g --R --R --R (7) - v - a n + (- c + 1)j l - a j + (c + 1)g + a --E 165 ---S 166 +--S 166 of 276 t8:=-c*j*n+c*j-c*n+j*n --R --R --R (8) ((- c + 1)j - c)n + c j --E 166 ---S 167 +--S 167 of 276 t9:=c*m*p-l*n*p+a*l+l*m+a*p-l*p+c-n-2 --R --R --R (9) (- l n + c m - l + a)p - n + l m + a l + c - 2 --E 167 ---S 168 +--S 168 of 276 t10:=-n^2*p+c*l+c*m+2*m*n+c*p-c*h+m --R --R @@ -1947,14 +1947,14 @@ t10:=-n^2*p+c*l+c*m+2*m*n+c*p-c*h+m --R (10) (- n + c)p + 2m n + (c + 1)m + c l - c h --E 168 ---S 169 +--S 169 of 276 t11:=-l*m*h+a*c+2*c*m-l*n+m*n-c*g-a+p+h --R --R --R (11) p + (m - l)n + (- h l + 2c)m + h - c g + a c - a --E 169 ---S 170 +--S 170 of 276 t12:=-c*l*m-c*m^2+a*m*n-m^2*n+c*m*v-m*n*h+c^2-c*j-n^2+n --R --R @@ -1962,7 +1962,7 @@ t12:=-c*l*m-c*m^2+a*m*n-m^2*n+c*m*v-m*n*h+c^2-c*j-n^2+n --R (12) c m v - n + (- m + (- h + a)m + 1)n - c m - c l m - c j + c --E 170 ---S 171 +--S 171 of 276 t13:=a^2*l-a*l^2+c*n*p-l*m*g-c*l-a*n+2*a-l+m-v+g --R --R @@ -1970,7 +1970,7 @@ t13:=a^2*l-a*l^2+c*n*p-l*m*g-c*l-a*n+2*a-l+m-v+g --R (13) - v + c n p - a n + (- g l + 1)m - a l + (- c + a - 1)l + g + 2a --E 171 ---S 172 +--S 172 of 276 t14:=a*c*l-c*l^2+a*m*n-l*m*n-m*n*g+c*l*h-m^2+c*n-n^2+m*v+2*c --R --R @@ -1978,7 +1978,7 @@ t14:=a*c*l-c*l^2+a*m*n-l*m*n-m*n*g+c*l*h-m^2+c*n-n^2+m*v+2*c --R (14) m v - n + ((- l - g + a)m + c)n - m - c l + (c h + a c)l + 2c --E 172 ---S 173 +--S 173 of 276 t15:=-j*l*m-l*n*v+c*l*g+a*l+c*n+n^2+j+1 --R --R @@ -1986,7 +1986,7 @@ t15:=-j*l*m-l*n*v+c*l*g+a*l+c*n+n^2+j+1 --R (15) - l n v + n + c n - j l m + (c g + a)l + j + 1 --E 173 ---S 174 +--S 174 of 276 t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+c*n*v-n^2*v+n*v --R --R @@ -1994,21 +1994,21 @@ t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+c*n*v-n^2*v+n*v --R (16) (- n + (c + 1)n)v + (- m + a)n + (- j m - c l)n + c j l --E 174 ---S 175 +--S 175 of 276 t17:=-j*l*p+c*m*p+n*p*h-a*l-a*m+a*g-p*g+a*h+c-j+n-1 --R --R --R (17) (h n + c m - j l - g)p + n - a m - a l - j + a h + a g + c - 1 --E 175 ---S 176 +--S 176 of 276 t18:=-j*n*p+l*m*h-c*l+j*m+c*g+n*h --R --R --R (18) - j n p + h n + (h l + j)m - c l + c g --E 176 ---S 177 +--S 177 of 276 t19:=l^2*h-l*h^2+a*c-c*l-j*l+c*m+j*m-n*g+c*h+n*h-a-l-g+h --R --R @@ -2017,7 +2017,7 @@ t19:=l^2*h-l*h^2+a*c-c*l-j*l+c*m+j*m-n*g+c*h+n*h-a-l-g+h --R (h - g)n + (j + c)m + h l + (- j - h - c - 1)l + (c + 1)h - g + a c - a --E 177 ---S 178 +--S 178 of 276 t20:=a*j*m-j*m^2+c*m*v-c*m*g-c*m*h+l*n*h+n*v*h-n*h^2+c^2-c*n-2*j*n --R --R @@ -2025,14 +2025,14 @@ t20:=a*j*m-j*m^2+c*m*v-c*m*g-c*m*h+l*n*h+n*v*h-n*h^2+c^2-c*n-2*j*n --R (20) (h n + c m)v + (h l - 2j - h - c)n - j m + (a j - c h - c g)m + c --E 178 ---S 179 +--S 179 of 276 t21:=j*n*p-l*g*h-j*l-n*g-m+h --R --R --R (21) j n p - g n - m + (- j - g h)l + h --E 179 ---S 180 +--S 180 of 276 t22:=j*l^2-j*l*v-a*n*g+n*g^2-j*l*h+2*j*n+l*g+m*g-v*g+j-1 --R --R @@ -2040,14 +2040,14 @@ t22:=j*l^2-j*l*v-a*n*g+n*g^2-j*l*h+2*j*n+l*g+m*g-v*g+j-1 --R (22) (- j l - g)v + (2j + g - a g)n + g m + j l + (- h j + g)l + j - 1 --E 180 ---S 181 +--S 181 of 276 t23:=j*l*n-j*m*n-c*n*g+j*n*g-j*n*h+j*m --R --R --R (23) (- j m + j l + (- h + g)j - c g)n + j m --E 181 ---S 182 +--S 182 of 276 t24:=-a^2*p+a*l*p+m^2*p-l*p*v+3*a+2*m-v --R --R @@ -2055,14 +2055,14 @@ t24:=-a^2*p+a*l*p+m^2*p-l*p*v+3*a+2*m-v --R (24) (- l p - 1)v + (m + a l - a )p + 2m + 3a --E 182 ---S 183 +--S 183 of 276 t25:=-a*c*p+c*l*p-n*p*v+n*p*h-a*m+l*m+m*v-m*h+2*c+2*n --R --R --R (25) (- n p + m)v + (h n + c l - a c)p + 2n + (l - h - a)m + 2c --E 183 ---S 184 +--S 184 of 276 t26:=-a*c*p+n*p*g+l^2-a*m-l*m+m^2+l*p-l*v+m*v-m*g-l*h-p*h+c+n --R --R @@ -2071,7 +2071,7 @@ t26:=-a*c*p+n*p*g+l^2-a*m-l*m+m^2+l*p-l*v+m*v-m*g-l*h-p*h+c+n --R (m - l)v + (g n + l - h - a c)p + n + m + (- l - g - a)m + l - h l + c --E 184 ---S 185 +--S 185 of 276 t27:=-c^2*p+j*n*p-2*c*m-j*m+l*n-m*n-n*h --R --R @@ -2079,21 +2079,21 @@ t27:=-c^2*p+j*n*p-2*c*m-j*m+l*n-m*n-n*h --R (27) (j n - c )p + (- m + l - h)n + (- j - 2c)m --E 185 ---S 186 +--S 186 of 276 t28:=m*n*p+n*p*v-a*l-l*m-a*p-l*v-l*g-p*g --R --R --R (28) (n p - l)v + (m n - g - a)p - l m + (- g - a)l --E 186 ---S 187 +--S 187 of 276 t29:=l*m*h-c*l-c*p-n*g+n*h-m --R --R --R (29) - c p + (h - g)n + (h l - 1)m - c l --E 187 ---S 188 +--S 188 of 276 t30:=l^2*v-l*v^2+l*m*g-j*l-a*n-l*n+m*n-j*p+2*n*v+n*g-v --R --R @@ -2101,7 +2101,7 @@ t30:=l^2*v-l*v^2+l*m*g-j*l-a*n-l*n+m*n-j*p+2*n*v+n*g-v --R (30) - l v + (2n + l - 1)v - j p + (m - l + g - a)n + g l m - j l --E 188 ---S 189 +--S 189 of 276 t31:=j*l*m+l*n*v-c*n-n^2 --R --R @@ -2115,7 +2115,7 @@ Variables $a,b,c,j,k,l,m,n,p,v$ <<*>>= )clear all ---S 190 +--S 190 of 276 t1:=-a*b*k+a*c*k+b*k*l-c*k*l-b^2*p+c^2*p+b*k --R --R @@ -2123,7 +2123,7 @@ t1:=-a*b*k+a*c*k+b*k*l-c*k*l-b^2*p+c^2*p+b*k --R (1) (c - b )p + (- c + b)k l + (a c + (- a + 1)b)k --E 190 ---S 191 +--S 191 of 276 t2:=-c^2*k+a*c*l+b*l*m-c*k*n+a*c+c^2+b*m --R --R @@ -2131,7 +2131,7 @@ t2:=-c^2*k+a*c*l+b*l*m-c*k*n+a*c+c^2+b*m --R (2) - c k n + (b l + b)m + a c l - c k + c + a c --E 191 ---S 192 +--S 192 of 276 t3:=a^2*b-a^2*c+2*b^2*k-2*c^2*k-a*b*l+a*c*l+b*l^2-c*l^2-a*b*m+a*c*m_ -a*b-b^2+c^2+b*l-c*l --R @@ -2144,7 +2144,7 @@ t3:=a^2*b-a^2*c+2*b^2*k-2*c^2*k-a*b*l+a*c*l+b*l^2-c*l^2-a*b*m+a*c*m_ --R - a c - b + (a - a)b --E 192 ---S 193 +--S 193 of 276 t4:=-a*c^2+a*c*j-b*c*m-c^2*m+a*c*n+b*l*n-c*l*n+c^2*v+b*n-c*n --R --R @@ -2152,7 +2152,7 @@ t4:=-a*c^2+a*c*j-b*c*m-c^2*m+a*c*n+b*l*n-c*l*n+c^2*v+b*n-c*n --R (4) c v + ((- c + b)l + (a - 1)c + b)n + (- c - b c)m + a c j - a c --E 193 ---S 194 +--S 194 of 276 t5:=b^2*k+b*j*k-a*b*l-c*l*m-b^2 --R --R @@ -2160,14 +2160,14 @@ t5:=b^2*k+b*j*k-a*b*l-c*l*m-b^2 --R (5) - c l m - a b l + (b j + b )k - b --E 194 ---S 195 +--S 195 of 276 t6:=b*j*m-c*m*n+b*c --R --R --R (6) - c m n + b j m + b c --E 195 ---S 196 +--S 196 of 276 t7:=a*b^2-a*b*j+b*j*l-c*j*l+b^2*m+b*c*m-a*b*n-b^2*v --R --R @@ -2175,14 +2175,14 @@ t7:=a*b^2-a*b*j+b*j*l-c*j*l+b^2*m+b*c*m-a*b*n-b^2*v --R (7) - b v - a b n + (b c + b )m + (- c + b)j l - a b j + a b --E 196 ---S 197 +--S 197 of 276 t8:=b*c*j-b*c*n+b*j*n-c*j*n --R --R --R (8) ((- c + b)j - b c)n + b c j --E 197 ---S 198 +--S 198 of 276 t9:=-2*b*k^2+c*k^2-a*k*l-k*l*m-k^2*n+a*b*p-b*l*p+c*m*p-l*n*p+b*k --R --R @@ -2190,7 +2190,7 @@ t9:=-2*b*k^2+c*k^2-a*k*l-k*l*m-k^2*n+a*b*p-b*l*p+c*m*p-l*n*p+b*k --R (9) (- l n + c m - b l + a b)p - k n - k l m - a k l + (c - 2b)k + b k --E 198 ---S 199 +--S 199 of 276 t10:=-b*k*m-c*k*m-2*k*m*n+b*c*p-n^2*p+c*k+b*m+c*m --R --R @@ -2198,7 +2198,7 @@ t10:=-b*k*m-c*k*m-2*k*m*n+b*c*p-n^2*p+c*k+b*m+c*m --R (10) (- n + b c)p - 2k m n + ((- c - b)k + c + b)m + c k --E 199 ---S 200 +--S 200 of 276 t11:=a*b*k-a*c*k-b*k*l-c*k*m-l^2*m+k*l*n-k*m*n+b^2*p-b*k+c*m-l*m-l*n --R --R @@ -2209,7 +2209,7 @@ t11:=a*b*k-a*c*k-b*k*l-c*k*m-l^2*m+k*l*n-k*m*n+b^2*p-b*k+c*m-l*m-l*n --R (- a c + (a - 1)b)k --E 200 ---S 201 +--S 201 of 276 t12:=-c^2*k+c*j*k-c*l*m-c*m^2-b*k*n+a*m*n-l*m*n-m^2*n+k*n^2+c*m*v+b*n-m*n-n^2 --R --R @@ -2221,7 +2221,7 @@ t12:=-c^2*k+c*j*k-c*l*m-c*m^2-b*k*n+a*m*n-l*m*n-m^2*n+k*n^2+c*m*v+b*n-m*n-n^2 --R (c j - c )k --E 201 ---S 202 +--S 202 of 276 t13:=-2*a*b*k+a^2*l+b*k*l+c*k*l-a*l^2-2*b*k*m-l*m^2+a*k*n+c*n*p_ +b*k*v+a*b-b*l-l*n --R @@ -2233,7 +2233,7 @@ t13:=-2*a*b*k+a^2*l+b*k*l+c*k*l-a*l^2-2*b*k*m-l*m^2+a*k*n+c*n*p_ --R - 2a b k + a b --E 202 ---S 203 +--S 203 of 276 t14:=-2*b*c*k+a*c*l-b*m^2-c*k*n+a*m*n-l*m*n-m^2*n+k*n^2+b*m*v_ +b*c+c*l+c*n-n^2 --R @@ -2245,7 +2245,7 @@ t14:=-2*b*c*k+a*c*l-b*m^2-c*k*n+a*m*n-l*m*n-m^2*n+k*n^2+b*m*v_ --R - 2b c k + b c --E 203 ---S 204 +--S 204 of 276 t15:=-b^2*k-b*j*k+a*b*l+c*l*m-j*l*m-c*k*n-k*n^2-l*n*v+b^2+c*n --R --R @@ -2254,7 +2254,7 @@ t15:=-b^2*k-b*j*k+a*b*l+c*l*m-j*l*m-c*k*n-k*n^2-l*n*v+b^2+c*n --R - l n v - k n + (- c k + c)n + (- j + c)l m + a b l + (- b j - b )k + b --E 204 ---S 205 +--S 205 of 276 t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+b*n*v+c*n*v-n^2*v --R --R @@ -2262,7 +2262,7 @@ t16:=c*j*l-c*l*n-j*m*n+a*n^2-m*n^2+b*n*v+c*n*v-n^2*v --R (16) (- n + (c + b)n)v + (- m + a)n + (- j m - c l)n + c j l --E 205 ---S 206 +--S 206 of 276 t17:=-b*k^2+c*k^2-j*k^2+k^2*n-j*l*p-b*m*p+c*m*p+l*n*p-a*k+n*p --R --R @@ -2270,7 +2270,7 @@ t17:=-b*k^2+c*k^2-j*k^2+k^2*n-j*l*p-b*m*p+c*m*p+l*n*p-a*k+n*p --R (17) ((l + 1)n + (c - b)m - j l)p + k n + (- j + c - b)k - a k --E 206 ---S 207 +--S 207 of 276 t18:=c*l*k-c*k*m-j*k*m+l^2*m-k*l*n-j*n*p+c*m+l*m-k*n+l*n+n --R --R @@ -2278,7 +2278,7 @@ t18:=c*l*k-c*k*m-j*k*m+l^2*m-k*l*n-j*n*p+c*m+l*m-k*n+l*n+n --R (18) - j n p + ((- k + 1)l - k + 1)n + (l + l + (- j - c)k + c)m + c k l --E 207 ---S 208 +--S 208 of 276 t19:=a*b*k-a*c*k+j*k*l+b*k*m-c*k*m-j*k*m-k*l*n+k*m*n_ -b*k-c*k-j*l-l^2-b*m+c*m-k*n+l*n-l+n --R @@ -2290,7 +2290,7 @@ t19:=a*b*k-a*c*k+j*k*l+b*k*m-c*k*m-j*k*m-k*l*n+k*m*n_ --R (j k - j - 1)l + ((- a - 1)c + (a - 1)b)k --E 208 ---S 209 +--S 209 of 276 t20:=-c^2*k+a*j*m-c*l*m-c*m^2-j*m^2+c*k*n+2*j*k*n+c*m*v+l*n*v_ -c*m-j*n-l*n+n*v-n --R @@ -2303,7 +2303,7 @@ t20:=-c^2*k+a*j*m-c*l*m-c*m^2-j*m^2+c*k*n+2*j*k*n+c*m*v+l*n*v_ --R (- c l + a j - c)m - c k --E 209 ---S 210 +--S 210 of 276 t21:=-b*k*l+j*k*l+b*k*m-l^2*m+k*m*n+j*n*p-b*k-j*l-b*m-l*m --R --R @@ -2311,7 +2311,7 @@ t21:=-b*k*l+j*k*l+b*k*m-l^2*m+k*m*n+j*n*p-b*k-j*l-b*m-l*m --R (21) j n p + k m n + (- l - l + b k - b)m + ((j - b)k - j)l - b k --E 210 ---S 211 +--S 211 of 276 t22:=b^2*k-b*j*k+b*l*m+b*m^2-2*j*k*n-a*m*n+m^2*n-j*l*v-b*m*v-j*l+j*n --R --R @@ -2320,14 +2320,14 @@ t22:=b^2*k-b*j*k+b*l*m+b*m^2-2*j*k*n-a*m*n+m^2*n-j*l*v-b*m*v-j*l+j*n --R (- b m - j l)v + (m - a m - 2j k + j)n + b m + b l m - j l + (- b j + b )k --E 211 ---S 212 +--S 212 of 276 t23:=b*j*m-c*m*n-j*n --R --R --R (23) (- c m - j)n + b j m --E 212 ---S 213 +--S 213 of 276 t24:=3*a*k^2+2*k^2*m-a^2*p+a*l*p+m^2*p-k^2*v-l*p*v-2*a*k-b*p+n*p --R --R @@ -2335,7 +2335,7 @@ t24:=3*a*k^2+2*k^2*m-a^2*p+a*l*p+m^2*p-k^2*v-l*p*v-2*a*k-b*p+n*p --R (24) (- l p - k )v + (n + m + a l - b - a )p + 2k m + 3a k - 2a k --E 213 ---S 214 +--S 214 of 276 t25:=2*c*k^2+a*k*m+2*k^2*n-a*c*p+c*l*p+l*n*p-k*m*v-n*p*v-c*k-a*m_ +k*m+l*m+m^2-3*k*n+n*p+n --R @@ -2348,7 +2348,7 @@ t25:=2*c*k^2+a*k*m+2*k^2*n-a*c*p+c*l*p+l*n*p-k*m*v-n*p*v-c*k-a*m_ --R (l + (a + 1)k - a)m + 2c k - c k --E 214 ---S 215 +--S 215 of 276 t26:=c*k^2+a*k*m+k*l*m+k^2*n-a*c*p+m*n*p+k*l*v-k*m*v_ +2*b*k-c*k+k*l-a*m+m^2-2*k*n-b*p-l*v-b-l+n --R @@ -2361,7 +2361,7 @@ t26:=c*k^2+a*k*m+k*l*m+k^2*n-a*c*p+m*n*p+k*l*v-k*m*v_ --R (k l + a k - a)m + (k - 1)l + c k + (- c + 2b)k - b --E 215 ---S 216 +--S 216 of 276 t27:=2*c*k*m+j*k*m+k*m*n-c^2*p+j*n*p-2*c*m+k*n-n --R --R @@ -2369,7 +2369,7 @@ t27:=2*c*k*m+j*k*m+k*m*n-c^2*p+j*n*p-2*c*m+k*n-n --R (27) (j n - c )p + (k m + k - 1)n + ((j + 2c)k - 2c)m --E 216 ---S 217 +--S 217 of 276 t28:=a*k*l+2*k*l*m-a*b*p-b*m*p+m*n*p+k*l*v+n*p*v+b*k-l*m+k*n-l*v-b --R --R @@ -2383,7 +2383,7 @@ Variables $x,y,z,t,u,v,w,a$ <<*>>= )clear all ---S 218 +--S 218 of 276 t1:=-x^2+y^2 --R --R @@ -2391,14 +2391,14 @@ t1:=-x^2+y^2 --R (1) y - x --E 218 ---S 219 +--S 219 of 276 t2:=x*u*v+y*u*a-x-w --R --R --R (2) a u y + (u v - 1)x - w --E 219 ---S 220 +--S 220 of 276 t3:=x*u^2-y*u^2+y*z*a-x*u*a+y*u*a-x*v*a+x*a^2-y*a^2 --R --R @@ -2406,7 +2406,7 @@ t3:=x*u^2-y*u^2+y*z*a-x*u*a+y*u*a-x*v*a+x*a^2-y*a^2 --R (3) a y z + (- u + a u - a )y + (- a v + u - a u + a )x --E 220 ---S 221 +--S 221 of 276 t4:=-x*y*v-y^2*v+x*u*w-y*u*w+y*t*a+y*w*a-v^2+a^2 --R --R @@ -2414,21 +2414,21 @@ t4:=-x*y*v-y^2*v+x*u*w-y*u*w+y*t*a+y*w*a-v^2+a^2 --R (4) - v y + (- v x + (- u + a)w + a t)y + u w x - v + a --E 221 ---S 222 +--S 222 of 276 t5:=-y*z*u-x*u*a+y+t --R --R --R (5) - u y z + y - a u x + t --E 222 ---S 223 +--S 223 of 276 t6:=x*y*z-x*y*v+x*t*v-y*z*w+z*u-u*v-z*a-v*a --R --R --R (6) ((x - w)y + u - a)z - v x y + t v x + (- u - a)v --E 223 ---S 224 +--S 224 of 276 t7:=x^2*z+x*y*z+x*t*u-y*t*u-x*t*a-x*w*a+z^2-a^2 --R --R @@ -2436,21 +2436,21 @@ t7:=x^2*z+x*y*z+x*t*u-y*t*u-x*t*a-x*w*a+z^2-a^2 --R (7) z + (x y + x )z - t u y + (- a w + t u - a t)x - a --E 224 ---S 225 +--S 225 of 276 t8:=x*y*t-x*y*w+x*t*w-y*t*w+x*z+z*t-y*v-v*w --R --R --R (8) (x + t)z + ((- w + t)x - t w - v)y + t w x - v w --E 225 ---S 226 +--S 226 of 276 t9:=-x*u+y*v-u*w+x*a --R --R --R (9) v y + (- u + a)x - u w --E 226 ---S 227 +--S 227 of 276 t10:=x*y-w^2 --R --R @@ -2458,7 +2458,7 @@ t10:=x*y-w^2 --R (10) x y - w --E 227 ---S 228 +--S 228 of 276 t11:=-u^2*v+x^2+z --R --R @@ -2466,7 +2466,7 @@ t11:=-u^2*v+x^2+z --R (11) z + x - u v --E 228 ---S 229 +--S 229 of 276 t12:=-y*u*v-y*v^2-u*v*w-v^2*w+y*v*a+u*w*a+x+t --R --R @@ -2474,7 +2474,7 @@ t12:=-y*u*v-y*v^2-u*v*w-v^2*w+y*v*a+u*w*a+x+t --R (12) (- v + (- u + a)v)y + x + (- v - u v + a u)w + t --E 229 ---S 230 +--S 230 of 276 t13:=-z*u*v-u^2*a+u*a^2+y*w+a --R --R @@ -2482,7 +2482,7 @@ t13:=-z*u*v-u^2*a+u*a^2+y*w+a --R (13) - u v z + w y - a u + a u + a --E 230 ---S 231 +--S 231 of 276 t14:=-x*v^2-z*v*w-u*v*w+y*u*a+x*v*a+v*w*a --R --R @@ -2490,14 +2490,14 @@ t14:=-x*v^2-z*v*w-u*v*w+y*u*a+x*v*a+v*w*a --R (14) - v w z + a u y + (- v + a v)x + (- u + a)v w --E 231 ---S 232 +--S 232 of 276 t15:=y*z*u-t*u*v+x*u*a-u*w*a --R --R --R (15) u y z + a u x - a u w - t u v --E 232 ---S 233 +--S 233 of 276 t16:=y*t*u-y*u*w-t*v*w-v*w^2+x*w*a+y*w*a-v^2+a^2 --R --R @@ -2505,14 +2505,14 @@ t16:=y*t*u-y*u*w-t*v*w-v*w^2+x*w*a+y*w*a-v^2+a^2 --R (16) ((- u + a)w + t u)y + a w x - v w - t v w - v + a --E 233 ---S 234 +--S 234 of 276 t17:=-x*z-t*u+y*v+u*w --R --R --R (17) - x z + v y + u w - t u --E 234 ---S 235 +--S 235 of 276 t18:=u^2*v-t*w-z --R --R @@ -2520,7 +2520,7 @@ t18:=u^2*v-t*w-z --R (18) - z - t w + u v --E 235 ---S 236 +--S 236 of 276 t19:=-y*z*v-y*u*v-t*v^2+y*v*a+t*v*a+u*w*a --R --R @@ -2528,7 +2528,7 @@ t19:=-y*z*v-y*u*v-t*v^2+y*v*a+t*v*a+u*w*a --R (19) - v y z + (- u + a)v y + a u w - t v + a t v --E 236 ---S 237 +--S 237 of 276 t20:=-z*u^2+t*w+v --R --R @@ -2536,7 +2536,7 @@ t20:=-z*u^2+t*w+v --R (20) - u z + t w + v --E 237 ---S 238 +--S 238 of 276 t21:=x*z*u+x*z*v+z^2*w-x*z*a-t*u*a-z*w*a --R --R @@ -2544,14 +2544,14 @@ t21:=x*z*u+x*z*v+z^2*w-x*z*a-t*u*a-z*w*a --R (21) w z + ((v + u - a)x - a w)z - a t u --E 238 ---S 239 +--S 239 of 276 t22:=x*t*v-y*z*w+z*t*w-t*v*w+z*u-u*v-z*a+v*a --R --R --R (22) (- w y + t w + u - a)z + t v x - t v w + (- u + a)v --E 239 ---S 240 +--S 240 of 276 t23:=v^2-a^2 --R --R @@ -2559,21 +2559,21 @@ t23:=v^2-a^2 --R (23) v - a --E 240 ---S 241 +--S 241 of 276 t24:=y*u+u*w-y*a-w*a --R --R --R (24) (u - a)y + (u - a)w --E 241 ---S 242 +--S 242 of 276 t25:=z*w-y*a --R --R --R (25) w z - a y --E 242 ---S 243 +--S 243 of 276 t26:=-y^2+t*w --R --R @@ -2581,14 +2581,14 @@ t26:=-y^2+t*w --R (26) - y + t w --E 243 ---S 244 +--S 244 of 276 t27:=-x*z+v*w-x*a+w*a --R --R --R (27) - x z - a x + (v + a)w --E 244 ---S 245 +--S 245 of 276 t28:=u^2*v-x*y-z --R --R @@ -2596,7 +2596,7 @@ t28:=u^2*v-x*y-z --R (28) - z - x y + u v --E 245 ---S 246 +--S 246 of 276 t29:=z*u*v+u^2*a-u*a^2-x*t-a --R --R @@ -2604,14 +2604,14 @@ t29:=z*u*v+u^2*a-u*a^2-x*t-a --R (29) u v z - t x + a u - a u - a --E 246 ---S 247 +--S 247 of 276 t30:=t*u*v+u*w*a-y-t --R --R --R (30) - y + a u w + t u v - t --E 247 ---S 248 +--S 248 of 276 t31:=-x*z+y*u+t*u-y*a --R --R @@ -2624,7 +2624,7 @@ Variables $x,y,z,t,u$ <<*>>= )clear all ---S 249 +--S 249 of 276 t1:=-x^5-y^5-z^5+5*x*y*z*t*u-u^5 --R --R @@ -2632,7 +2632,7 @@ t1:=-x^5-y^5-z^5+5*x*y*z*t*u-u^5 --R (1) - z + 5t u x y z - y - x - u --E 249 ---S 250 +--S 250 of 276 t2:=x*y^3*z+y*z^3*t+x^3*y*u+z*t^3*u+z*t*u^3 --R --R @@ -2640,7 +2640,7 @@ t2:=x*y^3*z+y*z^3*t+x^3*y*u+z*t^3*u+z*t*u^3 --R (2) t y z + (x y + t u + t u)z + u x y --E 250 ---S 251 +--S 251 of 276 t3:=x^2*y*z^2+y^2*z*t^2+x^2*t^2*u+x*y^2*u^2+z^2*t*u^2 --R --R @@ -2648,7 +2648,7 @@ t3:=x^2*y*z^2+y^2*z*t^2+x^2*t^2*u+x*y^2*u^2+z^2*t*u^2 --R (3) (x y + t u )z + t y z + u x y + t u x --E 251 ---S 252 +--S 252 of 276 t4:=x*y*z^5-y^4*z^2*t-2*x^2*y^2*z*t*u+x*z^3*t^2*u-x^4*t*u^2_ +y*z*t^2*u^3+x*y*u^5 --R @@ -2657,7 +2657,7 @@ t4:=x*y*z^5-y^4*z^2*t-2*x^2*y^2*z*t*u+x*z^3*t^2*u-x^4*t*u^2_ --R (4) x y z + t u x z - t y z + (- 2t u x y + t u y)z + u x y - t u x --E 252 ---S 253 +--S 253 of 276 t5:=x*y^2*z^4-y^5*z*t-x^2*y^3*t*u+2*x*y*z^2*t^2*u+x*t^4*u^2_ -x^2*y*z*u^3-z*t*u^5 --R @@ -2666,7 +2666,7 @@ t5:=x*y^2*z^4-y^5*z*t-x^2*y^3*t*u+2*x*y*z^2*t^2*u+x*t^4*u^2_ --R (5) x y z + 2t u x y z + (- t y - u x y - t u )z - t u x y + t u x --E 253 ---S 254 +--S 254 of 276 t6:=x^3*y^2*t-y*z^2*t^4+x*y^2*z^3*u-y^5*t*u-t^6*u+3*x*y*z*t^2*u^2_ -x^2*y*u^4-t*u^6 --R @@ -2675,7 +2675,7 @@ t6:=x^3*y^2*t-y*z^2*t^4+x*y^2*z^3*u-y^5*t*u-t^6*u+3*x*y*z*t^2*u^2_ --R (6) u x y z - t y z + 3t u x y z - t u y + t x y - u x y - t u - t u --E 254 ---S 255 +--S 255 of 276 t7:=x^4*y^2*z-x*y*z^2*t^3-x*y^5*u-y^3*z^2*t*u-x*t^5*u_ +2*x^2*y*z*t*u^2+z*t^2*u^4 --R @@ -2684,7 +2684,7 @@ t7:=x^4*y^2*z-x*y*z^2*t^3-x*y^5*u-y^3*z^2*t*u-x*t^5*u_ --R (7) (- t u y - t x y)z + (x y + 2t u x y + t u )z - u x y - t u x --E 255 ---S 256 +--S 256 of 276 t8:=y^6*z+y*z^6+x^2*y^4*u-3*x*y^2*z^2*t*u+z^4*t^2*u-x^3*z*t*u^2_ -x*y*t^3*u^3+y*z*u^5 --R @@ -2699,14 +2699,14 @@ Variables $a,b,c,d,e,f,g,h,k,l,m$ <<*>>= )clear all ---S 257 +--S 257 of 276 t1:=a+b+c+d+e+f+g+h-1 --R --R --R (1) h + g + f + e + d + c + b + a - 1 --E 257 ---S 258 +--S 258 of 276 t2:=-a^2*k-2*a*b*k-b^2*k-a*c*k-b*c*k-a*d*k-b*d*k-a*e*k_ -b*e*k-c*e*k-d*e*k-a*f*k-b*f*k-c*f*k-d*f*k+a+b --R @@ -2723,7 +2723,7 @@ t2:=-a^2*k-2*a*b*k-b^2*k-a*c*k-b*c*k-a*d*k-b*d*k-a*e*k_ --R b + a --E 258 ---S 259 +--S 259 of 276 t3:=-a^2*l-a*b*l-a*c*l-a*d*l-a*e*l-b*e*l-c*e*l-d*e*l_ +a^2+2*a*b+b^2+a*e+b*e+a*f+b*f --R @@ -2736,7 +2736,7 @@ t3:=-a^2*l-a*b*l-a*c*l-a*d*l-a*e*l-b*e*l-c*e*l-d*e*l_ --R 2a b + a --E 259 ---S 260 +--S 260 of 276 t4:=a+c+e+g-m --R --R @@ -2749,21 +2749,21 @@ Variables $x,y,z,t,u,v,w,a,b$ <<*>>= )clear all ---S 261 +--S 261 of 276 t1:=-y*z+x*t --R --R --R (1) - y z + t x --E 261 ---S 262 +--S 262 of 276 t2:=-y*u+x*v+y-v --R --R --R (2) (- u + 1)y + v x - v --E 262 ---S 263 +--S 263 of 276 t3:=z^2+t^2-w^2 --R --R @@ -2771,7 +2771,7 @@ t3:=z^2+t^2-w^2 --R (3) z - w + t --E 263 ---S 264 +--S 264 of 276 t4:=u^2+v^2-a^2-2*u+1 --R --R @@ -2779,7 +2779,7 @@ t4:=u^2+v^2-a^2-2*u+1 --R (4) v + u - 2u - a + 1 --E 264 ---S 265 +--S 265 of 276 t5:=z^2+t^2-2*z*u+u^2-2*t*v+v^2-b^2 --R --R @@ -2793,7 +2793,7 @@ Variables $x,y,z,t,u,v,w,a$ <<*>>= )clear all ---S 266 +--S 266 of 276 t1:=x*y+x*z+x*t-u^2 --R --R @@ -2801,7 +2801,7 @@ t1:=x*y+x*z+x*t-u^2 --R (1) x z + x y + t x - u --E 266 ---S 267 +--S 267 of 276 t2:=x*y+y*z+y*t-v^2 --R --R @@ -2809,7 +2809,7 @@ t2:=x*y+y*z+y*t-v^2 --R (2) y z + (x + t)y - v --E 267 ---S 268 +--S 268 of 276 t3:=x*z+y*z+z*t-w^2 --R --R @@ -2817,7 +2817,7 @@ t3:=x*z+y*z+z*t-w^2 --R (3) (y + x + t)z - w --E 268 ---S 269 +--S 269 of 276 t4:=x*t+y*t+z*t-a^2 --R --R @@ -2831,28 +2831,28 @@ Variables $x,y,z,t,u,v,w,a$ <<*>>= )clear all ---S 270 +--S 270 of 276 t1:=t+v-a --R --R --R (1) v + t - a --E 270 ---S 271 +--S 271 of 276 t2:=x+y+z+t-u-w-a --R --R --R (2) z + y + x - w - u + t - a --E 271 ---S 272 +--S 272 of 276 t3:=x*z+y*z+x*t+z*t-u*w-u*a-w*a --R --R --R (3) (y + x + t)z + t x + (- u - a)w - a u --E 272 ---S 273 +--S 273 of 276 t4:=x*z*t-u*w*a --R --R @@ -2864,7 +2864,7 @@ t4:=x*z*t-u*w*a Variables $x,y,z$ <<*>>= ---S 274 +--S 274 of 276 t1:=y^4-20/7*x^2 --R --R @@ -2873,7 +2873,7 @@ t1:=y^4-20/7*x^2 --R 7 --E 274 ---S 275 +--S 275 of 276 t2:=x^2*z^4 + 7/10*x*z^4 + 7/48*z^4 - 50/27*x^2 - 35/27*x - 49/216 --R --R @@ -2882,7 +2882,7 @@ t2:=x^2*z^4 + 7/10*x*z^4 + 7/48*z^4 - 50/27*x^2 - 35/27*x - 49/216 --R 10 48 27 27 216 --E 275 ---S 276 +--S 276 of 276 t3:=3/5*x^6*y^2*z + x^5*y^3 + 3/7*x^5*y^2*z + 7/5*x^4*y^3_ - 7/20*x^4*y*z^2 - 3/20*x^4*z^3 + 609/1000*x^3*y^3_ + 63/200*x^3*y^2*z - 77/125*x^3*y*z^2 - 21/50*x^3*z^3_ diff --git a/src/input/bugs.input.pamphlet b/src/input/bugs.input.pamphlet index be34030..161e380 100644 --- a/src/input/bugs.input.pamphlet +++ b/src/input/bugs.input.pamphlet @@ -501,7 +501,7 @@ f1 n == --R Type: Void --E 39 ---S 40 of 44 +--S 40 of 44 f2 n == m:=n if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2) @@ -509,7 +509,7 @@ f2 n == --R Type: Void --E 40 ---S 41 of 44 +--S 41 of 44 f3 n == n=0 => 1 n=1 => 1 diff --git a/src/input/calcprob.input.pamphlet b/src/input/calcprob.input.pamphlet index f41808d..3835a03 100644 --- a/src/input/calcprob.input.pamphlet +++ b/src/input/calcprob.input.pamphlet @@ -16,14 +16,14 @@ Cover a range of calculus problems )set message auto off )clear all ---S 1 +--S 1 of 12 solve(3*x-(x-7)=4*x-5,x) --R --R (1) [x= 6] --R Type: List Equation Fraction Polynomial Integer --E 1 ---S 2 +--S 2 of 12 solve(4*x-3*y=9,y)::List Equation Polynomial Fraction Integer --R --R 4 @@ -32,7 +32,7 @@ solve(4*x-3*y=9,y)::List Equation Polynomial Fraction Integer --R Type: List Equation Polynomial Fraction Integer --E 2 ---S 3 +--S 3 of 12 solve(A*x+B*y=C,y) --R --R - A x + C @@ -41,7 +41,7 @@ solve(A*x+B*y=C,y) --R Type: List Equation Fraction Polynomial Integer --E 3 ---S 4 +--S 4 of 12 m:=3*x-4*(x-(2/3)*y)=(4/5)*x-(7*y+3) --R --R 8 4 @@ -50,7 +50,7 @@ m:=3*x-4*(x-(2/3)*y)=(4/5)*x-(7*y+3) --R Type: Equation Polynomial Fraction Integer --E 4 ---S 5 +--S 5 of 12 n:=solve(m*15,y) --R --R 27x - 45 @@ -59,28 +59,28 @@ n:=solve(m*15,y) --R Type: List Equation Fraction Polynomial Integer --E 5 ---S 6 +--S 6 of 12 p:=n.1*145-27*x --R --R (6) 145y - 27x= - 45 --R Type: Equation Fraction Polynomial Integer --E 6 ---S 7 +--S 7 of 12 (x1,y1):=(-3,-8) --R --R (7) - 8 --R Type: Integer --E 7 ---S 8 +--S 8 of 12 (x2,y2):=(-6,2) --R --R (8) 2 --R Type: PositiveInteger --E 8 ---S 9 +--S 9 of 12 m:=(y2-y1)/(x2-x1) --R --R 10 @@ -89,21 +89,21 @@ m:=(y2-y1)/(x2-x1) --R Type: Fraction Integer --E 9 ---S 10 +--S 10 of 12 solve(y1=m*x1+b,b) --R --R (10) [b= - 18] --R Type: List Equation Fraction Polynomial Integer --E 10 ---S 11 +--S 11 of 12 b:=-18 --R --R (11) - 18 --R Type: Integer --E 11 ---S 12 +--S 12 of 12 y=m*x+b --R --R 10 diff --git a/src/input/ch.input.pamphlet b/src/input/ch.input.pamphlet index 3578f14..e9a9d41 100644 --- a/src/input/ch.input.pamphlet +++ b/src/input/ch.input.pamphlet @@ -21,7 +21,7 @@ --Cyclohexan ---S 1 of 7 +--S 1 of 7 mfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) :=_ [[0,1,1,1,1,1],[1,0,1,8/3,x,8/3],[1,1,0,1,8/3,y],_ [1,8/3,1,0,1,8/3],[1,x,8/3,1,0,1],[1,8/3,y,8/3,1,0]] diff --git a/src/input/classtalk.input.pamphlet b/src/input/classtalk.input.pamphlet index 2f3eca3..e216a34 100644 --- a/src/input/classtalk.input.pamphlet +++ b/src/input/classtalk.input.pamphlet @@ -20,14 +20,14 @@ These are examples from the talk ``Axiom in an Educational Setting''. @ \section{Numbers} <<*>>= ---S 1 +--S 1 of 72 1 --R --R (1) 1 --R Type: PositiveInteger --E 1 ---S 2 +--S 2 of 72 1/2 --R --R 1 @@ -36,35 +36,35 @@ These are examples from the talk ``Axiom in an Educational Setting''. --R Type: Fraction Integer --E 2 ---S 3 +--S 3 of 72 3+4*%i --R --R (3) 3 + 4%i --R Type: Complex Integer --E 3 ---S 4 +--S 4 of 72 3.4 --R --R (4) 3.4 --R Type: Float --E 4 ---S 5 +--S 5 of 72 X::ROMAN --R --R (5) X --R Type: RomanNumeral --E 5 ---S 6 +--S 6 of 72 binary(5) --R --R (6) 101 --R Type: BinaryExpansion --E 6 ---S 7 +--S 7 of 72 factor(60) --R --R 2 @@ -72,28 +72,28 @@ factor(60) --R Type: Factored Integer --E 7 ---S 8 +--S 8 of 72 q:=(y-1)*x*(z+5) --R --R (8) (x y - x)z + 5x y - 5x --R Type: Polynomial Integer --E 8 ---S 9 +--S 9 of 72 factor q --R --R (9) x(y - 1)(z + 5) --R Type: Factored Polynomial Integer --E 9 ---S 10 +--S 10 of 72 eval(q,[x=5,y=6,z=7]) --R --R (10) 300 --R Type: Polynomial Integer --E 10 ---S 11 +--S 11 of 72 eval(q,[x=5,y=6]) --R --R (11) 25z + 125 @@ -103,7 +103,7 @@ eval(q,[x=5,y=6]) @ \section{Trigonometry} <<*>>= ---S 12 +--S 12 of 72 b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a] --R --R a @@ -111,21 +111,21 @@ b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a] --R Type: List Expression Integer --E 12 ---S 13 +--S 13 of 72 [exp b.1, log b.2, sin b.3, cos b.4, tan b.5, cot b.6, asinh b.7] --R --R (13) [a,a,a,a,a,a,a] --R Type: List Expression Integer --E 13 ---S 14 +--S 14 of 72 a:=.7 --R --R (14) 0.7 --R Type: Float --E 14 ---S 15 +--S 15 of 72 b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a] --R --R (15) @@ -135,14 +135,14 @@ b:=[log a, exp a, asin a, acos a, atan a, acot a, sinh a] --R Type: List Float --E 15 ---S 16 +--S 16 of 72 [exp b.1, log b.2, sin b.3, cos b.4, tan b.5, cot b.6, asinh b.7] --R --R (16) [0.7,0.7,0.7,0.7,0.7,0.7,0.7] --R Type: List Float --E 16 ---S 17 +--S 17 of 72 simplify(sin(x)**2+cos(x)**2) --R --R (17) 1 @@ -153,7 +153,7 @@ simplify(sin(x)**2+cos(x)**2) \section{Polynomial Manipulations} <<*>>= )clear all ---S 18 +--S 18 of 72 eq1:=A*x^2 + B*x*y + C*y^2 + D*x + E*y + F --R --R 2 2 @@ -161,21 +161,21 @@ eq1:=A*x^2 + B*x*y + C*y^2 + D*x + E*y + F --R Type: Polynomial Integer --E 18 ---S 19 +--S 19 of 72 rotatex:=x'*cos(t)-y'*sin(t) --R --R (2) - y' sin(t) + x' cos(t) --R Type: Expression Integer --E 19 ---S 20 +--S 20 of 72 rotatey:=x'*sin(t)+y'*cos(t) --R --R (3) x' sin(t) + y' cos(t) --R Type: Expression Integer --E 20 ---S 21 +--S 21 of 72 eval(eq1,[x=rotatex, y=rotatey]) --R --R (4) @@ -194,14 +194,14 @@ eval(eq1,[x=rotatex, y=rotatey]) \section{Polynomials over Simple Algebraic Extension Fields} <<*>>= )clear all ---S 22 +--S 22 of 72 a:=rootOf(a^2+a+1) --R --R (1) a --R Type: AlgebraicNumber --E 22 ---S 23 +--S 23 of 72 factor(x^2+3) --R --R 2 @@ -209,14 +209,14 @@ factor(x^2+3) --R Type: Factored Polynomial Integer --E 23 ---S 24 +--S 24 of 72 factor(x^2+3,[a]) --R --R (3) (x - 2a - 1)(x + 2a + 1) --R Type: Factored Polynomial AlgebraicNumber --E 24 ---S 25 +--S 25 of 72 definingPolynomial(a) --R --R 2 @@ -224,7 +224,7 @@ definingPolynomial(a) --R Type: AlgebraicNumber --E 25 ---S 26 +--S 26 of 72 zerosOf(b^2+b+1,b) --R --R +---+ +---+ @@ -237,21 +237,21 @@ zerosOf(b^2+b+1,b) @ \section{Derivatives} <<*>>= ---S 27 +--S 27 of 72 differentiate(sin(x),x) --R --R (6) cos(x) --R Type: Expression Integer --E 27 ---S 28 +--S 28 of 72 differentiate(sin(x),x,2) --R --R (7) - sin(x) --R Type: Expression Integer --E 28 ---S 29 +--S 29 of 72 differentiate(cos(z)/(x^2+y^3),[x,y,z],[1,2,3]) --R --R 4 3 @@ -262,14 +262,14 @@ differentiate(cos(z)/(x^2+y^3),[x,y,z],[1,2,3]) --R Type: Expression Integer --E 29 ---S 30 +--S 30 of 72 y:=operator y --R --R (9) y --R Type: BasicOperator --E 30 ---S 31 +--S 31 of 72 deqx:=D(y(x),x,2)+D(y(x),x)+y(x) --R --R @@ -279,7 +279,7 @@ deqx:=D(y(x),x,2)+D(y(x),x)+y(x) --R Type: Expression Integer --E 31 ---S 32 +--S 32 of 72 solve(deqx,y,x) --R --R x x @@ -294,7 +294,7 @@ solve(deqx,y,x) \section{Limits} <<*>>= )clear all ---S 33 +--S 33 of 72 limit((x^2-3*x+2)/(x^2-1),x=1) --R --R 1 @@ -303,14 +303,14 @@ limit((x^2-3*x+2)/(x^2-1),x=1) --R Type: Union(OrderedCompletion Fraction Polynomial Integer,...) --E 33 ---S 34 +--S 34 of 72 limit(x*log(x),x=0) --R --R (2) [leftHandLimit= "failed",rightHandLimit= 0] --RType: Union(Record(leftHandLimit: Union(OrderedCompletion Expression Integer,"failed"),rightHandLimit: Union(OrderedCompletion Expression Integer,"failed")),...) --E 34 ---S 35 +--S 35 of 72 limit(sinh(a*x)/tan(b*x),x=0) --R --R a @@ -319,7 +319,7 @@ limit(sinh(a*x)/tan(b*x),x=0) --R Type: Union(OrderedCompletion Expression Integer,...) --E 35 ---S 36 +--S 36 of 72 limit(sqrt(3*x^2+1)/(5*x),x=%plusInfinity) --R --R +-+ @@ -329,7 +329,7 @@ limit(sqrt(3*x^2+1)/(5*x),x=%plusInfinity) --R Type: Union(OrderedCompletion Expression Integer,...) --E 36 ---S 37 +--S 37 of 72 complexLimit((2+z)/(1-z),z=%infinity) --R --R (5) - 1 @@ -340,7 +340,7 @@ complexLimit((2+z)/(1-z),z=%infinity) \section{Indefinite Integration} <<*>>= )clear all ---S 38 +--S 38 of 72 integrate(1+sqrt(x)/x,x) --R --R +-+ @@ -348,7 +348,7 @@ integrate(1+sqrt(x)/x,x) --R Type: Union(Expression Integer,...) --E 38 ---S 39 +--S 39 of 72 integrate(sin(x)/x,x) --R --R (2) Si(x) @@ -359,7 +359,7 @@ integrate(sin(x)/x,x) This used to give the answer: $$\frac{\sqrt{x}\sqrt{\pi} erf(x\sqrt{a})}{2a}$$ <<*>>= ---S 40 +--S 40 of 72 integrate(exp(-a*x^2),x) --R --R x 2 @@ -369,7 +369,7 @@ integrate(exp(-a*x^2),x) --R Type: Union(Expression Integer,...) --E 40 ---S 41 +--S 41 of 72 integrate(sin(x)/x^2,x) --R --R x @@ -384,7 +384,7 @@ integrate(sin(x)/x^2,x) \section{Definite Integration} <<*>>= )clear all ---S 42 +--S 42 of 72 integrate(exp(-x)/sqrt(x),x=0..%plusInfinity) --R --R _ 1 @@ -393,7 +393,7 @@ integrate(exp(-x)/sqrt(x),x=0..%plusInfinity) --R Type: Union(f1: OrderedCompletion Expression Integer,...) --E 42 ---S 43 +--S 43 of 72 integrate(1/x^2,x=-1..1) --R --R @@ -411,7 +411,7 @@ integrate(1/x^2,x=-1..1) This used to return $$\frac{4\log{(4)}-8\log{(2)}+3\pi}{12}$$ <<*>>= ---S 44 +--S 44 of 72 integrate(sin(x)^3/(sin(x)^3+cos(x)^3),x=0..%pi/2,"noPole") --R --R 2log(16) - 4log(4) + 3%pi @@ -420,7 +420,7 @@ integrate(sin(x)^3/(sin(x)^3+cos(x)^3),x=0..%pi/2,"noPole") --R Type: Union(f1: OrderedCompletion Expression Integer,...) --E 44 ---S 45 +--S 45 of 72 integrate(exp(-x^2)*log(x)^2,x=0..%plusInfinity) --R --R _ 1 1 _ 1 1 2 @@ -436,7 +436,7 @@ integrate(exp(-x^2)*log(x)^2,x=0..%plusInfinity) <<*>>= )clear all ---S 46 +--S 46 of 72 laplace(sin(a*t)*cosh(a*t)-cos(a*t)*sinh(a*t),t,s) --R --R 3 @@ -447,7 +447,7 @@ laplace(sin(a*t)*cosh(a*t)-cos(a*t)*sinh(a*t),t,s) --R Type: Expression Integer --E 46 ---S 47 +--S 47 of 72 laplace(2/t * (1-cos(a*t)),t,s) --R --R 2 2 @@ -455,14 +455,14 @@ laplace(2/t * (1-cos(a*t)),t,s) --R Type: Expression Integer --E 47 ---S 48 +--S 48 of 72 laplace((exp(a*t)-exp(b*t))/t,t,s) --R --R (3) - log(s - a) + log(s - b) --R Type: Expression Integer --E 48 ---S 49 +--S 49 of 72 laplace(exp(a*t+b)*Ei(c*t),t,s) --R --R b s + c - a @@ -479,14 +479,14 @@ laplace(exp(a*t+b)*Ei(c*t),t,s) over $K$, given a quadratic form $Q$ on $K^n$ (e.q. quaternions). <<*>>= )clear all ---S 50 +--S 50 of 72 K:=Fraction Polynomial Integer --R --R (1) Fraction Polynomial Integer --R Type: Domain --E 50 ---S 51 +--S 51 of 72 qf:QFORM(2,K):=quadraticForm matrix([[-1,0],[0,-1]])$(SQMATRIX(2,K)) --R --R +- 1 0 + @@ -495,7 +495,7 @@ qf:QFORM(2,K):=quadraticForm matrix([[-1,0],[0,-1]])$(SQMATRIX(2,K)) --R Type: QuadraticForm(2,Fraction Polynomial Integer) --E 51 ---S 52 +--S 52 of 72 i:=e(1)$CLIF(2,K,qf) --R --R (3) e @@ -503,7 +503,7 @@ i:=e(1)$CLIF(2,K,qf) --R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) --E 52 ---S 53 +--S 53 of 72 j:=e(2)$CLIF(2,K,qf) --R --R (4) e @@ -511,7 +511,7 @@ j:=e(2)$CLIF(2,K,qf) --R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) --E 53 ---S 54 +--S 54 of 72 k:=i*j --R --R (5) e e @@ -519,7 +519,7 @@ k:=i*j --R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) --E 54 ---S 55 +--S 55 of 72 x:=a+b*i+c*j+d*k --R --R (6) a + b e + c e + d e e @@ -527,7 +527,7 @@ x:=a+b*i+c*j+d*k --R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) --E 55 ---S 56 +--S 56 of 72 y:=m+f*i+g*j+h*k --R --R (7) m + f e + g e + h e e @@ -535,7 +535,7 @@ y:=m+f*i+g*j+h*k --R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) --E 56 ---S 57 +--S 57 of 72 x+y --R --R (8) m + a + (f + b)e + (g + c)e + (h + d)e e @@ -543,7 +543,7 @@ x+y --R Type: CliffordAlgebra(2,Fraction Polynomial Integer,MATRIX) --E 57 ---S 58 +--S 58 of 72 x*y --R --R (9) @@ -559,7 +559,7 @@ x*y \section{Taylor Series} <<*>>= )clear all ---S 59 +--S 59 of 72 taylor(sin(x),x=0) --R --R 1 3 1 5 1 7 1 9 11 @@ -571,7 +571,7 @@ taylor(sin(x),x=0) @ \section{Laurent Series} <<*>>= ---S 60 +--S 60 of 72 laurent(x/log(x),x=1) --R --R (2) @@ -592,7 +592,7 @@ laurent(x/log(x),x=1) @ \section{Puiseux Series} <<*>>= ---S 61 +--S 61 of 72 puiseux(sqrt(sec(x)),x=3*%pi/2) --R --R @@ -607,7 +607,7 @@ puiseux(sqrt(sec(x)),x=3*%pi/2) @ \section{General Series} <<*>>= ---S 62 +--S 62 of 72 series(x^x,x=0) --R --R (4) @@ -627,7 +627,7 @@ series(x^x,x=0) \section{Matrices} <<*>>= )clear all ---S 63 +--S 63 of 72 m:=matrix [[1,2],[3,4]] --R --R +1 2+ @@ -636,7 +636,7 @@ m:=matrix [[1,2],[3,4]] --R Type: Matrix Integer --E 63 ---S 64 +--S 64 of 72 4*m*(-5) --R --R +- 20 - 40+ @@ -645,7 +645,7 @@ m:=matrix [[1,2],[3,4]] --R Type: Matrix Integer --E 64 ---S 65 +--S 65 of 72 n:=matrix [[1,0,-2],[-3,5,1]] --R --R + 1 0 - 2+ @@ -654,7 +654,7 @@ n:=matrix [[1,0,-2],[-3,5,1]] --R Type: Matrix Integer --E 65 ---S 66 +--S 66 of 72 m*n --R --R +- 5 10 0 + @@ -663,7 +663,7 @@ m*n --R Type: Matrix Integer --E 66 ---S 67 +--S 67 of 72 hilb:=matrix([[1/(i+j) for i in 1..3] for j in 1..3]) --R --R +1 1 1+ @@ -680,7 +680,7 @@ hilb:=matrix([[1/(i+j) for i in 1..3] for j in 1..3]) --R Type: Matrix Fraction Integer --E 67 ---S 68 +--S 68 of 72 inverse(hilb) --R --R + 72 - 240 180 + @@ -695,28 +695,28 @@ inverse(hilb) \section{Systems of Equations} <<*>>= )clear all ---S 69 +--S 69 of 72 solve([x+y+z=8,3*x-2*y+z=0,x+2*y+2*z=17],[x,y,z]) --R --R (1) [[x= - 1,y= 2,z= 7]] --R Type: List List Equation Fraction Polynomial Integer --E 69 ---S 70 +--S 70 of 72 solve([x+2*y+3*z=2,2*x+3*y+4*z=2,3*x+4*y+5*z=2],[x,y,z]) --R --I (2) [[x= %W - 2,y= - 2%W + 2,z= %W]] --R Type: List List Equation Fraction Polynomial Integer --E 70 ---S 71 +--S 71 of 72 solve([[1,1,1],[3,-2,1],[1,2,2]],[8,0,17]) --R --R (3) [particular= [- 1,2,7],basis= [[0,0,0]]] --RType: Record(particular: Union(Vector Fraction Integer,"failed"),basis: List Vector Fraction Integer) --E 71 ---S 72 +--S 72 of 72 solve([[1,2,3],[2,3,4],[3,4,5]],[2,2,2]) --R --R (4) [particular= [- 2,2,0],basis= [[1,- 2,1]]] diff --git a/src/input/clifford.input.pamphlet b/src/input/clifford.input.pamphlet index 6052d52..226214f 100644 --- a/src/input/clifford.input.pamphlet +++ b/src/input/clifford.input.pamphlet @@ -132,7 +132,7 @@ x*% --% The quaternions as a Clifford Algebra )clear p qf ---S 11 of 39 +--S 11 of 39 qf:QFORM(2, K) :=quadraticForm matrix([[-1, 0], [0, -1]])$(SQMATRIX(2,K)) --R --R diff --git a/src/input/contfrac.input.pamphlet b/src/input/contfrac.input.pamphlet index 502d9bd..05c4442 100644 --- a/src/input/contfrac.input.pamphlet +++ b/src/input/contfrac.input.pamphlet @@ -39,7 +39,7 @@ r2 := 314159/100000 --R Type: Fraction Integer --E 2 ---S 3 of 40 +--S 3 of 40 c1 := r1 :: ContinuedFraction Integer --R --R @@ -60,7 +60,7 @@ c2 := r2 :: ContinuedFraction Integer --E 4 -- We can view these in the list notation ---S 5 of 40 +--S 5 of 40 partialQuotients c1 --R --R diff --git a/src/input/danzwill2.input.pamphlet b/src/input/danzwill2.input.pamphlet index d17eddb..97935b7 100644 --- a/src/input/danzwill2.input.pamphlet +++ b/src/input/danzwill2.input.pamphlet @@ -17,7 +17,7 @@ Problems from the MIT Integration Bee )clear all )set break resume ---S 1 of 17 +--S 1 of 50 i1:= integrate(e^(1991*x),x) --R --R @@ -28,7 +28,7 @@ i1:= integrate(e^(1991*x),x) --R Type: Union(Expression Integer,...) --E 1 ---S 2 of 17 +--S 2 of 50 i2:= integrate((sin(x)-cos(x))^2,x) --R --R @@ -37,7 +37,7 @@ i2:= integrate((sin(x)-cos(x))^2,x) --R Type: Union(Expression Integer,...) --E 2 ---S 3 of 17 +--S 3 of 50 i3:= integrate(log(x),x) --R --R @@ -45,7 +45,7 @@ i3:= integrate(log(x),x) --R Type: Union(Expression Integer,...) --E 3 ---S 4 of 17 +--S 4 of 50 i4:= integrate(1/(%pi*x),x) --R --R @@ -55,7 +55,7 @@ i4:= integrate(1/(%pi*x),x) --R Type: Union(Expression Integer,...) --E 4 ---S 5 of 17 +--S 5 of 50 i5:= integrate(%e^(sin(x)^2)*%e^(cos(x)^2),x) --R --R @@ -63,7 +63,7 @@ i5:= integrate(%e^(sin(x)^2)*%e^(cos(x)^2),x) --R Type: Union(Expression Integer,...) --E 5 ---S 6 of 17 +--S 6 of 50 i6:= integrate(1/(x*log(x)),x) --R --R @@ -71,7 +71,7 @@ i6:= integrate(1/(x*log(x)),x) --R Type: Union(Expression Integer,...) --E 6 ---S 7 of 17 +--S 7 of 50 i7:= integrate(x/(x^4+1),x) --R --R @@ -82,7 +82,7 @@ i7:= integrate(x/(x^4+1),x) --R Type: Union(Expression Integer,...) --E 7 ---S 8 of 17 +--S 8 of 50 i8:= integrate((x+1)/(x^2+2*x+2)^(1/3),x) --R --R @@ -94,7 +94,7 @@ i8:= integrate((x+1)/(x^2+2*x+2)^(1/3),x) --R Type: Union(Expression Integer,...) --E 8 ---S 9 of 17 +--S 9 of 50 i9:= integrate(x*%e^x*sin(x),x) --R --R @@ -105,7 +105,7 @@ i9:= integrate(x*%e^x*sin(x),x) --R Type: Union(Expression Integer,...) --E 9 ---S 10 of 17 +--S 10 of 50 i10:= integrate(%e^(%e^x+x),x) --R --R @@ -118,7 +118,7 @@ i10:= integrate(%e^(%e^x+x),x) --R Type: Union(Expression Integer,...) --E 10 ---S 11 of 17 +--S 11 of 50 i11:= integrate(1/(sec(x)+tan(x)*sin(x)),x) --R --R @@ -129,7 +129,7 @@ i11:= integrate(1/(sec(x)+tan(x)*sin(x)),x) --R Type: Union(Expression Integer,...) --E 11 ---S 12 of 17 +--S 12 of 50 i12:= integrate((%e^(5*x)+%e^(7*x))/(%e^x+%e^(-x)),x) --R --R @@ -140,7 +140,7 @@ i12:= integrate((%e^(5*x)+%e^(7*x))/(%e^x+%e^(-x)),x) --R Type: Union(Expression Integer,...) --E 12 ---S 13 of 17 +--S 13 of 50 i13:= integrate(sqrt(-1+2/(1+3*x)),x) --R --R @@ -153,7 +153,7 @@ i13:= integrate(sqrt(-1+2/(1+3*x)),x) --R Type: Union(Expression Integer,...) --E 13 ---S 14 of 17 +--S 14 of 50 i14:= integrate(sinh(x)-cosh(x),x) --R --R @@ -163,7 +163,7 @@ i14:= integrate(sinh(x)-cosh(x),x) --R Type: Union(Expression Integer,...) --E 14 ---S 15 of 17 +--S 15 of 50 i15:= integrate((sin(x)*%e^sec(x))/cos(x)^2,x) --R --R @@ -174,7 +174,7 @@ i15:= integrate((sin(x)*%e^sec(x))/cos(x)^2,x) --R Type: Union(Expression Integer,...) --E 15 ---S 16 of 17 +--S 16 of 50 i16:= integrate((x^2+1)/(x^4-x^2+1),x) --R --R @@ -183,7 +183,7 @@ i16:= integrate((x^2+1)/(x^4-x^2+1),x) --R Type: Union(Expression Integer,...) --E 16 ---S 17 of 17 +--S 17 of 50 i17:= integrate(1/(%pi*x^2+atan(x)+x^2*atan(x)+%pi),x) --R --R @@ -196,7 +196,7 @@ i17:= integrate(1/(%pi*x^2+atan(x)+x^2*atan(x)+%pi),x) --R Type: Union(Expression Integer,...) --E 17 ---S 18 of 18 +--S 18 of 50 i18:= integrate(sec(x)^3,x) --R --R @@ -210,7 +210,7 @@ i18:= integrate(sec(x)^3,x) --R Type: Union(Expression Integer,...) --E 18 ---S 19 of 19 +--S 19 of 50 i19:= integrate(1/(x^2-10*x+26),x) --R --R @@ -218,7 +218,7 @@ i19:= integrate(1/(x^2-10*x+26),x) --R Type: Union(Expression Integer,...) --E 19 ---S 20 of 20 +--S 20 of 50 i20:= integrate(1/(x^2-11*x-26),x) --R --R @@ -228,7 +228,7 @@ i20:= integrate(1/(x^2-11*x-26),x) --R Type: Union(Expression Integer,...) --E 20 ---S 21 of 21 +--S 21 of 50 i21:= integrate(1/(12+13*cos(x)),x) --R --R @@ -240,7 +240,7 @@ i21:= integrate(1/(12+13*cos(x)),x) --R Type: Union(Expression Integer,...) --E 21 ---S 22 of 22 +--S 22 of 50 i22:= integrate((x^3+1)/(x+1),x) --R --R @@ -251,7 +251,7 @@ i22:= integrate((x^3+1)/(x+1),x) --R Type: Union(Expression Integer,...) --E 22 ---S 23 of 23 +--S 23 of 50 i23:= integrate((1-4*x^4)^(-1/2)/(4*x)^(-1),x) --R --R @@ -264,7 +264,7 @@ i23:= integrate((1-4*x^4)^(-1/2)/(4*x)^(-1),x) --R Type: Union(Expression Integer,...) --E 23 ---S 24 of 24 +--S 24 of 50 i24:= integrate(%e^(1991),x) --R --R @@ -273,7 +273,7 @@ i24:= integrate(%e^(1991),x) --R Type: Union(Expression Integer,...) --E 24 ---S 25 of 25 +--S 25 of 50 i25:= integrate((log(x)+1)*x^x,x) --R --R @@ -282,7 +282,7 @@ i25:= integrate((log(x)+1)*x^x,x) --R Type: Union(Expression Integer,...) --E 25 ---S 26 of 26 +--S 26 of 50 i26:= integrate(cos(2*x)*sin(6*x),x) --R --R @@ -293,7 +293,7 @@ i26:= integrate(cos(2*x)*sin(6*x),x) --R Type: Union(Expression Integer,...) --E 26 ---S 27 of 27 +--S 27 of 50 i27:= integrate(1/(sqrt(x)*(1+sqrt(x))),x) --R --R @@ -302,7 +302,7 @@ i27:= integrate(1/(sqrt(x)*(1+sqrt(x))),x) --R Type: Union(Expression Integer,...) --E 27 ---S 28 of 28 +--S 28 of 50 i28:= integrate(e^(1/x)*x^(-3),x) --R --R @@ -316,7 +316,7 @@ i28:= integrate(e^(1/x)*x^(-3),x) --R Type: Union(Expression Integer,...) --E 28 ---S 29 of 29 +--S 29 of 50 i29:= integrate(sqrt(csc(x)-sin(x)),x) --R --R @@ -328,7 +328,7 @@ i29:= integrate(sqrt(csc(x)-sin(x)),x) --R Type: Union(Expression Integer,...) --E 29 ---S 30 of 30 +--S 30 of 50 i30:= integrate((x^2+1)/(x^3-x),x) --R --R @@ -337,7 +337,7 @@ i30:= integrate((x^2+1)/(x^3-x),x) --R Type: Union(Expression Integer,...) --E 30 ---S 31 of 31 +--S 31 of 50 i31:= integrate(42^x,x) --R --R @@ -348,7 +348,7 @@ i31:= integrate(42^x,x) --R Type: Union(Expression Integer,...) --E 31 ---S 32 of 32 +--S 32 of 50 i32:= integrate(x^5*%e^x,x) --R --R @@ -357,7 +357,7 @@ i32:= integrate(x^5*%e^x,x) --R Type: Union(Expression Integer,...) --E 32 ---S 33 of 33 +--S 33 of 50 i33:= integrate(x*%e^(x^2),x) --R --R @@ -369,7 +369,7 @@ i33:= integrate(x*%e^(x^2),x) --R Type: Union(Expression Integer,...) --E 33 ---S 34 of 34 +--S 34 of 50 i34:= integrate(1/(x^2+1)^2,x) --R --R @@ -381,7 +381,7 @@ i34:= integrate(1/(x^2+1)^2,x) --R Type: Union(Expression Integer,...) --E 34 ---S 35 of 35 +--S 35 of 50 i35:= integrate(1/(%e^x+%e^(-x)),x) --R --R @@ -390,7 +390,7 @@ i35:= integrate(1/(%e^x+%e^(-x)),x) --R Type: Union(Expression Integer,...) --E 35 ---S 36 of 36 +--S 36 of 50 i36:= integrate(tan(x)*log(abs(sec(x))),x) --R --R @@ -404,7 +404,7 @@ i36:= integrate(tan(x)*log(abs(sec(x))),x) --R Type: Union(Expression Integer,...) --E 36 ---S 37 of 37 +--S 37 of 50 i37:= integrate(cos(sin(x))*cos(x),x) --R --R @@ -412,7 +412,7 @@ i37:= integrate(cos(sin(x))*cos(x),x) --R Type: Union(Expression Integer,...) --E 37 ---S 38 of 38 +--S 38 of 50 i38:= integrate(1/(x^2-9),x) --R --R @@ -422,7 +422,7 @@ i38:= integrate(1/(x^2-9),x) --R Type: Union(Expression Integer,...) --E 38 ---S 39 of 39 +--S 39 of 50 i39:= integrate(%pi/sqrt(16-%e^2),x) --R --R @@ -434,7 +434,7 @@ i39:= integrate(%pi/sqrt(16-%e^2),x) --R Type: Union(Expression Integer,...) --E 39 ---S 40 of 40 +--S 40 of 50 i40:= integrate(sqrt(tan(x)),x) --R --R @@ -485,7 +485,7 @@ i40:= integrate(sqrt(tan(x)),x) --R Type: Union(Expression Integer,...) --E 40 ---S 41 of 41 +--S 41 of 50 i41:= integrate(sin(x)^(-1),x) --R --R @@ -495,7 +495,7 @@ i41:= integrate(sin(x)^(-1),x) --R Type: Union(Expression Integer,...) --E 41 ---S 42 of 42 +--S 42 of 50 i42:= integrate((x^2-2*x+2)/(x^2+1),x) --R --R @@ -504,7 +504,7 @@ i42:= integrate((x^2-2*x+2)/(x^2+1),x) --R Type: Union(Expression Integer,...) --E 42 ---S 43 of 43 +--S 43 of 50 i43:= integrate((sin(x)^2*cos(x)^2)/(1+cos(2*x)),x) --R --R @@ -514,7 +514,7 @@ i43:= integrate((sin(x)^2*cos(x)^2)/(1+cos(2*x)),x) --R Type: Union(Expression Integer,...) --E 43 ---S 44 of 44 +--S 44 of 50 i44:= integrate(sqrt(x+x^2*sqrt(x)),x) --R --R @@ -526,7 +526,7 @@ i44:= integrate(sqrt(x+x^2*sqrt(x)),x) --R Type: Union(Expression Integer,...) --E 44 ---S 45 of 45 +--S 45 of 50 i45:= integrate(cos(4*x)*cos(2*x),x) --R --R @@ -537,7 +537,7 @@ i45:= integrate(cos(4*x)*cos(2*x),x) --R Type: Union(Expression Integer,...) --E 45 ---S 46 of 46 +--S 46 of 50 i46:= integrate(sqrt(x^3-1)/x,x) --R --R @@ -549,7 +549,7 @@ i46:= integrate(sqrt(x^3-1)/x,x) --R Type: Union(Expression Integer,...) --E 46 ---S 47 of 47 +--S 47 of 50 i47:= integrate((%e^x*(x-2))/x^3,x) --R --R @@ -561,7 +561,7 @@ i47:= integrate((%e^x*(x-2))/x^3,x) --R Type: Union(Expression Integer,...) --E 47 ---S 48 of 48 +--S 48 of 50 i48:= integrate(cot(x)/log(sin(x)),x) --R --R @@ -569,7 +569,7 @@ i48:= integrate(cot(x)/log(sin(x)),x) --R Type: Union(Expression Integer,...) --E 48 ---S 49 of 49 +--S 49 of 50 i49:= integrate(x*sec(x)^2,x) --R --R @@ -581,7 +581,7 @@ i49:= integrate(x*sec(x)^2,x) --R Type: Union(Expression Integer,...) --E 49 ---S 50 of 50 +--S 50 of 50 i50:= integrate(x*sec(x)*(x*tan(x)+2),x) --R --R diff --git a/src/input/directproduct.input.pamphlet b/src/input/directproduct.input.pamphlet index cc99107..5fedb6c 100644 --- a/src/input/directproduct.input.pamphlet +++ b/src/input/directproduct.input.pamphlet @@ -23,7 +23,7 @@ product is a ring. (Bug report 117). This is fixed by patch )set message test on )clear all ---S 1 +--S 1 of 12 NNI has Monoid --R --R @@ -31,7 +31,7 @@ NNI has Monoid --R Type: Boolean --E 1 ---S 2 +--S 2 of 12 NNI2:=DirectProduct(2,NNI) --R --R @@ -39,7 +39,7 @@ NNI2:=DirectProduct(2,NNI) --R Type: Domain --E 2 ---S 3 +--S 3 of 12 NNI2 has Monoid --R --R @@ -47,7 +47,7 @@ NNI2 has Monoid --R Type: Boolean --E 3 ---S 4 +--S 4 of 12 a:NNI2:=directProduct([3,5]) --R --R @@ -55,7 +55,7 @@ a:NNI2:=directProduct([3,5]) --R Type: DirectProduct(2,NonNegativeInteger) --E 4 ---S 5 +--S 5 of 12 3*a --R --R @@ -63,7 +63,7 @@ a:NNI2:=directProduct([3,5]) --R Type: DirectProduct(2,NonNegativeInteger) --E 5 ---S 6 +--S 6 of 12 b:NNI2:=1 --R --R @@ -71,7 +71,7 @@ b:NNI2:=1 --R Type: DirectProduct(2,NonNegativeInteger) --E 6 ---S 7 +--S 7 of 12 1*a --R --R @@ -79,7 +79,7 @@ b:NNI2:=1 --R Type: DirectProduct(2,NonNegativeInteger) --E 7 ---S 8 +--S 8 of 12 b*a --R --R @@ -87,7 +87,7 @@ b*a --R Type: DirectProduct(2,NonNegativeInteger) --E 8 ---S 9 +--S 9 of 12 c:NNI2:=directProduct([1,1]) --R --R @@ -95,7 +95,7 @@ c:NNI2:=directProduct([1,1]) --R Type: DirectProduct(2,NonNegativeInteger) --E 9 ---S 10 +--S 10 of 12 c*a --R --R @@ -103,7 +103,7 @@ c*a --R Type: DirectProduct(2,NonNegativeInteger) --E 10 ---S 11 +--S 11 of 12 d:NNI2:=directProduct([1,2]) --R --R @@ -111,7 +111,7 @@ d:NNI2:=directProduct([1,2]) --R Type: DirectProduct(2,NonNegativeInteger) --E 11 ---S 12 +--S 12 of 12 d*a --R --R diff --git a/src/input/efi.input.pamphlet b/src/input/efi.input.pamphlet index 25952b4..0e61d9c 100644 --- a/src/input/efi.input.pamphlet +++ b/src/input/efi.input.pamphlet @@ -147,7 +147,7 @@ ss:=[1,1] --E 14 -- fJ doesn't know about the special definition at the origin ---S 15 of 15 of 15 +--S 15 of 15 fJ(ss) --R --R diff --git a/src/input/eigen.input.pamphlet b/src/input/eigen.input.pamphlet index ee529f6..447c15f 100644 --- a/src/input/eigen.input.pamphlet +++ b/src/input/eigen.input.pamphlet @@ -222,7 +222,7 @@ eigenvectors m --RType: List Record(eigval: Union(Fraction Polynomial Integer,SuchThat(Symbol,Polynomial Integer)),eigmult: NonNegativeInteger,eigvec: List Matrix Fraction Polynomial Integer) --E 14 ---S 15 of 36 +--S 15 of 36 q:=matrix [[x**2-y**2,(x-y)*(2*x+3*y)],[x+y,2*x+3*y]] --R --R diff --git a/src/input/elfuts.input.pamphlet b/src/input/elfuts.input.pamphlet index 05879e4..6ac403f 100644 --- a/src/input/elfuts.input.pamphlet +++ b/src/input/elfuts.input.pamphlet @@ -282,7 +282,7 @@ dnn**2+ksquared*snn**2 --RType: UnivariateTaylorSeries(Fraction UnivariatePolynomial(k,Fraction Integer),y,0) --E 19 ---S 20 of 40 +--S 20 of 40 kkk:=integrate(1/((1-yy**2)*(1-ksquared*yy**2))**(1/2)) --R --R diff --git a/src/input/equation2.input.pamphlet b/src/input/equation2.input.pamphlet index d099d61..6962f79 100644 --- a/src/input/equation2.input.pamphlet +++ b/src/input/equation2.input.pamphlet @@ -379,7 +379,7 @@ solve(1/x**3 + 1/x**2 + 1/x = 0,x,"sym") )clear all ---S 24 of 27 +--S 24 of 27 solve([[1,1,1],[3,-2,1],[1,2,2]],[8,0,17]) --R --R diff --git a/src/input/exprode.input.pamphlet b/src/input/exprode.input.pamphlet index 426a379..dd07129 100644 --- a/src/input/exprode.input.pamphlet +++ b/src/input/exprode.input.pamphlet @@ -25,7 +25,7 @@ We will solve $y^{'''} = \sin(y^{''}) * \exp(y) + \cos(x)$ subject to $y(0) = 1$, $y^{'}(0) = 0$, $y^{''}(0) = 0$ <<*>>= ---S 1 of 13 +--S 1 of 13 y := operator 'y --R --R @@ -33,7 +33,7 @@ y := operator 'y --R Type: BasicOperator --E 1 ---S 2 of 13 +--S 2 of 13 eq := differentiate(y x, x, 3) - sin differentiate(y x, x, 2) * exp y x = cos x --R @@ -44,7 +44,7 @@ eq := differentiate(y x, x, 3) - sin differentiate(y x, x, 2) * exp y x --R Type: Equation Expression Integer --E 2 ---S 3 of 13 +--S 3 of 13 seriesSolve(eq, y, x = 0, [1, 0, 0]) --R --R Compiling function %B with type List UnivariateTaylorSeries( @@ -75,7 +75,7 @@ airy := differentiate(y x, x, 2) - x * y x --R Type: Expression Integer --E 4 ---S 5 of 13 +--S 5 of 13 seriesSolve(airy, y, x = 0, [a0, a1]) --R --R Compiling function %D with type List UnivariateTaylorSeries( diff --git a/src/input/ffx72.input.pamphlet b/src/input/ffx72.input.pamphlet index 8bc70be..0e40969 100644 --- a/src/input/ffx72.input.pamphlet +++ b/src/input/ffx72.input.pamphlet @@ -26,7 +26,7 @@ This file demonstrates some calculations with the finite field of field with 7 elements. <<*>>= ---S 1 of 13 +--S 1 of 13 gf72 := FF(7, 2) --R --R diff --git a/src/input/fr.input.pamphlet b/src/input/fr.input.pamphlet index 2e739cc..b96261c 100644 --- a/src/input/fr.input.pamphlet +++ b/src/input/fr.input.pamphlet @@ -259,7 +259,7 @@ Manipulation of factored polynomials <<*>>= )clear all ---S 23 of 55 +--S 23 of 55 (u,v,w): FR POLY INT --R --R Type: Void diff --git a/src/input/gonshor.input.pamphlet b/src/input/gonshor.input.pamphlet index f67e552..748192c 100644 --- a/src/input/gonshor.input.pamphlet +++ b/src/input/gonshor.input.pamphlet @@ -311,7 +311,7 @@ r,s : R <<*>>= )clear prop AP ---S 28 of 98 +--S 28 of 98 AP := ALGPKG(R,A) --R --R diff --git a/src/input/heap.input.pamphlet b/src/input/heap.input.pamphlet index 65ac4dd..2ab444e 100644 --- a/src/input/heap.input.pamphlet +++ b/src/input/heap.input.pamphlet @@ -19,7 +19,7 @@ )set message auto off )clear all ---S 1 of 8 +--S 1 of 8 h := heap [-4,9,11,2,7,-7] --R --R diff --git a/src/input/herm.input.pamphlet b/src/input/herm.input.pamphlet index 02952e7..da4e7c8 100644 --- a/src/input/herm.input.pamphlet +++ b/src/input/herm.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 29 +--S 1 of 29 )lib $TEST_AXIOMXL/herm --R --R )library cannot find the file herm. diff --git a/src/input/intbypart.input.pamphlet b/src/input/intbypart.input.pamphlet index 0b26c61..e1972b8 100644 --- a/src/input/intbypart.input.pamphlet +++ b/src/input/intbypart.input.pamphlet @@ -56,7 +56,7 @@ $$=\frac{1}{2}x^2 ln(x) - {\frac{1}{2}}\int{x dx}$$ $$=\frac{1}{2} ln(x) - {\frac{1}{4}}x^2 + C$$ $$=\frac{1}{4}x^2(2 ln(x) - 1)+C$$ <<*>>= ---S 1 +--S 1 of 16 integrate(x*log(x),x) --R --R 2 2 @@ -83,7 +83,7 @@ $$= xe^x - \int{e^x dx}$$ $$= xe^x - e^x + C$$ $$= (x-1)e^x + C$$ <<*>>= ---S 2 +--S 2 of 16 integrate(x*exp(x),x) --R --R x @@ -134,7 +134,7 @@ $$=\frac{1}{2}(e^x sin(x) + e^x cos(x))$$ so $$\int{e^x cos(x) dx} = \frac{1}{2}(e^x sin(x) + e^x cos(x)) + C$$ <<*>>= ---S 3 +--S 3 of 16 integrate(exp(x)*sin(x),x) --R --R x x @@ -156,7 +156,7 @@ $$=\frac{1}{2}x^2 e^{x^2} - \int{x e^{x^2}} dx$$ $$=\frac{1}{2}x^2 e^{x^2} - {\frac{1}{2}} e^{x^2} + C$$ $$=\frac{1}{2}(x^2 -1)e^{x^2} + C$$ <<*>>= ---S 4 +--S 4 of 16 integrate(x^3*exp(x^2),x) --R --R 2 @@ -184,7 +184,7 @@ $$=x ln(x^2+2)-2x+ \frac{4}{\sqrt{2}}\tan^{-1}\left(\frac{x}{\sqrt{2}}\right) + C$$ $$x(ln(x^2+2)-2)+2\sqrt{2} \tan^{-1}\left(\frac{x}{\sqrt{2}}\right) + C$$ <<*>>= ---S 5 +--S 5 of 16 integrate(log(x^2+2),x) --R --R +-+ @@ -208,7 +208,7 @@ $$\int{x\ sin(x)\ dx}$$ $$= -x\ cos(x) - \int{-cos(x)\ dx}$$ $$= -x\ cos(x)+sin(x)+C$$ <<*>>= ---S 6 +--S 6 of 16 integrate(x*sin(x),x) --R --R (6) sin(x) - x cos(x) @@ -229,7 +229,7 @@ $$\int{x\ cos(x)\ dx}$$ $$= x\ sin(x) - \int{sin(x)\ dx}$$ $$= x\ sin(x)+cos(x)+C$$ <<*>>= ---S 7 +--S 7 of 16 integrate(x*cos(x),x) --R --R @@ -252,7 +252,7 @@ $$= -x^2\ cos(x) - \int{-2x\ cos(x)\ dx}$$ $$= -x^2\ cos(x)+2\int{x\ cos(x)\ dx}$$ $$=-x^2\ cos(x)+2(x\ sin(x)+cos(x))+C$$ <<*>>= ---S 8 +--S 8 of 16 integrate(x^2*cos(x),x) --R --R @@ -278,7 +278,7 @@ $$2\int{sin(x)cos(x)dx}=sin^2(x)$$ so $$\int{sin(x)cos(x)dx}=\frac{1}{2}sin^2(x)+C$$ <<*>>= ---S 9 +--S 9 of 16 integrate(sin(x)*cos(x),x) --R --R @@ -304,7 +304,7 @@ $$=x\ ln(x)=\int{1\ dx}$$ $$=x\ ln(x) - x + C$$ $$=x(ln(x)-1)+C$$ <<*>>= ---S 10 +--S 10 of 16 integrate(log(x),x) --R --R (10) x log(x) - x @@ -326,7 +326,7 @@ $$\frac{x^3}{3} ln(x) - \int{\frac{x^3}{3}\frac{dx}{x}}$$ $$\frac{x^3}{3} ln(x)-\frac{1}{3}\int{x^2\ dx}$$ $$\frac{x^3}{3}ln(x)-\frac{1}{9}x^3 + C$$ <<*>>= ---S 11 +--S 11 of 16 integrate(x^2*log(x),x) --R --R 3 3 @@ -350,7 +350,7 @@ $$\int{x^2\ e^x\ dx}$$ $$x^2\ e^x - 2x\ e^x - \int{e^x\ 2dx}$$ $$x^2\ e^x - 2x\ e^x+2\ e^x+C$$ <<*>>= ---S 12 +--S 12 of 16 integrate(x^2*exp(x),x) --R --R @@ -376,7 +376,7 @@ $$=x\ sin^{-1}(x) + \frac{1}{2}(2(1-x^2)^{1/2})+C$$ $$=x\ sin^{-1}(x)+(1-x^2)^{1/2}+C$$ $$=x\ sin^{-1}(x)+\sqrt{1-x^2}+C$$ <<*>>= ---S 13 +--S 13 of 16 integrate(asin(x),x) --R --R @@ -405,7 +405,7 @@ $$=x\ \tan^{-1}-\int{\frac{x}{1+x^2}\ dx}$$ $$=x\ tan^{-1}(x)-\frac{1}{2}\int{\frac{2x}{1+x^2}\ dx}$$ $$=x\ tan^{-1}(x)-\frac{1}{2}ln(1+x^2)+C$$ <<*>>= ---S 14 +--S 14 of 16 integrate(atan(x),x) --R --R @@ -438,7 +438,7 @@ so $$\int{sec^3(x)\ dx}= \frac{1}{2}(sec(x)tan(x)+ln(\vert sec(x)+\tan(x)\vert ))+C$$ <<*>>= ---S 15 +--S 15 of 16 integrate(sec(x)^3,x) --R --R @@ -487,7 +487,7 @@ $$=\frac{1}{2}x^3\ e^{2x}-\frac{3}{4}x^2\ e^{2x}+ $$=\frac{1}{2}x^3\ e^{2x}-\frac{3}{4}x^2\ e^{2x}+ \frac{3}{4}xe^{2x}-\frac{3}{8}e^{2x}+C$$ <<*>>= ---S 16 +--S 16 of 16 integrate(x^3*exp(2*x),x) --R --R diff --git a/src/input/intef2.input.pamphlet b/src/input/intef2.input.pamphlet index c33abac..7b1dbe2 100644 --- a/src/input/intef2.input.pamphlet +++ b/src/input/intef2.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 10 +--S 1 of 10 (a*x+b) / (b**2 * x * log(x)**2 + 2*a*b*x**2*log(x) + a**2*x**3 + x) --R --R diff --git a/src/input/lodo.input.pamphlet b/src/input/lodo.input.pamphlet index 61f5de8..5a25bcd 100644 --- a/src/input/lodo.input.pamphlet +++ b/src/input/lodo.input.pamphlet @@ -206,7 +206,7 @@ p: RFZ := x**2 + 1/x**2 @ Operator multiplication is not commutative <<*>>= ---S 17 of 55 +--S 17 of 55 (a*b - b*a) p --R --R @@ -226,7 +226,7 @@ sequences, and also the computation of left and right lcm's. The result is the quotient/remainder pair <<*>>= ---S 18 of 55 +--S 18 of 55 leftDivide(a,b) --R --R @@ -718,7 +718,7 @@ b: Modo := m*Dx + 1 --RType: LinearOrdinaryDifferentialOperator2(SquareMatrix(3,UnivariatePolynomial(x,Integer)),DirectProductMatrixModule(3,UnivariatePolynomial(x,Integer),SquareMatrix(3,UnivariatePolynomial(x,Integer)),UnivariatePolynomial(x,Integer))) --E 51 ---S 52 of 55 +--S 52 of 55 a*b --R --R diff --git a/src/input/lupfact.input.pamphlet b/src/input/lupfact.input.pamphlet index b7ee9d2..a1bca2c 100644 --- a/src/input/lupfact.input.pamphlet +++ b/src/input/lupfact.input.pamphlet @@ -32,7 +32,7 @@ algorithm. State the field here <<*>>= ---S 1 of 18 +--S 1 of 18 field := Fraction Integer --R --R @@ -69,7 +69,7 @@ nonZeroCol: Matrix field -> INT --R Type: Void --E 4 ---S 5 of 18 +--S 5 of 18 nonZeroCol(m) == foundit := false col := 1 @@ -87,7 +87,7 @@ nonZeroCol(m) == This embeds the given square matrix in a larger square matrix where the extra space is filled with 1s on the diagonal, 0 elsewhere. <<*>>= ---S 6 of 18 +--S 6 of 18 embedMatrix: (Matrix field,NNI,NNI) -> Matrix field --R --R Type: Void @@ -112,7 +112,7 @@ lupFactorEngine: (Matrix field, INT, INT) -> List Matrix field --R Type: Void --E 8 ---S 9 of 18 +--S 9 of 18 lupFactorEngine(a, m, p) == m = 1 => l : Matrix field := diagonalMatrix [1] @@ -152,7 +152,7 @@ lupFactorEngine(a, m, p) == @ Next computes floor of log base 2 of an integer <<*>>= ---S 10 of 18 +--S 10 of 18 intLog2: NNI -> NNI --R --R Type: Void diff --git a/src/input/mappkg1.input.pamphlet b/src/input/mappkg1.input.pamphlet index 6fa53bb..581590b 100644 --- a/src/input/mappkg1.input.pamphlet +++ b/src/input/mappkg1.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 26 +--S 1 of 26 power(q: FRAC INT, n: INT): FRAC INT == q**n --R --R Function declaration power : (Fraction Integer,Integer) -> Fraction diff --git a/src/input/matrix.input.pamphlet b/src/input/matrix.input.pamphlet index 067109d..2d35d55 100644 --- a/src/input/matrix.input.pamphlet +++ b/src/input/matrix.input.pamphlet @@ -251,7 +251,7 @@ minordet mat3 @ Same computation, work over the rationals <<*>>= ---S 15 of 42 +--S 15 of 42 mat4 : MATRIX FRAC INT := matrix [[j**i for i in 0..4] for j in 1..5] --R --R diff --git a/src/input/matrix22.input.pamphlet b/src/input/matrix22.input.pamphlet index 2fa445d..fe93939 100644 --- a/src/input/matrix22.input.pamphlet +++ b/src/input/matrix22.input.pamphlet @@ -64,7 +64,7 @@ because there is no function that computes the determinant of a matrix whose entries belong to a noncommutative ring <<*>>= )set mes test off ---S 4 of 8 +--S 4 of 8 determinant n --R --R There are 3 exposed and 1 unexposed library operations named diff --git a/src/input/mpoly.input.pamphlet b/src/input/mpoly.input.pamphlet index 9323ed3..950b67a 100644 --- a/src/input/mpoly.input.pamphlet +++ b/src/input/mpoly.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 10 +--S 1 of 10 m : MPOLY([x,y],INT) := (x**2 - x*y**3 +3*y)**2 --R --R diff --git a/src/input/mset2.input.pamphlet b/src/input/mset2.input.pamphlet index 354a3f8..074ce54 100644 --- a/src/input/mset2.input.pamphlet +++ b/src/input/mset2.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 12 +--S 1 of 12 s := multiset [1,2,3,4,5,4,3,2,3,4,5,6,7,4,10] --R --R diff --git a/src/input/ndftip.input.pamphlet b/src/input/ndftip.input.pamphlet index bbed72e..84578e4 100644 --- a/src/input/ndftip.input.pamphlet +++ b/src/input/ndftip.input.pamphlet @@ -814,7 +814,7 @@ badSeqs : List PackedHermitianSequence DoubleFloat -- -- Type: List Symbol ---S 44 of 45 +--S 44 of 45 nagDFT badSeqs --R --R There are no library operations named nagDFT diff --git a/src/input/noonburg.input.pamphlet b/src/input/noonburg.input.pamphlet index 90cf929..dbd6020 100644 --- a/src/input/noonburg.input.pamphlet +++ b/src/input/noonburg.input.pamphlet @@ -38,7 +38,7 @@ dmp0 := DMP([x,y,z,c],RN) --R Type: Domain --E 2 ---S 3 of 6 +--S 3 of 6 px : dmp0 := 1-c*x +x*(y**2 + z**2) --R --R diff --git a/src/input/nsfip.input.pamphlet b/src/input/nsfip.input.pamphlet index 2a24dc0..98aa59e 100644 --- a/src/input/nsfip.input.pamphlet +++ b/src/input/nsfip.input.pamphlet @@ -86,7 +86,7 @@ nagExpInt(-1) :: Float @ nagSinInt : DF -> DF ; <<*>>= ---S 4 of 141 used to work? +--S 4 of 141 used to work? nagSinInt(0) :: Float --R --R There are no library operations named nagSinInt diff --git a/src/input/oct.input.pamphlet b/src/input/oct.input.pamphlet index 28b7aab..3cd0c4b 100644 --- a/src/input/oct.input.pamphlet +++ b/src/input/oct.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 15 +--S 1 of 15 oci1 := octon(1,2,3,4,5,6,7,8) --R --R @@ -131,7 +131,7 @@ p : Octonion Polynomial Integer := octon(p1, pi, pj, pk, pE, pI, pJ, pK) --R Type: Octonion Polynomial Integer --E 14 ---S 15 +--S 15 of 15 norm(o*p)-norm(p)*norm(p) --R --R diff --git a/src/input/op1.input.pamphlet b/src/input/op1.input.pamphlet index 529bb28..2fdee44 100644 --- a/src/input/op1.input.pamphlet +++ b/src/input/op1.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 of 21 +--S 1 of 21 R := SQMATRIX(2, INT) --R --R diff --git a/src/input/page.input.pamphlet b/src/input/page.input.pamphlet index 8b21aaf..f1e01b4 100644 --- a/src/input/page.input.pamphlet +++ b/src/input/page.input.pamphlet @@ -50,21 +50,21 @@ interface, please review the following Axiom session. Consider the three strings: \end{verbatim} <<*>>= ---S 1 +--S 1 of 18 a1:="(a/x)+(a/y)" --R --R (1) "(a/x)+(a/y)" --R Type: String --E 1 ---S 2 +--S 2 of 18 a2:="(a/x) + (a/y)" --R --R (2) "(a/x) + (a/y)" --R Type: String --E 2 ---S 3 +--S 3 of 18 a3:="(a*x+a*y)/(x*y)" --R --R (3) "(a*x+a*y)/(x*y)" @@ -75,21 +75,21 @@ a3:="(a*x+a*y)/(x*y)" Of course as members of the Domain String these are all different. <<*>>= ---S 4 +--S 4 of 18 (a1=a2)::Boolean --R --R (4) false --R Type: Boolean --E 4 ---S 5 +--S 5 of 18 (a1=a3)::Boolean --R --R (5) false --R Type: Boolean --E 5 ---S 6 +--S 6 of 18 (a2=a3)::Boolean --R --R (6) false @@ -99,21 +99,21 @@ Of course as members of the Domain String these are all different. @ While as members of the Domain Expression Integer these are equal. <<*>>= ---S 7 +--S 7 of 18 interpretString(a1."=".a2)::Boolean --R --R (7) true --R Type: Boolean --E 7 ---S 8 +--S 8 of 18 interpretString(a1."=".a3)::Boolean --R --R (8) true --R Type: Boolean --E 8 ---S 9 +--S 9 of 18 interpretString(a2."=".a3)::Boolean --R --R (9) true @@ -124,21 +124,21 @@ interpretString(a2."=".a3)::Boolean But when we evaluate them as symbolic expressions in the domain InputForm: <<*>>= ---S 10 +--S 10 of 18 x:INFORM:=x --R --R (10) x --R Type: InputForm --E 10 ---S 11 +--S 11 of 18 y:INFORM:=y --R --R (11) y --R Type: InputForm --E 11 ---S 12 +--S 12 of 18 a:INFORM:=a --R --R (12) a @@ -148,21 +148,21 @@ a:INFORM:=a @ The first two are equal but the third is something different! <<*>>= ---S 13 +--S 13 of 18 interpretString(a1."=".a2)::Boolean --R --R (13) true --R Type: Boolean --E 13 ---S 14 +--S 14 of 18 interpretString(a1."=".a3)::Boolean --R --R (14) false --R Type: Boolean --E 14 ---S 15 +--S 15 of 18 interpretString(a2."=".a3)::Boolean --R --R (15) false @@ -180,7 +180,7 @@ need for an OutputForm for InputForm that is equivalent the actual input to the Axiom interpreter. The function that I was looking for is called 'expr' in the domain InputForm. <<*>>= ---S 16 +--S 16 of 18 map(expr,map(interpretString,a1=a2)::Equation(INFORM)) --R --R a a a a @@ -189,7 +189,7 @@ map(expr,map(interpretString,a1=a2)::Equation(INFORM)) --R Type: Equation OutputForm --E 16 ---S 17 +--S 17 of 18 map(expr,map(interpretString,a2=a3)::Equation(INFORM)) --R --R a a a x + a y @@ -198,7 +198,7 @@ map(expr,map(interpretString,a2=a3)::Equation(INFORM)) --R Type: Equation OutputForm --E 17 ---S 18 +--S 18 of 18 map(expr,map(interpretString,a1=a3)::Equation(INFORM)) --R --R a a a x + a y diff --git a/src/input/patch51.input.pamphlet b/src/input/patch51.input.pamphlet index 66ca072..27afdd4 100644 --- a/src/input/patch51.input.pamphlet +++ b/src/input/patch51.input.pamphlet @@ -19,7 +19,7 @@ These are bug fixes available in patch51 The besselK function was missing a minus sign as of patch50. This is fixed as of patch51. <<*>>= ---S 1 bug #355 fix +--S 1 of 1 bug #355 fix D(besselK(a,x),x) --R --R diff --git a/src/input/quat.input.pamphlet b/src/input/quat.input.pamphlet index 60d5ad5..445ae09 100644 --- a/src/input/quat.input.pamphlet +++ b/src/input/quat.input.pamphlet @@ -38,7 +38,7 @@ The four arguments are the real part, the i imaginary part, the j imaginary part and the k imaginary part, respectively. These are extracted with the following functions. <<*>>= ---S 2 of 25 +--S 2 of 25 real q --R --R @@ -157,7 +157,7 @@ r * q There are no predefined constants for the imaginary i, j and k but you can easily define them. <<*>>= ---S 13 of 25 +--S 13 of 25 i := quatern(0,1,0,0) --R --R @@ -181,7 +181,7 @@ k := quatern(0,0,0,1) --R Type: Quaternion Integer --E 15 ---S 16 of 25 +--S 16 of 25 i*i --R --R diff --git a/src/input/r21bugsbig.input.pamphlet b/src/input/r21bugsbig.input.pamphlet index 61eccd1..e035c15 100644 --- a/src/input/r21bugsbig.input.pamphlet +++ b/src/input/r21bugsbig.input.pamphlet @@ -23,7 +23,7 @@ )set message type off )set message time off ---S 1 of 22 +--S 1 of 22 n : PositiveInteger := 5 --R --R @@ -41,11 +41,17 @@ UZn : List(PositiveInteger) := [i for i in 1 .. n-1 | gcd(i,n) = 1] K = Q(t), corps des fractions rationnelles a Phi(n) indeterminees sur Q <<*>>= --S 3 of 22 -vars : List(Symbol) := [concat("t", i::String)::Symbol for i in 0 ..#UZn-1] ; +vars : List(Symbol) := [concat("t", i::String)::Symbol for i in 0 ..#UZn-1] +--R +--R +--R (3) [t0,t1,t2,t3] --E 3 ---S 4 of 22 -Zt := DistributedMultivariatePolynomial(vars, Integer) ; K :=Fraction(Zt) ; +--S 4 of 22 +Zt := DistributedMultivariatePolynomial(vars, Integer) ; K :=Fraction(Zt) +--R +--R +--R (4) Fraction DistributedMultivariatePolynomial([t0,t1,t2,t3],Integer) --E 4 --S 5 of 22 @@ -66,7 +72,10 @@ t(#t) := 0 ; t --E 6 --S 7 of 22 -Zn := IntegerMod(n) ; +Zn := IntegerMod(n) +--R +--R +--R (7) IntegerMod 5 --E 7 --S 8 of 22 @@ -90,11 +99,20 @@ Phi : UP('xi, K) := map(coerce, cyclotomic(n)) E est l'extension cyclotomique de K par les racines n-iemes de l'unite <<*>>= --S 10 of 22 -E := SimpleAlgebraicExtension(K, UP('xi, K), Phi) ; +E := SimpleAlgebraicExtension(K, UP('xi, K), Phi) +--R +--R +--R (10) +--R SimpleAlgebraicExtension(Fraction DistributedMultivariatePolynomial([t0,t1,t2 +--R ,t3],Integer),UnivariatePolynomial(xi,Fraction DistributedMultivariatePolynom +--R ial([t0,t1,t2,t3],Integer)),xi**4+xi**3+xi*xi+xi+1) --E 10 --S 11 of 22 -xi : E := generator()$E ; +xi : E := generator()$E +--R +--R +--R (11) xi --E 11 --S 12 of 22 @@ -113,27 +131,720 @@ delta(j) = delta(j, 1) avec les nouvelles notations <<*>>= --S 13 of 22 delta : List(E) := - [reduce(*, [b**((j*rapport(1,k)) quo n) for b in bList for k in UZn]) for j in UZn] ; + [reduce(*, [b**((j*rapport(1,k)) quo n) for b in bList for k in UZn]) for j in UZn] --R --R Compiling function rapport with type (Integer,Integer) -> Integer --R +--R (13) +--R [1, +--R +--R 3 2 2 2 +--R (- t0 t1 + t1 t2)xi + (- t0 t2 + t2 )xi + (- t0 t1 - t0 t2 + t1 )xi +--R + +--R 2 +--R t0 - t0 t1 - t0 t2 + t1 t2 +--R , +--R +--R 3 3 2 2 2 2 2 3 2 +--R - t0 t1 + t0 t2 + t0 t1 + 3t0 t1 t2 - 2t0 t2 - 2t0 t1 - t0 t1 t2 +--R + +--R 3 4 2 2 +--R 2t0 t2 + t1 - t1 t2 +--R * +--R 3 +--R xi +--R + +--R 3 3 2 2 2 3 2 3 +--R - t0 t1 - t0 t2 + 2t0 t1 + 3t0 t1 t2 - 2t0 t1 - 3t0 t1 t2 + t0 t2 +--R + +--R 3 2 2 3 +--R 2t1 t2 - 2t1 t2 + t1 t2 +--R * +--R 2 +--R xi +--R + +--R 3 2 2 2 2 2 3 2 +--R - 2t0 t1 + 2t0 t1 + 2t0 t1 t2 - t0 t2 - t0 t1 - t0 t1 t2 +--R + +--R 2 3 2 2 3 4 +--R t0 t1 t2 + t1 t2 - t1 t2 - t1 t2 + t2 +--R * +--R xi +--R + +--R 4 3 3 2 2 2 2 2 3 2 +--R t0 - 2t0 t1 - t0 t2 + t0 t1 + 4t0 t1 t2 - t0 t2 - t0 t1 - t0 t1 t2 +--R + +--R 2 3 3 3 +--R - t0 t1 t2 + t0 t2 + t1 t2 - t1 t2 +--R , +--R +--R 5 5 4 2 4 4 2 3 3 +--R - 2t0 t1 + t0 t2 + 2t0 t1 + 8t0 t1 t2 - 2t0 t2 - 3t0 t1 +--R + +--R 3 2 3 2 3 3 2 4 2 3 +--R - 11t0 t1 t2 - 3t0 t1 t2 + 4t0 t2 + 4t0 t1 + t0 t1 t2 +--R + +--R 2 2 2 2 3 2 4 4 3 2 +--R 12t0 t1 t2 - 6t0 t1 t2 - t0 t2 - 3t0 t1 t2 - 3t0 t1 t2 +--R + +--R 2 3 4 5 6 5 4 2 2 4 +--R - 4t0 t1 t2 + 9t0 t1 t2 - 2t0 t2 - t1 + 3t1 t2 - t1 t2 + t1 t2 +--R + +--R 5 6 +--R - 3t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 5 5 4 2 4 4 2 3 3 +--R - t0 t1 - 2t0 t2 + 2t0 t1 + 8t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 3 2 3 2 3 3 2 4 2 2 2 2 3 +--R - 2t0 t1 t2 - 10t0 t1 t2 + t0 t2 + t0 t1 + 3t0 t1 t2 + 4t0 t1 t2 +--R + +--R 5 4 3 2 2 3 4 5 +--R 2t0 t1 - 2t0 t1 t2 + 2t0 t1 t2 - 8t0 t1 t2 + 5t0 t1 t2 - t0 t2 +--R + +--R 6 5 4 2 3 3 2 4 5 +--R - t1 + t1 t2 + t1 t2 - 3t1 t2 + 5t1 t2 - 3t1 t2 +--R * +--R 2 +--R xi +--R + +--R 5 5 4 2 4 3 3 3 2 +--R - 3t0 t1 - t0 t2 + 5t0 t1 + 5t0 t1 t2 - 3t0 t1 - 8t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 2 3 +--R 4t0 t1 t2 + t0 t2 + t0 t1 + 2t0 t1 t2 + 3t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 4 5 4 2 3 4 5 +--R 3t0 t2 + t0 t1 - 2t0 t1 t2 - 2t0 t1 t2 + 8t0 t1 t2 - 2t0 t2 +--R + +--R 6 5 4 2 3 3 2 4 5 +--R - t1 + 2t1 t2 + t1 t2 - 4t1 t2 + 2t1 t2 - t1 t2 +--R * +--R xi +--R + +--R 6 5 5 4 2 4 4 2 3 2 +--R t0 - 3t0 t1 - 2t0 t2 + t0 t1 + 9t0 t1 t2 - t0 t2 - 4t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 2 3 +--R - 6t0 t1 t2 + 4t0 t2 - t0 t1 - 3t0 t1 t2 + 12t0 t1 t2 - 3t0 t1 t2 +--R + +--R 2 4 5 4 3 2 2 3 4 +--R - 2t0 t2 + 3t0 t1 - 3t0 t1 t2 + t0 t1 t2 - 11t0 t1 t2 + 8t0 t1 t2 +--R + +--R 5 6 4 2 3 3 2 4 5 +--R t0 t2 - t1 + 4t1 t2 - 3t1 t2 + 2t1 t2 - 2t1 t2 +--R ] --E 13 @ verification en introduisant la liste B des Bj <<*>>= --S 14 of 22 -B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) for j in UZn] ; +B : List(E) := [reduce(*, [b**rapport(j,i) for b in bList for i in UZn]) for j in UZn] +--R +--R +--R (14) +--R [ +--R 9 9 8 2 8 8 2 7 3 +--R - 2t0 t1 + t0 t2 + 4t0 t1 + 9t0 t1 t2 - 3t0 t2 - 7t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 +--R - 24t0 t1 t2 - 9t0 t1 t2 + 7t0 t2 + 11t0 t1 + 32t0 t1 t2 +--R + +--R 6 2 2 6 3 6 4 5 5 5 4 +--R 35t0 t1 t2 + t0 t1 t2 - 8t0 t2 - 11t0 t1 - 36t0 t1 t2 +--R + +--R 5 3 2 5 4 5 5 4 6 4 5 +--R - 65t0 t1 t2 + 6t0 t1 t2 + 6t0 t2 + 8t0 t1 + 41t0 t1 t2 +--R + +--R 4 4 2 4 3 3 4 2 4 4 5 4 6 +--R 45t0 t1 t2 + 20t0 t1 t2 - 20t0 t1 t2 + 3t0 t1 t2 - 4t0 t2 +--R + +--R 3 7 3 6 3 5 2 3 4 3 3 3 4 +--R - 6t0 t1 - 26t0 t1 t2 - 13t0 t1 t2 - 45t0 t1 t2 + 40t0 t1 t2 +--R + +--R 3 2 5 3 6 3 7 2 8 2 7 +--R - 11t0 t1 t2 + 4t0 t1 t2 + 2t0 t2 + 3t0 t1 + t0 t1 t2 +--R + +--R 2 6 2 2 5 3 2 4 4 2 3 5 2 2 6 +--R 31t0 t1 t2 - 13t0 t1 t2 + 20t0 t1 t2 - 47t0 t1 t2 + 41t0 t1 t2 +--R + +--R 2 7 2 8 9 8 7 2 +--R - 19t0 t1 t2 + 2t0 t2 + t0 t1 - 3t0 t1 t2 - 10t0 t1 t2 +--R + +--R 6 3 5 4 4 5 3 6 2 7 +--R 6t0 t1 t2 + 7t0 t1 t2 - 14t0 t1 t2 + 22t0 t1 t2 - 25t0 t1 t2 +--R + +--R 8 9 10 9 8 2 7 3 6 4 +--R 16t0 t1 t2 - 3t0 t2 - t1 + 4t1 t2 - 5t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 4 6 3 7 2 8 9 10 +--R 4t1 t2 - 5t1 t2 + 5t1 t2 - 4t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 3 +--R - t0 t1 - 2t0 t2 + 3t0 t1 + 11t0 t1 t2 + 5t0 t2 - 7t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 +--R - 16t0 t1 t2 - 26t0 t1 t2 - 4t0 t2 + 8t0 t1 + 23t0 t1 t2 +--R + +--R 6 2 2 6 3 6 4 5 5 5 4 +--R 40t0 t1 t2 + 24t0 t1 t2 + 4t0 t2 - 6t0 t1 - 28t0 t1 t2 +--R + +--R 5 3 2 5 2 3 5 4 5 5 4 6 +--R - 41t0 t1 t2 - 32t0 t1 t2 - 8t0 t1 t2 - 5t0 t2 + 4t0 t1 +--R + +--R 4 5 4 4 2 4 3 3 4 2 4 4 5 +--R 23t0 t1 t2 + 10t0 t1 t2 + 45t0 t1 t2 - 5t0 t1 t2 + 14t0 t1 t2 +--R + +--R 4 6 3 7 3 6 3 5 2 3 4 3 3 3 4 +--R 3t0 t2 - 2t0 t1 + t0 t1 t2 - 15t0 t1 t2 - 5t0 t1 t2 - 30t0 t1 t2 +--R + +--R 3 2 5 3 6 2 8 2 7 2 6 2 +--R 13t0 t1 t2 - 9t0 t1 t2 - 2t0 t1 - 6t0 t1 t2 + 14t0 t1 t2 +--R + +--R 2 5 3 2 4 4 2 3 5 2 2 6 2 7 +--R - 4t0 t1 t2 + 25t0 t1 t2 - 27t0 t1 t2 + 19t0 t1 t2 - 6t0 t1 t2 +--R + +--R 2 8 9 8 6 3 5 4 +--R t0 t2 + 3t0 t1 - 2t0 t1 t2 - 11t0 t1 t2 + 24t0 t1 t2 +--R + +--R 4 5 3 6 2 7 8 9 +--R - 37t0 t1 t2 + 38t0 t1 t2 - 25t0 t1 t2 + 9t0 t1 t2 - t0 t2 +--R + +--R 10 9 8 2 7 3 6 4 5 5 4 6 +--R - t1 + 2t1 t2 - t1 t2 - 2t1 t2 + 7t1 t2 - 11t1 t2 + 12t1 t2 +--R + +--R 3 7 2 8 9 +--R - 11t1 t2 + 8t1 t2 - 3t1 t2 +--R * +--R 2 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 3 +--R - 3t0 t1 - t0 t2 + 8t0 t1 + 9t0 t1 t2 + t0 t2 - 11t0 t1 +--R + +--R 7 2 7 2 6 4 6 3 6 2 2 +--R - 25t0 t1 t2 - 6t0 t1 t2 + 12t0 t1 + 38t0 t1 t2 + 19t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 +--R - 9t0 t1 t2 + 3t0 t2 - 11t0 t1 - 37t0 t1 t2 - 27t0 t1 t2 +--R + +--R 5 2 3 5 4 5 5 4 6 4 5 +--R 13t0 t1 t2 + 14t0 t1 t2 - 5t0 t2 + 7t0 t1 + 24t0 t1 t2 +--R + +--R 4 4 2 4 3 3 4 2 4 4 5 4 6 +--R 25t0 t1 t2 - 30t0 t1 t2 - 5t0 t1 t2 - 8t0 t1 t2 + 4t0 t2 +--R + +--R 3 7 3 6 3 5 2 3 4 3 3 3 4 +--R - 2t0 t1 - 11t0 t1 t2 - 4t0 t1 t2 - 5t0 t1 t2 + 45t0 t1 t2 +--R + +--R 3 2 5 3 6 3 7 2 8 2 6 2 +--R - 32t0 t1 t2 + 24t0 t1 t2 - 4t0 t2 - t0 t1 + 14t0 t1 t2 +--R + +--R 2 5 3 2 4 4 2 3 5 2 2 6 2 7 +--R - 15t0 t1 t2 + 10t0 t1 t2 - 41t0 t1 t2 + 40t0 t1 t2 - 26t0 t1 t2 +--R + +--R 2 8 9 8 7 2 6 3 5 4 +--R 5t0 t2 + 2t0 t1 - 2t0 t1 t2 - 6t0 t1 t2 + t0 t1 t2 + 23t0 t1 t2 +--R + +--R 4 5 3 6 2 7 8 9 +--R - 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9t0 t1 t2 - 3t0 t2 + 4t0 t1 - 3t0 t1 t2 + t0 t1 t2 - 26t0 t1 t2 +--R + +--R 5 4 4 5 3 6 2 7 8 +--R 41t0 t1 t2 - 36t0 t1 t2 + 32t0 t1 t2 - 24t0 t1 t2 + 9t0 t1 t2 +--R + +--R 9 10 9 8 2 7 3 6 4 5 5 4 6 +--R t0 t2 - t1 + t1 t2 + 3t1 t2 - 6t1 t2 + 8t1 t2 - 11t1 t2 + 11t1 t2 +--R + +--R 3 7 2 8 9 +--R - 7t1 t2 + 4t1 t2 - 2t1 t2 +--R , +--R +--R 9 9 8 2 8 8 2 7 3 +--R t0 t1 + 2t0 t2 - 3t0 t1 - 11t0 t1 t2 - 5t0 t2 + 7t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 +--R 16t0 t1 t2 + 26t0 t1 t2 + 4t0 t2 - 8t0 t1 - 23t0 t1 t2 +--R + +--R 6 2 2 6 3 6 4 5 5 5 4 +--R - 40t0 t1 t2 - 24t0 t1 t2 - 4t0 t2 + 6t0 t1 + 28t0 t1 t2 +--R + +--R 5 3 2 5 2 3 5 4 5 5 4 6 +--R 41t0 t1 t2 + 32t0 t1 t2 + 8t0 t1 t2 + 5t0 t2 - 4t0 t1 +--R + +--R 4 5 4 4 2 4 3 3 4 2 4 4 5 +--R - 23t0 t1 t2 - 10t0 t1 t2 - 45t0 t1 t2 + 5t0 t1 t2 - 14t0 t1 t2 +--R + +--R 4 6 3 7 3 6 3 5 2 3 4 3 +--R - 3t0 t2 + 2t0 t1 - t0 t1 t2 + 15t0 t1 t2 + 5t0 t1 t2 +--R + +--R 3 3 4 3 2 5 3 6 2 8 2 7 +--R 30t0 t1 t2 - 13t0 t1 t2 + 9t0 t1 t2 + 2t0 t1 + 6t0 t1 t2 +--R + +--R 2 6 2 2 5 3 2 4 4 2 3 5 2 2 6 +--R - 14t0 t1 t2 + 4t0 t1 t2 - 25t0 t1 t2 + 27t0 t1 t2 - 19t0 t1 t2 +--R + +--R 2 7 2 8 9 8 6 3 5 4 +--R 6t0 t1 t2 - t0 t2 - 3t0 t1 + 2t0 t1 t2 + 11t0 t1 t2 - 24t0 t1 t2 +--R + +--R 4 5 3 6 2 7 8 9 10 +--R 37t0 t1 t2 - 38t0 t1 t2 + 25t0 t1 t2 - 9t0 t1 t2 + t0 t2 + t1 +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R - 2t1 t2 + t1 t2 + 2t1 t2 - 7t1 t2 + 11t1 t2 - 12t1 t2 +--R + +--R 3 7 2 8 9 +--R 11t1 t2 - 8t1 t2 + 3t1 t2 +--R * +--R 3 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 3 +--R - 2t0 t1 + t0 t2 + 5t0 t1 - 2t0 t1 t2 - 4t0 t2 - 4t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 +--R - 9t0 t1 t2 + 20t0 t1 t2 + 4t0 t2 + 4t0 t1 + 15t0 t1 t2 +--R + +--R 6 2 2 6 3 6 4 5 5 5 4 +--R - 21t0 t1 t2 - 33t0 t1 t2 - t0 t2 - 5t0 t1 - 9t0 t1 t2 +--R + +--R 5 3 2 5 2 3 5 4 4 6 4 5 +--R 14t0 t1 t2 + 45t0 t1 t2 + 22t0 t1 t2 + 3t0 t1 + t0 t1 t2 +--R + +--R 4 4 2 4 3 3 4 5 4 6 3 6 +--R 15t0 t1 t2 - 75t0 t1 t2 - 22t0 t1 t2 + t0 t2 - 12t0 t1 t2 +--R + +--R 3 5 2 3 3 4 3 2 5 3 6 3 7 +--R 11t0 t1 t2 + 75t0 t1 t2 - 45t0 t1 t2 + 33t0 t1 t2 - 4t0 t2 +--R + +--R 2 8 2 7 2 5 3 2 4 4 2 3 5 +--R t0 t1 + 6t0 t1 t2 - 11t0 t1 t2 - 15t0 t1 t2 - 14t0 t1 t2 +--R + +--R 2 2 6 2 7 2 8 9 7 2 +--R 21t0 t1 t2 - 20t0 t1 t2 + 4t0 t2 - t0 t1 - 6t0 t1 t2 +--R + +--R 6 3 5 4 4 5 3 6 2 7 +--R 12t0 t1 t2 - t0 t1 t2 + 9t0 t1 t2 - 15t0 t1 t2 + 9t0 t1 t2 +--R + +--R 8 9 9 8 2 6 4 5 5 4 6 +--R 2t0 t1 t2 - t0 t2 + t1 t2 - t1 t2 - 3t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 3 7 2 8 9 +--R 4t1 t2 - 5t1 t2 + 2t1 t2 +--R * +--R 2 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 2 +--R - t0 t1 + 3t0 t2 + t0 t1 - 2t0 t1 t2 - 8t0 t2 - 8t0 t1 t2 +--R + +--R 7 2 7 3 6 4 6 3 6 2 2 +--R 17t0 t1 t2 + 11t0 t2 + 3t0 t1 + 9t0 t1 t2 - 5t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 +--R - 23t0 t1 t2 - 12t0 t2 - 5t0 t1 - 8t0 t1 t2 - 24t0 t1 t2 +--R + +--R 5 2 3 5 4 5 5 4 6 4 5 +--R 32t0 t1 t2 + 14t0 t1 t2 + 11t0 t2 + 4t0 t1 + 18t0 t1 t2 +--R + +--R 4 4 2 4 3 3 4 2 4 4 5 4 6 +--R 35t0 t1 t2 - 25t0 t1 t2 - 15t0 t1 t2 - 11t0 t1 t2 - 7t0 t2 +--R + +--R 3 7 3 6 3 5 2 3 4 3 3 3 4 +--R - 4t0 t1 - 27t0 t1 t2 + 2t0 t1 t2 - 40t0 t1 t2 + 70t0 t1 t2 +--R + +--R 3 2 5 3 6 3 7 2 8 2 7 +--R - 24t0 t1 t2 + 13t0 t1 t2 + 2t0 t2 + 5t0 t1 + 7t0 t1 t2 +--R + +--R 2 6 2 2 5 3 2 4 4 2 3 5 2 2 6 +--R 17t0 t1 t2 - 9t0 t1 t2 - 5t0 t1 t2 - 20t0 t1 t2 + 22t0 t1 t2 +--R + +--R 2 7 2 8 9 8 7 2 +--R - 13t0 t1 t2 + t0 t2 - 2t0 t1 - t0 t1 t2 - 10t0 t1 t2 +--R + +--R 6 3 5 4 4 5 3 6 8 +--R 17t0 t1 t2 - 17t0 t1 t2 + 23t0 t1 t2 - 16t0 t1 t2 + 7t0 t1 t2 +--R + +--R 9 9 8 2 7 3 6 4 5 5 +--R - 2t0 t2 + 2t1 t2 - 4t1 t2 + 7t1 t2 - 11t1 t2 + 11t1 t2 +--R + +--R 4 6 3 7 2 8 9 10 +--R - 8t1 t2 + 6t1 t2 - 3t1 t2 - t1 t2 + t2 +--R * +--R xi +--R + +--R 10 9 9 8 2 8 8 2 7 3 +--R t0 - 3t0 t1 - t0 t2 + 2t0 t1 + 5t0 t1 t2 - 3t0 t2 + 2t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 6 2 2 +--R - 9t0 t1 t2 + 7t0 t1 t2 + 6t0 t2 - 4t0 t1 - t0 t1 t2 + t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 5 2 3 +--R - 20t0 t1 t2 - 8t0 t2 + 6t0 t1 + 14t0 t1 t2 - 6t0 t1 t2 + 21t0 t1 t2 +--R + +--R 5 4 5 5 4 6 4 5 4 4 2 4 3 3 +--R 11t0 t1 t2 + 11t0 t2 - 8t0 t1 - 16t0 t1 t2 + 10t0 t1 t2 - 5t0 t1 t2 +--R + +--R 4 2 4 4 5 4 6 3 7 3 6 3 5 2 +--R - 15t0 t1 t2 - 8t0 t1 t2 - 11t0 t2 + 7t0 t1 + 5t0 t1 t2 + 2t0 t1 t2 +--R + +--R 3 4 3 3 3 4 3 2 5 3 6 3 7 +--R - 40t0 t1 t2 + 50t0 t1 t2 - 13t0 t1 t2 + 10t0 t1 t2 + 7t0 t2 +--R + +--R 2 8 2 7 2 6 2 2 5 3 2 4 4 +--R - 3t0 t1 - 4t0 t1 t2 + 17t0 t1 t2 - 9t0 t1 t2 + 20t0 t1 t2 +--R + +--R 2 3 5 2 2 6 2 7 2 8 9 8 +--R - 38t0 t1 t2 + 16t0 t1 t2 - 3t0 t1 t2 - 4t0 t2 + t0 t1 - t0 t1 t2 +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R t0 t1 t2 - 15t0 t1 t2 + 17t0 t1 t2 + t0 t1 t2 - 6t0 t1 t2 +--R + +--R 2 7 9 9 8 2 7 3 6 4 4 6 +--R t0 t1 t2 + 2t0 t2 - t1 t2 + 4t1 t2 - 4t1 t2 + t1 t2 - t1 t2 +--R + +--R 3 7 2 8 9 +--R 4t1 t2 - 4t1 t2 + t1 t2 +--R , +--R +--R 9 9 8 2 8 2 7 3 7 2 +--R - t0 t1 - 2t0 t2 + 4t0 t1 + 4t0 t2 - 4t0 t1 - t0 t1 t2 +--R + +--R 7 2 7 3 6 4 6 3 6 2 2 6 3 +--R 3t0 t1 t2 - 7t0 t2 + t0 t1 + 6t0 t1 t2 - 16t0 t1 t2 - 10t0 t1 t2 +--R + +--R 6 4 5 4 5 3 2 5 2 3 5 4 +--R 11t0 t2 - t0 t1 t2 + 38t0 t1 t2 + 13t0 t1 t2 + 8t0 t1 t2 +--R + +--R 5 5 4 6 4 5 4 4 2 4 3 3 +--R - 11t0 t2 - t0 t1 - 17t0 t1 t2 - 20t0 t1 t2 - 50t0 t1 t2 +--R + +--R 4 2 4 4 5 4 6 3 7 3 6 +--R 15t0 t1 t2 - 11t0 t1 t2 + 8t0 t2 + 4t0 t1 + 15t0 t1 t2 +--R + +--R 3 5 2 3 4 3 3 3 4 3 2 5 3 6 +--R 9t0 t1 t2 + 40t0 t1 t2 + 5t0 t1 t2 - 21t0 t1 t2 + 20t0 t1 t2 +--R + +--R 3 7 2 8 2 7 2 6 2 2 5 3 +--R - 6t0 t2 - 4t0 t1 - t0 t1 t2 - 17t0 t1 t2 - 2t0 t1 t2 +--R + +--R 2 4 4 2 3 5 2 2 6 2 7 2 8 +--R - 10t0 t1 t2 + 6t0 t1 t2 - t0 t1 t2 - 7t0 t1 t2 + 3t0 t2 +--R + +--R 9 8 7 2 6 3 5 4 +--R t0 t1 + t0 t1 t2 + 4t0 t1 t2 - 5t0 t1 t2 + 16t0 t1 t2 +--R + +--R 4 5 3 6 2 7 8 9 9 +--R - 14t0 t1 t2 + t0 t1 t2 + 9t0 t1 t2 - 5t0 t1 t2 + t0 t2 - t1 t2 +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 3t1 t2 - 7t1 t2 + 8t1 t2 - 6t1 t2 + 4t1 t2 - 2t1 t2 - 2t1 t2 +--R + +--R 9 10 +--R 3t1 t2 - t2 +--R * +--R 3 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 3 7 2 +--R 2t0 t1 - t0 t2 - 4t0 t1 - 9t0 t1 t2 + 3t0 t2 + 7t0 t1 + 24t0 t1 t2 +--R + +--R 7 2 7 3 6 4 6 3 6 2 2 +--R 9t0 t1 t2 - 7t0 t2 - 11t0 t1 - 32t0 t1 t2 - 35t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 +--R - t0 t1 t2 + 8t0 t2 + 11t0 t1 + 36t0 t1 t2 + 65t0 t1 t2 +--R + +--R 5 4 5 5 4 6 4 5 4 4 2 +--R - 6t0 t1 t2 - 6t0 t2 - 8t0 t1 - 41t0 t1 t2 - 45t0 t1 t2 +--R + +--R 4 3 3 4 2 4 4 5 4 6 3 7 +--R - 20t0 t1 t2 + 20t0 t1 t2 - 3t0 t1 t2 + 4t0 t2 + 6t0 t1 +--R + +--R 3 6 3 5 2 3 4 3 3 3 4 3 2 5 +--R 26t0 t1 t2 + 13t0 t1 t2 + 45t0 t1 t2 - 40t0 t1 t2 + 11t0 t1 t2 +--R + +--R 3 6 3 7 2 8 2 7 2 6 2 +--R - 4t0 t1 t2 - 2t0 t2 - 3t0 t1 - t0 t1 t2 - 31t0 t1 t2 +--R + +--R 2 5 3 2 4 4 2 3 5 2 2 6 2 7 +--R 13t0 t1 t2 - 20t0 t1 t2 + 47t0 t1 t2 - 41t0 t1 t2 + 19t0 t1 t2 +--R + +--R 2 8 9 8 7 2 6 3 +--R - 2t0 t2 - t0 t1 + 3t0 t1 t2 + 10t0 t1 t2 - 6t0 t1 t2 +--R + +--R 5 4 4 5 3 6 2 7 8 +--R - 7t0 t1 t2 + 14t0 t1 t2 - 22t0 t1 t2 + 25t0 t1 t2 - 16t0 t1 t2 +--R + +--R 9 10 9 8 2 7 3 6 4 4 6 +--R 3t0 t2 + t1 - 4t1 t2 + 5t1 t2 - 5t1 t2 + 4t1 t2 - 4t1 t2 +--R + +--R 3 7 2 8 9 10 +--R 5t1 t2 - 5t1 t2 + 4t1 t2 - t2 +--R * +--R 2 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 2 +--R t0 t1 - 3t0 t2 - t0 t1 + 2t0 t1 t2 + 8t0 t2 + 8t0 t1 t2 +--R + +--R 7 2 7 3 6 4 6 3 6 2 2 +--R - 17t0 t1 t2 - 11t0 t2 - 3t0 t1 - 9t0 t1 t2 + 5t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 +--R 23t0 t1 t2 + 12t0 t2 + 5t0 t1 + 8t0 t1 t2 + 24t0 t1 t2 +--R + +--R 5 2 3 5 4 5 5 4 6 4 5 +--R - 32t0 t1 t2 - 14t0 t1 t2 - 11t0 t2 - 4t0 t1 - 18t0 t1 t2 +--R + +--R 4 4 2 4 3 3 4 2 4 4 5 4 6 +--R - 35t0 t1 t2 + 25t0 t1 t2 + 15t0 t1 t2 + 11t0 t1 t2 + 7t0 t2 +--R + +--R 3 7 3 6 3 5 2 3 4 3 3 3 4 +--R 4t0 t1 + 27t0 t1 t2 - 2t0 t1 t2 + 40t0 t1 t2 - 70t0 t1 t2 +--R + +--R 3 2 5 3 6 3 7 2 8 2 7 +--R 24t0 t1 t2 - 13t0 t1 t2 - 2t0 t2 - 5t0 t1 - 7t0 t1 t2 +--R + +--R 2 6 2 2 5 3 2 4 4 2 3 5 2 2 6 +--R - 17t0 t1 t2 + 9t0 t1 t2 + 5t0 t1 t2 + 20t0 t1 t2 - 22t0 t1 t2 +--R + +--R 2 7 2 8 9 8 7 2 6 3 +--R 13t0 t1 t2 - t0 t2 + 2t0 t1 + t0 t1 t2 + 10t0 t1 t2 - 17t0 t1 t2 +--R + +--R 5 4 4 5 3 6 8 9 +--R 17t0 t1 t2 - 23t0 t1 t2 + 16t0 t1 t2 - 7t0 t1 t2 + 2t0 t2 +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R - 2t1 t2 + 4t1 t2 - 7t1 t2 + 11t1 t2 - 11t1 t2 + 8t1 t2 +--R + +--R 3 7 2 8 9 10 +--R - 6t1 t2 + 3t1 t2 + t1 t2 - t2 +--R * +--R xi +--R + +--R 10 9 9 8 2 8 8 2 7 3 +--R t0 - 2t0 t1 - 4t0 t2 + t0 t1 + 7t0 t1 t2 + 5t0 t2 + 2t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 6 2 2 +--R - t0 t1 t2 - 10t0 t1 t2 - 5t0 t2 - 7t0 t1 - 10t0 t1 t2 + 6t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 5 2 3 +--R 3t0 t1 t2 + 4t0 t2 + 11t0 t1 + 22t0 t1 t2 + 18t0 t1 t2 - 11t0 t1 t2 +--R + +--R 5 4 4 6 4 5 4 4 2 4 3 3 +--R - 3t0 t1 t2 - 12t0 t1 - 34t0 t1 t2 - 25t0 t1 t2 + 20t0 t1 t2 +--R + +--R 4 5 4 6 3 7 3 6 3 3 4 3 2 5 +--R 3t0 t1 t2 - 4t0 t2 + 11t0 t1 + 32t0 t1 t2 - 20t0 t1 t2 + 11t0 t1 t2 +--R + +--R 3 6 3 7 2 8 2 7 2 4 4 2 3 5 +--R - 3t0 t1 t2 + 5t0 t2 - 8t0 t1 - 11t0 t1 t2 + 25t0 t1 t2 - 18t0 t1 t2 +--R + +--R 2 2 6 2 7 2 8 9 7 2 +--R - 6t0 t1 t2 + 10t0 t1 t2 - 5t0 t2 + 3t0 t1 + 11t0 t1 t2 +--R + +--R 6 3 5 4 4 5 3 6 2 7 +--R - 32t0 t1 t2 + 34t0 t1 t2 - 22t0 t1 t2 + 10t0 t1 t2 + t0 t1 t2 +--R + +--R 8 9 9 8 2 7 3 6 4 +--R - 7t0 t1 t2 + 4t0 t2 - 3t1 t2 + 8t1 t2 - 11t1 t2 + 12t1 t2 +--R + +--R 5 5 4 6 3 7 2 8 9 10 +--R - 11t1 t2 + 7t1 t2 - 2t1 t2 - t1 t2 + 2t1 t2 - t2 +--R , +--R +--R 9 9 8 2 8 8 2 7 3 7 2 +--R 2t0 t1 - t0 t2 - 5t0 t1 + 2t0 t1 t2 + 4t0 t2 + 4t0 t1 + 9t0 t1 t2 +--R + +--R 7 2 7 3 6 4 6 3 6 2 2 +--R - 20t0 t1 t2 - 4t0 t2 - 4t0 t1 - 15t0 t1 t2 + 21t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 +--R 33t0 t1 t2 + t0 t2 + 5t0 t1 + 9t0 t1 t2 - 14t0 t1 t2 +--R + +--R 5 2 3 5 4 4 6 4 5 4 4 2 +--R - 45t0 t1 t2 - 22t0 t1 t2 - 3t0 t1 - t0 t1 t2 - 15t0 t1 t2 +--R + +--R 4 3 3 4 5 4 6 3 6 3 5 2 +--R 75t0 t1 t2 + 22t0 t1 t2 - t0 t2 + 12t0 t1 t2 - 11t0 t1 t2 +--R + +--R 3 3 4 3 2 5 3 6 3 7 2 8 +--R - 75t0 t1 t2 + 45t0 t1 t2 - 33t0 t1 t2 + 4t0 t2 - t0 t1 +--R + +--R 2 7 2 5 3 2 4 4 2 3 5 2 2 6 +--R - 6t0 t1 t2 + 11t0 t1 t2 + 15t0 t1 t2 + 14t0 t1 t2 - 21t0 t1 t2 +--R + +--R 2 7 2 8 9 7 2 6 3 5 4 +--R 20t0 t1 t2 - 4t0 t2 + t0 t1 + 6t0 t1 t2 - 12t0 t1 t2 + t0 t1 t2 +--R + +--R 4 5 3 6 2 7 8 9 9 +--R - 9t0 t1 t2 + 15t0 t1 t2 - 9t0 t1 t2 - 2t0 t1 t2 + t0 t2 - t1 t2 +--R + +--R 8 2 6 4 5 5 4 6 3 7 2 8 9 +--R t1 t2 + 3t1 t2 - 5t1 t2 + 4t1 t2 - 4t1 t2 + 5t1 t2 - 2t1 t2 +--R * +--R 3 +--R xi +--R + +--R 9 9 8 2 8 2 7 3 7 2 7 2 +--R t0 t1 + 2t0 t2 - 4t0 t1 - 4t0 t2 + 4t0 t1 + t0 t1 t2 - 3t0 t1 t2 +--R + +--R 7 3 6 4 6 3 6 2 2 6 3 6 4 +--R 7t0 t2 - t0 t1 - 6t0 t1 t2 + 16t0 t1 t2 + 10t0 t1 t2 - 11t0 t2 +--R + +--R 5 4 5 3 2 5 2 3 5 4 5 5 4 6 +--R t0 t1 t2 - 38t0 t1 t2 - 13t0 t1 t2 - 8t0 t1 t2 + 11t0 t2 + t0 t1 +--R + +--R 4 5 4 4 2 4 3 3 4 2 4 4 5 +--R 17t0 t1 t2 + 20t0 t1 t2 + 50t0 t1 t2 - 15t0 t1 t2 + 11t0 t1 t2 +--R + +--R 4 6 3 7 3 6 3 5 2 3 4 3 +--R - 8t0 t2 - 4t0 t1 - 15t0 t1 t2 - 9t0 t1 t2 - 40t0 t1 t2 +--R + +--R 3 3 4 3 2 5 3 6 3 7 2 8 +--R - 5t0 t1 t2 + 21t0 t1 t2 - 20t0 t1 t2 + 6t0 t2 + 4t0 t1 +--R + +--R 2 7 2 6 2 2 5 3 2 4 4 2 3 5 +--R t0 t1 t2 + 17t0 t1 t2 + 2t0 t1 t2 + 10t0 t1 t2 - 6t0 t1 t2 +--R + +--R 2 2 6 2 7 2 8 9 8 7 2 +--R t0 t1 t2 + 7t0 t1 t2 - 3t0 t2 - t0 t1 - t0 t1 t2 - 4t0 t1 t2 +--R + +--R 6 3 5 4 4 5 3 6 2 7 +--R 5t0 t1 t2 - 16t0 t1 t2 + 14t0 t1 t2 - t0 t1 t2 - 9t0 t1 t2 +--R + +--R 8 9 9 8 2 7 3 6 4 5 5 +--R 5t0 t1 t2 - t0 t2 + t1 t2 - 3t1 t2 + 7t1 t2 - 8t1 t2 + 6t1 t2 +--R + +--R 4 6 3 7 2 8 9 10 +--R - 4t1 t2 + 2t1 t2 + 2t1 t2 - 3t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 9 9 8 2 8 8 2 7 3 7 2 +--R 3t0 t1 + t0 t2 - 8t0 t1 - 9t0 t1 t2 - t0 t2 + 11t0 t1 + 25t0 t1 t2 +--R + +--R 7 2 6 4 6 3 6 2 2 6 3 +--R 6t0 t1 t2 - 12t0 t1 - 38t0 t1 t2 - 19t0 t1 t2 + 9t0 t1 t2 +--R + +--R 6 4 5 5 5 4 5 3 2 5 2 3 +--R - 3t0 t2 + 11t0 t1 + 37t0 t1 t2 + 27t0 t1 t2 - 13t0 t1 t2 +--R + +--R 5 4 5 5 4 6 4 5 4 4 2 +--R - 14t0 t1 t2 + 5t0 t2 - 7t0 t1 - 24t0 t1 t2 - 25t0 t1 t2 +--R + +--R 4 3 3 4 2 4 4 5 4 6 3 7 +--R 30t0 t1 t2 + 5t0 t1 t2 + 8t0 t1 t2 - 4t0 t2 + 2t0 t1 +--R + +--R 3 6 3 5 2 3 4 3 3 3 4 3 2 5 +--R 11t0 t1 t2 + 4t0 t1 t2 + 5t0 t1 t2 - 45t0 t1 t2 + 32t0 t1 t2 +--R + +--R 3 6 3 7 2 8 2 6 2 2 5 3 +--R - 24t0 t1 t2 + 4t0 t2 + t0 t1 - 14t0 t1 t2 + 15t0 t1 t2 +--R + +--R 2 4 4 2 3 5 2 2 6 2 7 2 8 +--R - 10t0 t1 t2 + 41t0 t1 t2 - 40t0 t1 t2 + 26t0 t1 t2 - 5t0 t2 +--R + +--R 9 8 7 2 6 3 5 4 +--R - 2t0 t1 + 2t0 t1 t2 + 6t0 t1 t2 - t0 t1 t2 - 23t0 t1 t2 +--R + +--R 4 5 3 6 2 7 8 9 +--R 28t0 t1 t2 - 23t0 t1 t2 + 16t0 t1 t2 - 11t0 t1 t2 + 2t0 t2 +--R + +--R 10 9 8 2 7 3 6 4 5 5 4 6 +--R t1 - 3t1 t2 + 2t1 t2 + 2t1 t2 - 4t1 t2 + 6t1 t2 - 8t1 t2 +--R + +--R 3 7 2 8 9 +--R 7t1 t2 - 3t1 t2 + t1 t2 +--R * +--R xi +--R + +--R 10 9 9 8 2 8 8 2 7 3 +--R t0 - t0 t1 - 2t0 t2 - 3t0 t1 + 7t0 t1 t2 + t0 t2 + 6t0 t1 +--R + +--R 7 2 7 3 6 4 6 3 6 2 2 +--R - 13t0 t1 t2 + 2t0 t2 - 8t0 t1 - 16t0 t1 t2 + 22t0 t1 t2 +--R + +--R 6 3 6 4 5 5 5 4 5 3 2 5 2 3 +--R 13t0 t1 t2 - 7t0 t2 + 11t0 t1 + 23t0 t1 t2 - 20t0 t1 t2 - 24t0 t1 t2 +--R + +--R 5 4 5 5 4 6 4 5 4 4 2 +--R - 11t0 t1 t2 + 11t0 t2 - 11t0 t1 - 17t0 t1 t2 - 5t0 t1 t2 +--R + +--R 4 3 3 4 2 4 4 5 4 6 3 7 3 6 +--R 70t0 t1 t2 - 15t0 t1 t2 + 14t0 t1 t2 - 12t0 t2 + 7t0 t1 + 17t0 t1 t2 +--R + +--R 3 5 2 3 4 3 3 3 4 3 2 5 3 6 +--R - 9t0 t1 t2 - 40t0 t1 t2 - 25t0 t1 t2 + 32t0 t1 t2 - 23t0 t1 t2 +--R + +--R 3 7 2 8 2 7 2 6 2 2 5 3 2 4 4 +--R 11t0 t2 - 4t0 t1 - 10t0 t1 t2 + 17t0 t1 t2 + 2t0 t1 t2 + 35t0 t1 t2 +--R + +--R 2 3 5 2 2 6 2 7 2 8 9 8 +--R - 24t0 t1 t2 - 5t0 t1 t2 + 17t0 t1 t2 - 8t0 t2 + 2t0 t1 - t0 t1 t2 +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R 7t0 t1 t2 - 27t0 t1 t2 + 18t0 t1 t2 - 8t0 t1 t2 + 9t0 t1 t2 +--R + +--R 2 7 8 9 9 8 2 7 3 +--R - 8t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 6 4 5 5 4 6 2 8 9 +--R 4t1 t2 - 5t1 t2 + 3t1 t2 + t1 t2 - t1 t2 +--R ] --E 14 ---S 15 of 22 +--S 15 of 22 [B(1)**j - b * d**n for b in B for d in delta for j in UZn] --R --R (15) [0,0,0,0] --E 15 --S 16 of 22 -L := SimpleAlgebraicExtension(E, UP('C1, E), C1**n - B(1)) ; C1 : L := generator()$L ; +L := SimpleAlgebraicExtension(E, UP('C1, E), C1**n - B(1)) ; C1 : L := generator()$L +--R +--R +--R (16) C1 --E 16 @ @@ -229,23 +940,3023 @@ retraction(z : L) : Zt == --R added to workspace. --E 17 ---S 18 of 22 -C : List(L) := [C1**j / d for j in UZn for d in delta] ; +--S 18 of 22 +C : List(L) := [C1**j / d for j in UZn for d in delta] +--R +--R +--R (18) +--R [C1, +--R +--R 2 2 +--R t0 t1 - t1 + t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 3 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 - t1 t2 +--R + +--R 4 +--R t2 +--R * +--R 3 +--R xi +--R + +--R 2 +--R t0 t2 - t1 + t1 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 3 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 - t1 t2 +--R + +--R 4 +--R t2 +--R * +--R 2 +--R xi +--R + +--R 2 +--R t0 t1 + t0 t2 - t1 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 3 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 - t1 t2 +--R + +--R 4 +--R t2 +--R * +--R xi +--R + +--R 2 2 +--R t0 - t1 + t1 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 3 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 - t1 t2 +--R + +--R 4 +--R t2 +--R * +--R 2 +--R C1 +--R , +--R +--R 3 3 2 2 2 3 2 +--R t0 t1 - t0 t2 + t0 t1 t2 + t0 t2 - t0 t1 + t0 t1 t2 +--R + +--R 2 3 3 2 2 3 4 +--R - 4t0 t1 t2 + t0 t2 + t1 t2 - t1 t2 + 2t1 t2 - t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 + 6t0 t1 t2 +--R + +--R 7 8 7 6 2 5 3 4 4 3 5 +--R - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 2 6 7 8 +--R 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 3 3 2 2 2 2 2 3 2 +--R t0 t1 + t0 t2 - t0 t1 + t0 t1 t2 - t0 t2 - t0 t1 - t0 t1 t2 +--R + +--R 3 4 3 3 4 +--R 2t0 t2 + t1 - t1 t2 + t1 t2 - t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 + 6t0 t1 t2 +--R + +--R 7 8 7 6 2 5 3 4 4 3 5 +--R - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 2 6 7 8 +--R 3t1 t2 - 2t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 3 2 2 2 2 2 3 2 +--R 2t0 t1 - 2t0 t1 - 2t0 t1 t2 + t0 t2 + t0 t1 + t0 t1 t2 +--R + +--R 2 3 2 2 3 4 +--R - t0 t1 t2 - t1 t2 + t1 t2 + t1 t2 - t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 + 6t0 t1 t2 +--R + +--R 7 8 7 6 2 5 3 4 4 3 5 +--R - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 2 6 7 8 +--R 3t1 t2 - 2t1 t2 + t2 +--R * +--R xi +--R + +--R 4 3 2 2 2 2 3 2 2 4 +--R t0 - t0 t2 - t0 t1 + 2t0 t1 t2 - 2t0 t1 t2 + t0 t2 + t1 t2 - t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 + 6t0 t1 t2 +--R + +--R 7 8 7 6 2 5 3 4 4 3 5 +--R - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 2 6 7 8 +--R 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R C1 +--R , +--R +--R 5 5 4 2 4 4 2 3 3 +--R 2t0 t1 - t0 t2 - 3t0 t1 + 3t0 t1 t2 + 3t0 t2 - t0 t1 +--R + +--R 3 2 3 2 2 3 2 3 2 4 +--R 6t0 t1 t2 - 14t0 t1 t2 - 2t0 t1 t2 + 14t0 t1 t2 - 3t0 t2 +--R + +--R 5 3 2 2 3 4 5 5 +--R t0 t1 + 2t0 t1 t2 - 6t0 t1 t2 - 3t0 t1 t2 + t0 t2 - t1 t2 +--R + +--R 3 3 2 4 5 +--R t1 t2 + 3t1 t2 - 2t1 t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 7 5 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 - 18t0 t2 +--R + +--R 6 6 6 5 6 4 2 6 3 3 6 2 4 +--R 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 6 6 5 7 5 6 5 5 2 +--R 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 4 3 5 3 4 5 2 5 5 6 5 7 +--R - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 + 9t0 t1 t2 - 18t0 t2 +--R + +--R 4 8 4 7 4 6 2 4 5 3 4 3 5 +--R 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 +--R + +--R 4 2 6 4 7 4 8 3 9 3 8 +--R 45t0 t1 t2 - 15t0 t1 t2 + 15t0 t2 - 10t0 t1 - 30t0 t1 t2 +--R + +--R 3 7 2 3 6 3 3 5 4 3 4 5 +--R - 30t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 - 60t0 t1 t2 +--R + +--R 3 3 6 3 2 7 3 8 3 9 2 10 +--R 20t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 - 10t0 t2 + 6t0 t1 +--R + +--R 2 9 2 7 3 2 6 4 2 5 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 60t0 t1 t2 - 63t0 t1 t2 +--R + +--R 2 4 6 2 3 7 2 2 8 2 9 2 10 +--R 90t0 t1 t2 - 75t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 +--R + +--R 11 10 9 2 8 3 7 4 +--R - 3t0 t1 - 3t0 t1 t2 + 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 5 6 4 7 3 8 +--R - 66t0 t1 t2 + 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 +--R + +--R 2 9 10 11 12 11 +--R - 30t0 t1 t2 + 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 +--R 6t1 t2 - 10t1 t2 + 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 +--R + +--R 4 8 3 9 2 10 11 12 +--R 15t1 t2 - 10t1 t2 + 6t1 t2 - 3t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 5 5 4 2 4 4 2 3 2 +--R t0 t1 + 2t0 t2 - 3t0 t1 + 3t0 t1 t2 - 2t0 t2 - 3t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 +--R - 7t0 t1 t2 + 3t0 t2 + 3t0 t1 - t0 t1 t2 + 9t0 t1 t2 +--R + +--R 2 3 2 4 5 4 3 2 +--R 4t0 t1 t2 - 4t0 t2 - t0 t1 - t0 t1 t2 - 3t0 t1 t2 +--R + +--R 2 3 4 5 4 2 3 3 2 4 +--R - 2t0 t1 t2 + t0 t1 t2 + t1 t2 - 2t1 t2 + 4t1 t2 - t1 t2 +--R + +--R 5 6 +--R - 2t1 t2 + t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 7 5 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 - 18t0 t2 +--R + +--R 6 6 6 5 6 4 2 6 3 3 6 2 4 +--R 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 6 6 5 7 5 6 5 5 2 +--R 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 4 3 5 3 4 5 2 5 5 6 5 7 +--R - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 + 9t0 t1 t2 - 18t0 t2 +--R + +--R 4 8 4 7 4 6 2 4 5 3 4 3 5 +--R 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 +--R + +--R 4 2 6 4 7 4 8 3 9 3 8 +--R 45t0 t1 t2 - 15t0 t1 t2 + 15t0 t2 - 10t0 t1 - 30t0 t1 t2 +--R + +--R 3 7 2 3 6 3 3 5 4 3 4 5 +--R - 30t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 - 60t0 t1 t2 +--R + +--R 3 3 6 3 2 7 3 8 3 9 2 10 +--R 20t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 - 10t0 t2 + 6t0 t1 +--R + +--R 2 9 2 7 3 2 6 4 2 5 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 60t0 t1 t2 - 63t0 t1 t2 +--R + +--R 2 4 6 2 3 7 2 2 8 2 9 2 10 +--R 90t0 t1 t2 - 75t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 +--R + +--R 11 10 9 2 8 3 7 4 +--R - 3t0 t1 - 3t0 t1 t2 + 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 5 6 4 7 3 8 +--R - 66t0 t1 t2 + 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 +--R + +--R 2 9 10 11 12 11 +--R - 30t0 t1 t2 + 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 +--R 6t1 t2 - 10t1 t2 + 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 +--R + +--R 4 8 3 9 2 10 11 12 +--R 15t1 t2 - 10t1 t2 + 6t1 t2 - 3t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 5 5 4 2 4 3 3 3 2 +--R 3t0 t1 + t0 t2 - 5t0 t1 - 5t0 t1 t2 + 3t0 t1 + 8t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 +--R - 4t0 t1 t2 - t0 t2 - t0 t1 - 2t0 t1 t2 - 3t0 t1 t2 +--R + +--R 2 3 2 4 5 4 2 3 +--R 10t0 t1 t2 - 3t0 t2 - t0 t1 + 2t0 t1 t2 + 2t0 t1 t2 +--R + +--R 4 5 6 5 4 2 3 3 +--R - 8t0 t1 t2 + 2t0 t2 + t1 - 2t1 t2 - t1 t2 + 4t1 t2 +--R + +--R 2 4 5 +--R - 2t1 t2 + t1 t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 7 5 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 - 18t0 t2 +--R + +--R 6 6 6 5 6 4 2 6 3 3 6 2 4 +--R 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 6 6 5 7 5 6 5 5 2 +--R 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 4 3 5 3 4 5 2 5 5 6 5 7 +--R - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 + 9t0 t1 t2 - 18t0 t2 +--R + +--R 4 8 4 7 4 6 2 4 5 3 4 3 5 +--R 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 +--R + +--R 4 2 6 4 7 4 8 3 9 3 8 +--R 45t0 t1 t2 - 15t0 t1 t2 + 15t0 t2 - 10t0 t1 - 30t0 t1 t2 +--R + +--R 3 7 2 3 6 3 3 5 4 3 4 5 +--R - 30t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 - 60t0 t1 t2 +--R + +--R 3 3 6 3 2 7 3 8 3 9 2 10 +--R 20t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 - 10t0 t2 + 6t0 t1 +--R + +--R 2 9 2 7 3 2 6 4 2 5 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 60t0 t1 t2 - 63t0 t1 t2 +--R + +--R 2 4 6 2 3 7 2 2 8 2 9 2 10 +--R 90t0 t1 t2 - 75t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 +--R + +--R 11 10 9 2 8 3 7 4 +--R - 3t0 t1 - 3t0 t1 t2 + 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 5 6 4 7 3 8 +--R - 66t0 t1 t2 + 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 +--R + +--R 2 9 10 11 12 11 +--R - 30t0 t1 t2 + 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 +--R 6t1 t2 - 10t1 t2 + 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 +--R + +--R 4 8 3 9 2 10 11 12 +--R 15t1 t2 - 10t1 t2 + 6t1 t2 - 3t1 t2 + t2 +--R * +--R xi +--R + +--R 6 5 4 2 4 4 2 3 3 3 2 +--R t0 - t0 t2 - 4t0 t1 + 4t0 t1 t2 - t0 t2 + 3t0 t1 + 4t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 +--R - 10t0 t1 t2 + 3t0 t2 - 2t0 t1 - 5t0 t1 t2 + 9t0 t1 t2 +--R + +--R 2 3 2 4 5 4 3 2 2 3 +--R 7t0 t1 t2 - 5t0 t2 + 2t0 t1 - t0 t1 t2 + t0 t1 t2 - 9t0 t1 t2 +--R + +--R 5 5 4 2 3 3 5 +--R 3t0 t2 - 2t1 t2 + 3t1 t2 + t1 t2 - t1 t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 7 5 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 - 18t0 t2 +--R + +--R 6 6 6 5 6 4 2 6 3 3 6 2 4 +--R 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 6 6 5 7 5 6 5 5 2 +--R 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 4 3 5 3 4 5 2 5 5 6 5 7 +--R - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 + 9t0 t1 t2 - 18t0 t2 +--R + +--R 4 8 4 7 4 6 2 4 5 3 4 3 5 +--R 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 +--R + +--R 4 2 6 4 7 4 8 3 9 3 8 +--R 45t0 t1 t2 - 15t0 t1 t2 + 15t0 t2 - 10t0 t1 - 30t0 t1 t2 +--R + +--R 3 7 2 3 6 3 3 5 4 3 4 5 +--R - 30t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 - 60t0 t1 t2 +--R + +--R 3 3 6 3 2 7 3 8 3 9 2 10 +--R 20t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 - 10t0 t2 + 6t0 t1 +--R + +--R 2 9 2 7 3 2 6 4 2 5 5 2 4 6 +--R 15t0 t1 t2 - 30t0 t1 t2 + 60t0 t1 t2 - 63t0 t1 t2 + 90t0 t1 t2 +--R + +--R 2 3 7 2 2 8 2 9 2 10 11 +--R - 75t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 - 3t0 t1 +--R + +--R 10 9 2 8 3 7 4 +--R - 3t0 t1 t2 + 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 5 6 4 7 3 8 +--R - 66t0 t1 t2 + 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 +--R + +--R 2 9 10 11 12 11 10 2 +--R - 30t0 t1 t2 + 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 + 6t1 t2 +--R + +--R 9 3 8 4 7 5 6 6 5 7 4 8 +--R - 10t1 t2 + 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 + 15t1 t2 +--R + +--R 3 9 2 10 11 12 +--R - 10t1 t2 + 6t1 t2 - 3t1 t2 + t2 +--R * +--R 4 +--R C1 +--R ] --E 18 @ en principe [c**n for c in C] = B <<*>>= --S 19 of 22 -r : List(L) := [reduce(+, [c * xi**(k*j) for j in UZn for c in C]) for k in 0 .. n-1] ; +r : List(L) := [reduce(+, [c * xi**(k*j) for j in UZn for c in C]) for k in 0 .. n-1] +--R +--R +--R (19) +--R [ +--R 5 5 4 2 4 4 2 3 3 +--R 2t0 t1 - t0 t2 - 3t0 t1 + 3t0 t1 t2 + 3t0 t2 - t0 t1 +--R + +--R 3 2 3 2 2 3 2 3 2 4 +--R 6t0 t1 t2 - 14t0 t1 t2 - 2t0 t1 t2 + 14t0 t1 t2 - 3t0 t2 +--R + +--R 5 3 2 2 3 4 5 5 +--R t0 t1 + 2t0 t1 t2 - 6t0 t1 t2 - 3t0 t1 t2 + t0 t2 - t1 t2 +--R + +--R 3 3 2 4 5 +--R t1 t2 + 3t1 t2 - 2t1 t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 +--R + +--R 7 5 6 6 6 5 6 4 2 6 3 3 +--R - 18t0 t2 + 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 +--R + +--R 6 2 4 6 5 6 6 5 7 5 6 +--R 45t0 t1 t2 + 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 +--R + +--R 5 5 2 5 4 3 5 3 4 5 2 5 +--R - 63t0 t1 t2 - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 6 5 7 4 8 4 7 4 6 2 +--R 9t0 t1 t2 - 18t0 t2 + 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 +--R + +--R 4 5 3 4 3 5 4 2 6 4 7 +--R 15t0 t1 t2 + 15t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 +--R + +--R 4 8 3 9 3 8 3 7 2 3 6 3 +--R 15t0 t2 - 10t0 t1 - 30t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 +--R + +--R 3 5 4 3 4 5 3 3 6 3 2 7 +--R 15t0 t1 t2 - 60t0 t1 t2 + 20t0 t1 t2 - 30t0 t1 t2 +--R + +--R 3 8 3 9 2 10 2 9 2 7 3 +--R 15t0 t1 t2 - 10t0 t2 + 6t0 t1 + 15t0 t1 t2 - 30t0 t1 t2 +--R + +--R 2 6 4 2 5 5 2 4 6 2 3 7 +--R 60t0 t1 t2 - 63t0 t1 t2 + 90t0 t1 t2 - 75t0 t1 t2 +--R + +--R 2 2 8 2 9 2 10 11 10 +--R 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 - 3t0 t1 - 3t0 t1 t2 +--R + +--R 9 2 8 3 7 4 6 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 - 66t0 t1 t2 +--R + +--R 5 6 4 7 3 8 2 9 +--R 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 - 30t0 t1 t2 +--R + +--R 10 11 12 11 10 2 9 3 +--R 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 + 6t1 t2 - 10t1 t2 +--R + +--R 8 4 7 5 6 6 5 7 4 8 3 9 +--R 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 + 15t1 t2 - 10t1 t2 +--R + +--R 2 10 11 12 +--R 6t1 t2 - 3t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 5 5 4 2 4 4 2 3 2 +--R t0 t1 + 2t0 t2 - 3t0 t1 + 3t0 t1 t2 - 2t0 t2 - 3t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 +--R - 7t0 t1 t2 + 3t0 t2 + 3t0 t1 - t0 t1 t2 + 9t0 t1 t2 +--R + +--R 2 3 2 4 5 4 3 2 +--R 4t0 t1 t2 - 4t0 t2 - t0 t1 - t0 t1 t2 - 3t0 t1 t2 +--R + +--R 2 3 4 5 4 2 3 3 2 4 +--R - 2t0 t1 t2 + t0 t1 t2 + t1 t2 - 2t1 t2 + 4t1 t2 - t1 t2 +--R + +--R 5 6 +--R - 2t1 t2 + t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 +--R + +--R 7 5 6 6 6 5 6 4 2 6 3 3 +--R - 18t0 t2 + 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 +--R + +--R 6 2 4 6 5 6 6 5 7 5 6 +--R 45t0 t1 t2 + 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 +--R + +--R 5 5 2 5 4 3 5 3 4 5 2 5 +--R - 63t0 t1 t2 - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 6 5 7 4 8 4 7 4 6 2 +--R 9t0 t1 t2 - 18t0 t2 + 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 +--R + +--R 4 5 3 4 3 5 4 2 6 4 7 +--R 15t0 t1 t2 + 15t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 +--R + +--R 4 8 3 9 3 8 3 7 2 3 6 3 +--R 15t0 t2 - 10t0 t1 - 30t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 +--R + +--R 3 5 4 3 4 5 3 3 6 3 2 7 +--R 15t0 t1 t2 - 60t0 t1 t2 + 20t0 t1 t2 - 30t0 t1 t2 +--R + +--R 3 8 3 9 2 10 2 9 2 7 3 +--R 15t0 t1 t2 - 10t0 t2 + 6t0 t1 + 15t0 t1 t2 - 30t0 t1 t2 +--R + +--R 2 6 4 2 5 5 2 4 6 2 3 7 +--R 60t0 t1 t2 - 63t0 t1 t2 + 90t0 t1 t2 - 75t0 t1 t2 +--R + +--R 2 2 8 2 9 2 10 11 10 +--R 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 - 3t0 t1 - 3t0 t1 t2 +--R + +--R 9 2 8 3 7 4 6 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 - 66t0 t1 t2 +--R + +--R 5 6 4 7 3 8 2 9 +--R 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 - 30t0 t1 t2 +--R + +--R 10 11 12 11 10 2 9 3 +--R 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 + 6t1 t2 - 10t1 t2 +--R + +--R 8 4 7 5 6 6 5 7 4 8 3 9 +--R 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 + 15t1 t2 - 10t1 t2 +--R + +--R 2 10 11 12 +--R 6t1 t2 - 3t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 5 5 4 2 4 3 3 3 2 +--R 3t0 t1 + t0 t2 - 5t0 t1 - 5t0 t1 t2 + 3t0 t1 + 8t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 +--R - 4t0 t1 t2 - t0 t2 - t0 t1 - 2t0 t1 t2 - 3t0 t1 t2 +--R + +--R 2 3 2 4 5 4 2 3 +--R 10t0 t1 t2 - 3t0 t2 - t0 t1 + 2t0 t1 t2 + 2t0 t1 t2 +--R + +--R 4 5 6 5 4 2 3 3 +--R - 8t0 t1 t2 + 2t0 t2 + t1 - 2t1 t2 - t1 t2 + 4t1 t2 +--R + +--R 2 4 5 +--R - 2t1 t2 + t1 t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 +--R + +--R 7 5 6 6 6 5 6 4 2 6 3 3 +--R - 18t0 t2 + 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 +--R + +--R 6 2 4 6 5 6 6 5 7 5 6 +--R 45t0 t1 t2 + 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 +--R + +--R 5 5 2 5 4 3 5 3 4 5 2 5 +--R - 63t0 t1 t2 - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 6 5 7 4 8 4 7 4 6 2 +--R 9t0 t1 t2 - 18t0 t2 + 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 +--R + +--R 4 5 3 4 3 5 4 2 6 4 7 +--R 15t0 t1 t2 + 15t0 t1 t2 + 45t0 t1 t2 - 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4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 3 2 2 2 2 2 3 2 +--R - 2t0 t1 + 2t0 t1 + 2t0 t1 t2 - t0 t2 - t0 t1 - t0 t1 t2 +--R + +--R 2 3 2 2 3 4 +--R t0 t1 t2 + t1 t2 - t1 t2 - t1 t2 + t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 3 3 2 2 2 3 2 +--R - t0 t1 - t0 t2 + 2t0 t1 + 3t0 t1 t2 - 2t0 t1 - 3t0 t1 t2 +--R + +--R 3 3 2 2 3 +--R t0 t2 + 2t1 t2 - 2t1 t2 + t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R xi +--R + +--R 3 3 2 2 2 2 2 3 +--R - t0 t1 + t0 t2 + t0 t1 + 3t0 t1 t2 - 2t0 t2 - 2t0 t1 +--R + +--R 2 3 4 2 2 +--R - t0 t1 t2 + 2t0 t2 + t1 - t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 + 6t0 t1 t2 +--R + +--R 7 8 7 6 2 5 3 4 4 3 5 +--R - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 2 6 7 8 +--R 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R C1 +--R + +--R t0 t1 - t1 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 +--R + +--R 3 4 +--R - t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 2 +--R t0 - t0 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 +--R + +--R 3 4 +--R - t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 2 +--R - t0 t2 + t1 - t1 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 +--R + +--R 3 4 +--R - t1 t2 + t2 +--R * +--R xi +--R + +--R 2 +--R t0 t1 - t0 t2 - t1 t2 + t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 3 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 - t1 t2 +--R + +--R 4 +--R t2 +--R * +--R 2 +--R C1 +--R + +--R xi C1 +--R , +--R +--R 6 5 5 4 2 4 4 2 3 2 +--R t0 - 3t0 t1 - 2t0 t2 + t0 t1 + 9t0 t1 t2 - t0 t2 - 4t0 t1 t2 +--R + +--R 3 2 3 3 2 4 2 3 2 2 2 +--R - 6t0 t1 t2 + 4t0 t2 - t0 t1 - 3t0 t1 t2 + 12t0 t1 t2 +--R + +--R 2 3 2 4 5 4 3 2 +--R - 3t0 t1 t2 - 2t0 t2 + 3t0 t1 - 3t0 t1 t2 + t0 t1 t2 +--R + +--R 2 3 4 5 6 4 2 3 3 +--R - 11t0 t1 t2 + 8t0 t1 t2 + t0 t2 - t1 + 4t1 t2 - 3t1 t2 +--R + +--R 2 4 5 +--R 2t1 t2 - 2t1 t2 +--R / +--R 12 11 11 10 2 10 10 2 +--R t0 - 3t0 t1 - 3t0 t2 + 6t0 t1 + 12t0 t1 t2 + 6t0 t2 +--R + +--R 9 3 9 2 9 2 9 3 8 4 +--R - 10t0 t1 - 30t0 t1 t2 - 15t0 t1 t2 - 10t0 t2 + 15t0 t1 +--R + +--R 8 3 8 2 2 8 3 8 4 7 5 +--R 45t0 t1 t2 + 45t0 t1 t2 + 15t0 t1 t2 + 15t0 t2 - 18t0 t1 +--R + +--R 7 4 7 3 2 7 2 3 7 4 +--R - 60t0 t1 t2 - 75t0 t1 t2 - 30t0 t1 t2 - 15t0 t1 t2 +--R + +--R 7 5 6 6 6 5 6 4 2 6 3 3 +--R - 18t0 t2 + 19t0 t1 + 69t0 t1 t2 + 90t0 t1 t2 + 20t0 t1 t2 +--R + +--R 6 2 4 6 5 6 6 5 7 5 6 +--R 45t0 t1 t2 + 9t0 t1 t2 + 19t0 t2 - 18t0 t1 - 66t0 t1 t2 +--R + +--R 5 5 2 5 4 3 5 3 4 5 2 5 +--R - 63t0 t1 t2 - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 6 5 7 4 8 4 7 4 6 2 +--R 9t0 t1 t2 - 18t0 t2 + 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 +--R + +--R 4 5 3 4 3 5 4 2 6 4 7 +--R 15t0 t1 t2 + 15t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 +--R + +--R 4 8 3 9 3 8 3 7 2 3 6 3 +--R 15t0 t2 - 10t0 t1 - 30t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 +--R + +--R 3 5 4 3 4 5 3 3 6 3 2 7 +--R 15t0 t1 t2 - 60t0 t1 t2 + 20t0 t1 t2 - 30t0 t1 t2 +--R + +--R 3 8 3 9 2 10 2 9 2 7 3 +--R 15t0 t1 t2 - 10t0 t2 + 6t0 t1 + 15t0 t1 t2 - 30t0 t1 t2 +--R + +--R 2 6 4 2 5 5 2 4 6 2 3 7 +--R 60t0 t1 t2 - 63t0 t1 t2 + 90t0 t1 t2 - 75t0 t1 t2 +--R + +--R 2 2 8 2 9 2 10 11 10 +--R 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 - 3t0 t1 - 3t0 t1 t2 +--R + +--R 9 2 8 3 7 4 6 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 - 66t0 t1 t2 +--R + +--R 5 6 4 7 3 8 2 9 +--R 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 - 30t0 t1 t2 +--R + +--R 10 11 12 11 10 2 9 3 +--R 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 + 6t1 t2 - 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18t0 t1 - 66t0 t1 t2 - 63t0 t1 t2 +--R + +--R 5 4 3 5 3 4 5 2 5 5 6 5 7 +--R - 60t0 t1 t2 + 15t0 t1 t2 - 63t0 t1 t2 + 9t0 t1 t2 - 18t0 t2 +--R + +--R 4 8 4 7 4 6 2 4 5 3 4 3 5 +--R 15t0 t1 + 45t0 t1 t2 + 60t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 +--R + +--R 4 2 6 4 7 4 8 3 9 3 8 +--R 45t0 t1 t2 - 15t0 t1 t2 + 15t0 t2 - 10t0 t1 - 30t0 t1 t2 +--R + +--R 3 7 2 3 6 3 3 5 4 3 4 5 +--R - 30t0 t1 t2 + 15t0 t1 t2 + 15t0 t1 t2 - 60t0 t1 t2 +--R + +--R 3 3 6 3 2 7 3 8 3 9 2 10 +--R 20t0 t1 t2 - 30t0 t1 t2 + 15t0 t1 t2 - 10t0 t2 + 6t0 t1 +--R + +--R 2 9 2 7 3 2 6 4 2 5 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 60t0 t1 t2 - 63t0 t1 t2 +--R + +--R 2 4 6 2 3 7 2 2 8 2 9 2 10 +--R 90t0 t1 t2 - 75t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 +--R + +--R 11 10 9 2 8 3 7 4 +--R - 3t0 t1 - 3t0 t1 t2 + 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 5 6 4 7 3 8 +--R - 66t0 t1 t2 + 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 +--R + +--R 2 9 10 11 12 11 +--R - 30t0 t1 t2 + 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 +--R 6t1 t2 - 10t1 t2 + 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 +--R + +--R 4 8 3 9 2 10 11 12 +--R 15t1 t2 - 10t1 t2 + 6t1 t2 - 3t1 t2 + t2 +--R * +--R 4 +--R C1 +--R + +--R 3 2 2 2 2 2 2 3 +--R 2t0 t2 - t0 t1 - 2t0 t2 - t0 t1 t2 + 3t0 t1 t2 + t0 t2 +--R + +--R 4 3 2 2 3 +--R t1 - 2t1 t2 + t1 t2 - t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 3 3 2 2 2 3 2 +--R t0 t1 + t0 t2 - 2t0 t1 - 3t0 t1 t2 + 2t0 t1 + 3t0 t1 t2 +--R + +--R 3 3 2 2 3 +--R - t0 t2 - 2t1 t2 + 2t1 t2 - t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 4 3 2 2 2 2 2 3 2 +--R t0 - t0 t1 - t0 t1 + t0 t1 t2 - t0 t2 + t0 t1 - t0 t1 t2 +--R + +--R 2 3 2 2 3 +--R 2t0 t1 t2 - t1 t2 + 2t1 t2 - 2t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R xi +--R + +--R 3 3 2 2 2 3 2 +--R - t0 t1 + t0 t2 - t0 t1 t2 - t0 t2 + t0 t1 - t0 t1 t2 +--R + +--R 2 3 3 2 2 3 4 +--R 4t0 t1 t2 - t0 t2 - t1 t2 + t1 t2 - 2t1 t2 + t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 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10t0 t2 + 6t0 t1 +--R + +--R 2 9 2 7 3 2 6 4 2 5 5 +--R 15t0 t1 t2 - 30t0 t1 t2 + 60t0 t1 t2 - 63t0 t1 t2 +--R + +--R 2 4 6 2 3 7 2 2 8 2 9 2 10 +--R 90t0 t1 t2 - 75t0 t1 t2 + 45t0 t1 t2 - 15t0 t1 t2 + 6t0 t2 +--R + +--R 11 10 9 2 8 3 7 4 +--R - 3t0 t1 - 3t0 t1 t2 + 15t0 t1 t2 - 30t0 t1 t2 + 45t0 t1 t2 +--R + +--R 6 5 5 6 4 7 3 8 +--R - 66t0 t1 t2 + 69t0 t1 t2 - 60t0 t1 t2 + 45t0 t1 t2 +--R + +--R 2 9 10 11 12 11 +--R - 30t0 t1 t2 + 12t0 t1 t2 - 3t0 t2 + t1 - 3t1 t2 +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 +--R 6t1 t2 - 10t1 t2 + 15t1 t2 - 18t1 t2 + 19t1 t2 - 18t1 t2 +--R + +--R 4 8 3 9 2 10 11 12 +--R 15t1 t2 - 10t1 t2 + 6t1 t2 - 3t1 t2 + t2 +--R * +--R 4 +--R C1 +--R + +--R 3 3 2 2 2 2 2 3 +--R t0 t1 - t0 t2 - t0 t1 - 3t0 t1 t2 + 2t0 t2 + 2t0 t1 +--R + +--R 2 3 4 2 2 +--R t0 t1 t2 - 2t0 t2 - t1 + t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 4 3 3 2 2 2 3 2 +--R t0 - t0 t1 - 2t0 t2 + t0 t1 t2 + t0 t2 + t0 t1 - t0 t1 t2 +--R + +--R 3 4 3 2 2 3 +--R - t0 t2 - t1 + t1 t2 + t1 t2 - t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 3 3 2 2 2 2 2 3 +--R - t0 t1 - t0 t2 + t0 t1 - t0 t1 t2 + t0 t2 + t0 t1 +--R + +--R 2 3 4 3 3 4 +--R t0 t1 t2 - 2t0 t2 - t1 + t1 t2 - t1 t2 + t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 6t0 t1 t2 - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 +--R + +--R 4 4 3 5 2 6 7 8 +--R 5t1 t2 - 4t1 t2 + 3t1 t2 - 2t1 t2 + t2 +--R * +--R xi +--R + +--R 3 2 2 2 2 2 2 3 +--R - 2t0 t2 + t0 t1 + 2t0 t2 + t0 t1 t2 - 3t0 t1 t2 - t0 t2 +--R + +--R 4 3 2 2 3 +--R - t1 + 2t1 t2 - t1 t2 + t1 t2 +--R / +--R 8 7 7 6 2 6 6 2 5 3 +--R t0 - 2t0 t1 - 2t0 t2 + 3t0 t1 + 6t0 t1 t2 + 3t0 t2 - 4t0 t1 +--R + +--R 5 2 5 2 5 3 4 4 4 3 +--R - 12t0 t1 t2 - 2t0 t1 t2 - 4t0 t2 + 5t0 t1 + 10t0 t1 t2 +--R + +--R 4 2 2 4 4 3 5 3 4 3 3 2 +--R 10t0 t1 t2 + 5t0 t2 - 4t0 t1 - 10t0 t1 t2 - 10t0 t1 t2 +--R + +--R 3 5 2 6 2 5 2 4 2 2 3 3 +--R - 4t0 t2 + 3t0 t1 + 8t0 t1 t2 + 5t0 t1 t2 - 10t0 t1 t2 +--R + +--R 2 2 4 2 5 2 6 7 6 +--R 10t0 t1 t2 - 2t0 t1 t2 + 3t0 t2 - 2t0 t1 - 4t0 t1 t2 +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8t0 t1 t2 - 10t0 t1 t2 + 10t0 t1 t2 - 12t0 t1 t2 + 6t0 t1 t2 +--R + +--R 7 8 7 6 2 5 3 4 4 3 5 +--R - 2t0 t2 + t1 - 2t1 t2 + 3t1 t2 - 4t1 t2 + 5t1 t2 - 4t1 t2 +--R + +--R 2 6 7 8 +--R 3t1 t2 - 2t1 t2 + t2 +--R * +--R 3 +--R C1 +--R + +--R 2 +--R t0 - t0 t1 - t0 t2 + t1 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 +--R + +--R 3 4 +--R - t1 t2 + t2 +--R * +--R 3 +--R xi +--R + +--R 2 +--R - t0 t1 - t0 t2 + t1 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 +--R + +--R 3 4 +--R - t1 t2 + t2 +--R * +--R 2 +--R xi +--R + +--R 2 +--R - t0 t2 + t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 +--R + +--R 3 4 +--R - t1 t2 + t2 +--R * +--R xi +--R + +--R - t0 t1 + t1 t2 +--R / +--R 4 3 3 2 2 2 2 2 3 +--R t0 - t0 t1 - t0 t2 + t0 t1 + 2t0 t1 t2 + t0 t2 - t0 t1 +--R + +--R 2 2 3 4 3 2 2 3 +--R - 3t0 t1 t2 + 2t0 t1 t2 - t0 t2 + t1 - t1 t2 + t1 t2 - t1 t2 +--R + +--R 4 +--R t2 +--R * +--R 2 +--R C1 +--R + +--R 3 2 +--R (- xi - xi - xi - 1)C1 +--R ] --E 19 --S 20 of 22 -LX := UP('X, L) ; X : LX := monomial(1, 1) ; +LX := UP('X, L) ; X : LX := monomial(1, 1) +--R +--R +--R (20) X --E 20 --S 21 of 22 -g : LX := reduce(*, [X - rho for rho in r]) ; +g : LX := reduce(*, [X - rho for rho in r]) +--R +--R +--R (21) +--R 5 +--R X +--R + +--R 4 3 3 2 2 2 2 2 +--R - 10t0 + 10t0 t1 + 10t0 t2 - 10t0 t1 - 20t0 t1 t2 - 10t0 t2 +--R + +--R 3 2 2 3 4 3 +--R 10t0 t1 + 30t0 t1 t2 - 20t0 t1 t2 + 10t0 t2 - 10t1 + 10t1 t2 +--R + +--R 2 2 3 4 +--R - 10t1 t2 + 10t1 t2 - 10t2 +--R * +--R 3 +--R X +--R + +--R 6 5 5 4 2 4 4 2 +--R - 20t0 + 30t0 t1 + 30t0 t2 - 25t0 t1 - 75t0 t1 t2 - 25t0 t2 +--R + +--R 3 3 3 2 3 3 2 4 2 3 2 2 2 +--R 25t0 t1 + 100t0 t1 t2 + 25t0 t2 - 25t0 t1 - 25t0 t1 t2 - 50t0 t1 t2 +--R + +--R 2 3 2 4 5 3 2 2 3 +--R 25t0 t1 t2 - 25t0 t2 + 5t0 t1 + 50t0 t1 t2 - 50t0 t1 t2 +--R + +--R 4 5 6 5 4 2 3 3 2 4 +--R 25t0 t1 t2 + 5t0 t2 + 5t1 - 20t1 t2 + 25t1 t2 - 25t1 t2 + 25t1 t2 +--R + +--R 5 6 +--R - 20t1 t2 + 5t2 +--R * +--R 2 +--R X +--R + +--R 8 7 7 6 2 6 6 2 +--R - 15t0 + 30t0 t1 + 30t0 t2 - 20t0 t1 - 90t0 t1 t2 - 20t0 t2 +--R + +--R 5 3 5 2 5 2 5 3 4 3 +--R 10t0 t1 + 105t0 t1 t2 + 55t0 t1 t2 + 10t0 t2 - 50t0 t1 t2 +--R + +--R 4 2 2 4 3 3 5 3 4 3 3 2 +--R - 100t0 t1 t2 + 25t0 t1 t2 - 15t0 t1 - 25t0 t1 t2 + 125t0 t1 t2 +--R + +--R 3 2 3 3 4 3 5 2 6 2 5 +--R - 75t0 t1 t2 + 25t0 t1 t2 - 15t0 t2 + 30t0 t1 + 5t0 t1 t2 +--R + +--R 2 3 3 2 2 4 2 5 2 6 7 +--R - 125t0 t1 t2 + 150t0 t1 t2 - 45t0 t1 t2 + 30t0 t2 - 20t0 t1 +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 15t0 t1 t2 + 80t0 t1 t2 - 25t0 t1 t2 - 50t0 t1 t2 - 20t0 t1 t2 +--R + +--R 6 7 8 7 6 2 5 3 +--R 35t0 t1 t2 - 20t0 t2 + 10t1 - 20t1 t2 + 5t1 t2 + 10t1 t2 +--R + +--R 3 5 2 6 7 8 +--R 10t1 t2 - 20t1 t2 + 5t1 t2 + 10t2 +--R * +--R X +--R + +--R 10 9 9 8 2 8 8 2 7 3 +--R - 4t0 + 10t0 t1 + 10t0 t2 - 5t0 t1 - 35t0 t1 t2 - 5t0 t2 - 5t0 t1 +--R + +--R 7 2 7 2 7 3 6 4 6 3 6 2 2 +--R 35t0 t1 t2 + 35t0 t1 t2 - 5t0 t2 + 15t0 t1 + 5t0 t1 t2 - 70t0 t1 t2 +--R + +--R 6 4 5 5 5 4 5 3 2 5 2 3 5 5 +--R 15t0 t2 - 28t0 t1 - 45t0 t1 t2 + 55t0 t1 t2 + 25t0 t1 t2 - 28t0 t2 +--R + +--R 4 6 4 5 4 3 3 4 2 4 4 5 4 6 +--R 35t0 t1 + 60t0 t1 t2 - 125t0 t1 t2 + 50t0 t1 t2 - 15t0 t1 t2 + 35t0 t2 +--R + +--R 3 7 3 6 3 5 2 3 4 3 3 3 4 +--R - 30t0 t1 - 60t0 t1 t2 + 20t0 t1 t2 + 125t0 t1 t2 - 25t0 t1 t2 +--R + +--R 3 2 5 3 6 3 7 2 8 2 7 +--R - 30t0 t1 t2 + 15t0 t1 t2 - 30t0 t2 + 20t0 t1 + 35t0 t1 t2 +--R + +--R 2 6 2 2 5 3 2 4 4 2 3 5 2 2 6 +--R - 65t0 t1 t2 + 20t0 t1 t2 - 125t0 t1 t2 + 145t0 t1 t2 - 40t0 t1 t2 +--R + +--R 2 7 2 8 9 8 7 2 +--R - 15t0 t1 t2 + 20t0 t2 - 10t0 t1 + 5t0 t1 t2 - 20t0 t1 t2 +--R + +--R 6 3 5 4 4 5 3 6 2 7 +--R 100t0 t1 t2 - 110t0 t1 t2 + 65t0 t1 t2 - 45t0 t1 t2 + 30t0 t1 t2 +--R + +--R 9 10 9 8 2 7 3 6 4 5 5 +--R - 10t0 t2 + t1 + 5t1 t2 - 20t1 t2 + 25t1 t2 - 25t1 t2 + 27t1 t2 +--R + +--R 4 6 3 7 10 +--R - 20t1 t2 + 5t1 t2 + t2 --E 21 --S 22 of 22 diff --git a/src/input/reclos.input.pamphlet b/src/input/reclos.input.pamphlet index 5967963..1e96d74 100644 --- a/src/input/reclos.input.pamphlet +++ b/src/input/reclos.input.pamphlet @@ -425,7 +425,7 @@ These came from J.M. Arnaudies )cl prop s4 s7 e1 e2 ---S 39 of 70 +--S 39 of 70 s3 := sqrt(3)$Ran --R --R @@ -486,7 +486,7 @@ ee1::Boolean )cl prop pol r1 alpha beta ---S 45 of 70 +--S 45 of 70 pol : UP(x,Ran) := x**4+(7/3)*x**2+30*x-(100/3) --R --R @@ -544,7 +544,7 @@ pol.(alpha+beta-1/3) )cl prop qol r2 alpha beta ---S 50 of 70 +--S 50 of 70 r2 := sqrt(153)$Ran --R --R diff --git a/src/input/schaum1.input.pamphlet b/src/input/schaum1.input.pamphlet index 615d907..6af52a9 100644 --- a/src/input/schaum1.input.pamphlet +++ b/src/input/schaum1.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 108 aa:=integrate(1/(a*x+b),x) --R --R log(a x + b) @@ -27,7 +27,7 @@ aa:=integrate(1/(a*x+b),x) --R Type: Union(Expression Integer,...) --E 1 ---S 2 +--S 2 of 108 bb:=1/a*log(a*x+b) --R --R log(a x + b) @@ -36,7 +36,7 @@ bb:=1/a*log(a*x+b) --R Type: Expression Integer --E ---S 3 14:59 Schaums and Axiom agree +--S 3 of 108 14:59 Schaums and Axiom agree cc:=bb-aa --R --R (3) 0 @@ -51,7 +51,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 108 aa:=integrate(x/(a*x+b),x) --R --R @@ -62,7 +62,7 @@ aa:=integrate(x/(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 108 bb:=x/a-b/a^2*log(a*x+b) --R --R - b log(a x + b) + a x @@ -72,7 +72,7 @@ bb:=x/a-b/a^2*log(a*x+b) --R Type: Expression Integer --E ---S 6 14:60 Schaums and Axiom agree +--S 6 of 108 14:60 Schaums and Axiom agree cc:=bb-aa --R --R (3) 0 @@ -88,7 +88,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 108 aa:=integrate(x^2/(a*x+b),x) --R --R 2 2 2 @@ -99,7 +99,7 @@ aa:=integrate(x^2/(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 108 bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b) --R --R 2 2 2 2 @@ -110,7 +110,7 @@ bb:=(a*x+b)^2/(2*a^3)-(2*b*(a*x+b))/a^3+b^2/a^3*log(a*x+b) --R Type: Expression Integer --E ---S 9 +--S 9 of 108 cc:=bb-aa --R --R 2 @@ -124,7 +124,7 @@ cc:=bb-aa This factor is constant with respect to $x$ as shown by taking the derivative. It is a constant of integration. <<*>>= ---S 10 14:61 Schaums and Axiom differ by a constant +--S 10 of 108 14:61 Schaums and Axiom differ by a constant differentiate(cc,x) --R --R (4) 0 @@ -140,7 +140,7 @@ $$ <<*>>= )clear all ---S 11 +--S 11 of 108 aa:=integrate(x^3/(a*x+b),x) --R --R 3 3 3 2 2 2 @@ -153,7 +153,7 @@ aa:=integrate(x^3/(a*x+b),x) @ and the book expression is: <<*>>= ---S 12 +--S 12 of 108 bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log(a*x+b) --R --R 3 3 3 2 2 2 3 @@ -167,7 +167,7 @@ bb:=(a*x+b)^3/(3*a^4)-(3*b*(a*x+b)^2)/(2*a^4)+(3*b^2*(a*x+b))/a^4-(b^3/a^4)*log( The difference is a constant with respect to x: <<*>>= ---S 13 +--S 13 of 108 cc:=aa-bb --R --R 3 @@ -182,7 +182,7 @@ cc:=aa-bb If we differentiate each expression we see that this is the integration constant. <<*>>= ---S 14 14:62 Schaums and Axiom differ by a constant +--S 14 of 108 14:62 Schaums and Axiom differ by a constant dd:=D(cc,x) --R --R (4) 0 @@ -198,7 +198,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 108 aa:=integrate(1/(x*(a*x+b)),x) --R --R - log(a x + b) + log(x) @@ -207,7 +207,7 @@ aa:=integrate(1/(x*(a*x+b)),x) --R Type: Union(Expression Integer,...) --E ---S 16 +--S 16 of 108 bb:=1/b*log(x/(a*x+b)) --R --R x @@ -218,7 +218,7 @@ bb:=1/b*log(x/(a*x+b)) --R Type: Expression Integer --E ---S 17 +--S 17 of 108 cc:=aa-bb --R --R x @@ -233,7 +233,7 @@ but we know that $$\log(a)-\log(b)=\log(\frac{a}{b})$$ We can express this fact as a rule: <<*>>= ---S 18 +--S 18 of 108 logdiv:=rule(log(a)-log(b) == log(a/b)) --R --R a @@ -244,7 +244,7 @@ logdiv:=rule(log(a)-log(b) == log(a/b)) @ and use this rule to rewrite the logs into divisions: <<*>>= ---S 19 14:63 Schaums and Axiom agree +--S 19 of 108 14:63 Schaums and Axiom agree dd:=logdiv cc --R --R (5) 0 @@ -261,7 +261,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 108 aa:=integrate(1/(x^2*(a*x+b)),x) --R --R a x log(a x + b) - a x log(x) - b @@ -274,7 +274,7 @@ aa:=integrate(1/(x^2*(a*x+b)),x) The original form given in the book expands to: <<*>>= ---S 21 +--S 21 of 108 bb:=-1/(b*x)+a/b^2*log((a*x+b)/x) --R --R a x + b @@ -286,7 +286,7 @@ bb:=-1/(b*x)+a/b^2*log((a*x+b)/x) --R Type: Expression Integer --E ---S 22 +--S 22 of 108 cc:=aa-bb --R --R a x + b @@ -301,7 +301,7 @@ cc:=aa-bb We can define the following rule to expand log forms: <<*>>= ---S 23 +--S 23 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -312,7 +312,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) @ and apply it to the difference <<*>>= ---S 24 14:64 Schaums and Axiom agree +--S 24 of 108 14:64 Schaums and Axiom agree divlog cc --R --R (5) 0 @@ -327,7 +327,7 @@ $$\int{\frac{1}{x^3~(ax+b)}}= $$ <<*>>= )clear all ---S 25 +--S 25 of 108 aa:=integrate(1/(x^3*(a*x+b)),x) --R --R 2 2 2 2 2 @@ -338,7 +338,7 @@ aa:=integrate(1/(x^3*(a*x+b)),x) --R Type: Union(Expression Integer,...) --E ---S 26 +--S 26 of 108 bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b)) --R --R 2 2 x 2 @@ -350,7 +350,7 @@ bb:=(2*a*x-b)/(2*b^2*x^2)+a^2/b^3*log(x/(a*x+b)) --R Type: Expression Integer --E ---S 27 +--S 27 of 108 cc:=aa-bb --R --R 2 2 2 x @@ -362,7 +362,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 28 +--S 28 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -371,7 +371,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 29 14:65 Schaums and Axiom agree +--S 29 of 108 14:65 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -387,7 +387,7 @@ $$ <<*>>= )clear all ---S 30 +--S 30 of 108 aa:=integrate(1/(a*x+b)^2,x) --R --R 1 @@ -397,7 +397,7 @@ aa:=integrate(1/(a*x+b)^2,x) --R Type: Union(Expression Integer,...) --E ---S 31 +--S 31 of 108 bb:=-1/(a*(a*x+b)) --R --R 1 @@ -407,7 +407,7 @@ bb:=-1/(a*(a*x+b)) --R Type: Fraction Polynomial Integer --E ---S 32 14:66 Schaums and Axiom agree +--S 32 of 108 14:66 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -424,7 +424,7 @@ $$ <<*>>= )clear all ---S 33 +--S 33 of 108 aa:=integrate(x/(a*x+b)^2,x) --R --R (a x + b)log(a x + b) + b @@ -434,7 +434,7 @@ aa:=integrate(x/(a*x+b)^2,x) --R Type: Union(Expression Integer,...) --E ---S 34 +--S 34 of 108 bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b) --R --R (a x + b)log(a x + b) + b @@ -444,7 +444,7 @@ bb:=b/(a^2*(a*x+b))+1/a^2*log(a*x+b) --R Type: Expression Integer --E ---S 35 14:67 Schaums and Axiom agree +--S 35 of 108 14:67 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -462,7 +462,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 108 aa:=integrate(x^2/(a*x+b)^2,x) --R --R 2 2 2 2 @@ -475,7 +475,7 @@ aa:=integrate(x^2/(a*x+b)^2,x) @ and the book expression expands into <<*>>= ---S 37 +--S 37 of 108 bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b) --R --R 2 2 2 @@ -489,7 +489,7 @@ bb:=(a*x+b)/a^3-b^2/(a^3*(a*x+b))-((2*b)/a^3)*log(a*x+b) These two expressions differ by the constant <<*>>= ---S 38 +--S 38 of 108 cc:=aa-bb --R --R b @@ -502,7 +502,7 @@ cc:=aa-bb That this expression is constant can be shown by differentiation: <<*>>= ---S 39 14:68 Schaums and Axiom differ by a constant +--S 39 of 108 14:68 Schaums and Axiom differ by a constant D(cc,x) --R --R (4) 0 @@ -519,7 +519,7 @@ $$ <<*>>= )clear all ---S 40 +--S 40 of 108 aa:=integrate(x^3/(a*x+b)^2,x) --R --R 2 3 3 3 2 2 2 3 @@ -530,7 +530,7 @@ aa:=integrate(x^3/(a*x+b)^2,x) --R Type: Union(Expression Integer,...) --E ---S 41 +--S 41 of 108 bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b) --R --R 2 3 3 3 2 2 2 3 @@ -541,7 +541,7 @@ bb:=(a*x+b)^2/(2*a^4)-(3*b*(a*x+b))/a^4+b^3/(a^4*(a*x+b))+(3*b^2/a^4)*log(a*x+b) --R Type: Expression Integer --E ---S 42 +--S 42 of 108 cc:=aa-bb --R --R 2 @@ -552,7 +552,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 43 14:69 Schaums and Axiom differ by a constant +--S 43 of 108 14:69 Schaums and Axiom differ by a constant dd:=D(cc,x) --R --R (4) 0 @@ -567,7 +567,7 @@ $$ <<*>>= )clear all ---S 44 +--S 44 of 108 aa:=integrate(1/(x*(a*x+b)^2),x) --R --R (- a x - b)log(a x + b) + (a x + b)log(x) + b @@ -579,7 +579,7 @@ aa:=integrate(1/(x*(a*x+b)^2),x) @ and the book says: <<*>>= ---S 45 +--S 45 of 108 bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b))) --R --R x @@ -591,7 +591,7 @@ bb:=(1/(b*(a*x+b))+(1/b^2)*log(x/(a*x+b))) --R Type: Expression Integer --E ---S 46 +--S 46 of 108 cc:=aa-bb --R --R x @@ -605,7 +605,7 @@ cc:=aa-bb @ So we look at the divlog rule again: <<*>>= ---S 47 +--S 47 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -617,7 +617,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) we apply it: <<*>>= ---S 48 14:70 Schaums and Axiom agree +--S 48 of 108 14:70 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -634,7 +634,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 108 aa:=integrate(1/(x^2*(a*x+b)^2),x) --R --R 2 2 2 2 2 @@ -647,7 +647,7 @@ aa:=integrate(1/(x^2*(a*x+b)^2),x) @ and the book says: <<*>>= ---S 50 +--S 50 of 108 bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x) --R --R 2 2 a x + b 2 @@ -659,7 +659,7 @@ bb:=(-a/(b^2*(a*x+b)))-(1/(b^2*x))+((2*a)/b^3)*log((a*x+b)/x) --R Type: Expression Integer --E ---S 51 +--S 51 of 108 cc:=aa-bb --R --R a x + b @@ -673,7 +673,7 @@ cc:=aa-bb @ which calls for our divlog rule: <<*>>= ---S 52 +--S 52 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -684,7 +684,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) @ which we use to transform the result: <<*>>= ---S 53 14:71 Schaums and Axiom agree +--S 53 of 108 14:71 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -700,7 +700,7 @@ $$ <<*>>= )clear all ---S 54 +--S 54 of 108 aa:=integrate(1/(x^3*(a*x+b)^2),x) --R --R (1) @@ -715,7 +715,7 @@ aa:=integrate(1/(x^3*(a*x+b)^2),x) --R Type: Union(Expression Integer,...) --E ---S 55 +--S 55 of 108 bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/b^4)*log((a*x+b)/x) --R --R 3 3 2 2 a x + b 3 3 2 2 2 3 @@ -727,7 +727,7 @@ bb:=-(a*x+b)^2/(2*b^4*x^2)+(3*a*(a*x+b))/(b^4*x)-(a^3*x)/(b^4*(a*x+b))-((3*a^2)/ --R Type: Expression Integer --E ---S 56 +--S 56 of 108 cc:=aa-bb --R --R 2 2 2 a x + b 2 @@ -739,7 +739,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 57 +--S 57 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -748,7 +748,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 58 +--S 58 of 108 dd:=divlog cc --R --R 2 @@ -759,7 +759,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 59 14:72 Schaums and Axiom differ by a constant +--S 59 of 108 14:72 Schaums and Axiom differ by a constant ee:=D(dd,x) --R --R (6) 0 @@ -775,7 +775,7 @@ $$ <<*>>= )clear all ---S 60 +--S 60 of 108 aa:=integrate(1/(a*x+b)^3,x) --R --R 1 @@ -785,7 +785,7 @@ aa:=integrate(1/(a*x+b)^3,x) --R Type: Union(Expression Integer,...) --E ---S 61 +--S 61 of 108 bb:=-1/(2*(a*x+b)^2) --R --R 1 @@ -795,7 +795,7 @@ bb:=-1/(2*(a*x+b)^2) --R Type: Fraction Polynomial Integer --E ---S 62 +--S 62 of 108 cc:=aa-bb --R --R a - 1 @@ -805,7 +805,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 63 +--S 63 of 108 dd:=aa/bb --R --R 1 @@ -814,7 +814,7 @@ dd:=aa/bb --R Type: Expression Integer --E ---S 64 14:73 Schaums and Axiom differ by a constant +--S 64 of 108 14:73 Schaums and Axiom differ by a constant ee:=D(dd,x) --R --R (5) 0 @@ -830,7 +830,7 @@ $$ <<*>>= )clear all ---S 65 +--S 65 of 108 aa:=integrate(x/(a*x+b)^3,x) --R --R - 2a x - b @@ -840,7 +840,7 @@ aa:=integrate(x/(a*x+b)^3,x) --R Type: Union(Expression Integer,...) --E ---S 66 +--S 66 of 108 bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2) --R --R - 2a x - b @@ -850,7 +850,7 @@ bb:=-1/(a^2*(a*x+b))+b/(2*a^2*(a*x+b)^2) --R Type: Fraction Polynomial Integer --E ---S 67 14:74 Schaums and Axiom agree +--S 67 of 108 14:74 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -867,7 +867,7 @@ $$ <<*>>= )clear all ---S 68 +--S 68 of 108 aa:=integrate(x^2/(a*x+b)^3,x) --R --R 2 2 2 2 @@ -878,7 +878,7 @@ aa:=integrate(x^2/(a*x+b)^3,x) --R Type: Union(Expression Integer,...) --E ---S 69 +--S 69 of 108 bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b) --R --R 2 2 2 2 @@ -889,7 +889,7 @@ bb:=(2*b)/(a^3*(a*x+b))-(b^2)/(2*a^3*(a*x+b)^2)+1/a^3*log(a*x+b) --R Type: Expression Integer --E ---S 70 14:75 Schaums and Axiom agree +--S 70 of 108 14:75 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -905,7 +905,7 @@ $$\int{\frac{x^3}{(ax+b)^3}}= $$ <<*>>= )clear all ---S 71 +--S 71 of 108 aa:=integrate(x^3/(a*x+b)^3,x) --R --R (1) @@ -917,7 +917,7 @@ aa:=integrate(x^3/(a*x+b)^3,x) --R Type: Union(Expression Integer,...) --E ---S 72 +--S 72 of 108 bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b) --R --R (2) @@ -929,7 +929,7 @@ bb:=(x/a^3)-(3*b^2)/(a^4*(a*x+b))+b^3/(2*a^4*(a*x+b)^2)-(3*b)/a^4*log(a*x+b) --R Type: Expression Integer --E ---S 73 14:76 Schaums and Axiom agree +--S 73 of 108 14:76 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -947,7 +947,7 @@ $$ <<*>>= )clear all ---S 74 +--S 74 of 108 aa:=integrate(1/(x*(a*x+b)^3),x) --R --R (1) @@ -962,7 +962,7 @@ aa:=integrate(1/(x*(a*x+b)^3),x) --R Type: Union(Expression Integer,...) --E ---S 75 +--S 75 of 108 bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x) --R --R 2 2 2 a x + b 2 2 @@ -974,7 +974,7 @@ bb:=(a^2*x^2)/(2*b^3*(a*x+b)^2)-(2*a*x)/(b^3*(a*x+b))-(1/b^3)*log((a*x+b)/x) --R Type: Expression Integer --E ---S 76 +--S 76 of 108 cc:=aa-bb --R --R a x + b @@ -986,7 +986,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 77 +--S 77 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -995,7 +995,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 78 +--S 78 of 108 dd:=divlog cc --R --R 3 @@ -1005,7 +1005,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 79 14:77 Schaums and Axiom differ by a constant +--S 79 of 108 14:77 Schaums and Axiom differ by a constant ee:=D(dd,x) --R --R (6) 0 @@ -1022,7 +1022,7 @@ $$ <<*>>= )clear all ---S 80 +--S 80 of 108 aa:=integrate(1/(x^2*(a*x+b)^3),x) --R --R (1) @@ -1037,7 +1037,7 @@ aa:=integrate(1/(x^2*(a*x+b)^3),x) --R Type: Union(Expression Integer,...) --E ---S 81 +--S 81 of 108 bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x) --R --R 3 3 2 2 2 a x + b 2 2 2 3 @@ -1049,7 +1049,7 @@ bb:=-a/(2*b^2*(a*x+b)^2)-(2*a)/(b^3*(a*x+b))-1/(b^3*x)+((3*a)/b^4)*log((a*x+b)/x --R Type: Expression Integer --E ---S 82 +--S 82 of 108 cc:=aa-bb --R --R a x + b @@ -1061,7 +1061,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 83 +--S 83 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -1070,7 +1070,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 84 14:78 Schaums and Axiom agree +--S 84 of 108 14:78 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -1090,7 +1090,7 @@ $$\int{\frac{1}{x^3(ax+b)^3}}= <<*>>= )clear all ---S 85 +--S 85 of 108 aa:=integrate(1/(x^3*(a*x+b)^3),x) --R --R (1) @@ -1105,7 +1105,7 @@ aa:=integrate(1/(x^3*(a*x+b)^3),x) --R Type: Union(Expression Integer,...) --E ---S 86 +--S 86 of 108 bb:=-1/(2*b*x^2*(a*x+b)^2)_ +(2*a)/(b^2*x*(a*x+b)^2)_ +(9*a^2)/(b^3*(a*x+b)^2)_ @@ -1125,7 +1125,7 @@ bb:=-1/(2*b*x^2*(a*x+b)^2)_ --R Type: Expression Integer --E ---S 87 +--S 87 of 108 cc:=aa-bb --R --R 2 2 2 a x + b @@ -1137,7 +1137,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 88 +--S 88 of 108 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -1146,7 +1146,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 89 14:79 Schaums and Axiom agree +--S 89 of 108 14:79 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -1161,7 +1161,7 @@ $$\int{(ax+b)^n}= $$ <<*>>= )clear all ---S 90 +--S 90 of 108 aa:=integrate((a*x+b)^n,x) --R --R n log(a x + b) @@ -1171,7 +1171,7 @@ aa:=integrate((a*x+b)^n,x) --R Type: Union(Expression Integer,...) --E ---S 91 +--S 91 of 108 bb:=(a*x+b)^(n+1)/((n+1)*a) --R --R n + 1 @@ -1181,7 +1181,7 @@ bb:=(a*x+b)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 92 +--S 92 of 108 cc:=aa-bb --R --R n log(a x + b) n + 1 @@ -1193,7 +1193,7 @@ cc:=aa-bb @ This messy formula can be simplified using the explog rule: <<*>>= ---S 93 +--S 93 of 108 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1201,7 +1201,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 94 +--S 94 of 108 dd:=explog cc --R --R n + 1 n @@ -1211,7 +1211,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 95 14:80 Schaums and Axiom agree +--S 95 of 108 14:80 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1227,7 +1227,7 @@ $$\int{x(ax+b)^n}= $$ <<*>>= )clear all ---S 96 +--S 96 of 108 aa:=integrate(x*(a*x+b)^n,x) --R --R 2 2 2 2 n log(a x + b) @@ -1238,7 +1238,7 @@ aa:=integrate(x*(a*x+b)^n,x) --R Type: Union(Expression Integer,...) --E ---S 97 +--S 97 of 108 bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2) --R --R n + 2 n + 1 @@ -1249,7 +1249,7 @@ bb:=((a*x+b)^(n+2))/((n+2)*a^2)-(b*(a*x+b)^(n+1))/((n+1)*a^2) --R Type: Expression Integer --E ---S 98 +--S 98 of 108 cc:=aa-bb --R --R (3) @@ -1264,7 +1264,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 99 +--S 99 of 108 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1272,7 +1272,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 100 +--S 100 of 108 dd:=explog cc --R --R (5) @@ -1287,7 +1287,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 101 +--S 101 of 108 ee:=complexNormalize dd --R --R (6) 0 @@ -1305,7 +1305,7 @@ $$ <<*>>= )clear all ---S 102 +--S 102 of 108 aa:=integrate(x^2*(a*x+b)^n,x) --R --R (1) @@ -1317,7 +1317,7 @@ aa:=integrate(x^2*(a*x+b)^n,x) --R Type: Union(Expression Integer,...) --E ---S 103 +--S 103 of 108 bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1))/((n+1)*a^3) --R --R (2) @@ -1332,7 +1332,7 @@ bb:=(a*x+b)^(n+3)/((n+3)*a^3)-(2*b*(a*x+b)^(n+2))/((n+2)*a^3)+(b^2*(a*x+b)^(n+1) --R Type: Expression Integer --E ---S 104 +--S 104 of 108 cc:=aa-bb --R --R (3) @@ -1353,7 +1353,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 105 +--S 105 of 108 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1361,7 +1361,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 106 +--S 106 of 108 dd:=explog cc --R --R (5) @@ -1379,7 +1379,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 107 14:82 Schaums and Axiom agree +--S 107 of 108 14:82 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1407,7 +1407,7 @@ $$\int{x^m(ax+b)^n} $$ <<*>>= ---S 108 14:83 Axiom cannot do this integration +--S 108 of 108 14:83 Axiom cannot do this integration aa:=integrate(x^m*(a*x+b)^n,x) --R --R x diff --git a/src/input/schaum10.input.pamphlet b/src/input/schaum10.input.pamphlet index 6149cc0..4daac8c 100644 --- a/src/input/schaum10.input.pamphlet +++ b/src/input/schaum10.input.pamphlet @@ -15,7 +15,7 @@ $$\int{\frac{1}{\sqrt{x^2-a^2}}}=\ln\left(x+\sqrt{x^2-a^2}\right)$$ )set message auto off )clear all ---S 1 +--S 1 of 150 aa:=integrate(1/(sqrt(x^2-a^2)),x) --R --R @@ -25,7 +25,7 @@ aa:=integrate(1/(sqrt(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 150 bb:=log(x+sqrt(x^2-a^2)) --R --R +-------+ @@ -34,7 +34,7 @@ bb:=log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 3 +--S 3 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -43,14 +43,14 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 150 logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b)) --R --I (4) c log(b) + c log(a) + %I == c log(a b) + %I --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 14:210 Schaums and Axiom differ by a constant +--S 5 of 150 14:210 Schaums and Axiom differ by a constant dd:=logmul1 cc --R --R 2 @@ -64,7 +64,7 @@ $$\int{\frac{x}{\sqrt{x^2-a^2}}}=\sqrt{x^2-a^2}$$ <<*>>= )clear all ---S 6 +--S 6 of 150 aa:=integrate(x/(sqrt(x^2-a^2)),x) --R --R @@ -78,7 +78,7 @@ aa:=integrate(x/(sqrt(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 7 +--S 7 of 150 bb:=sqrt(x^2-a^2) --R --R +-------+ @@ -87,7 +87,7 @@ bb:=sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 8 14:xxx Schaums and Axiom agree +--S 8 of 150 14:xxx Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -103,7 +103,7 @@ $$ <<*>>= )clear all ---S 9 +--S 9 of 150 aa:=integrate(x^2/sqrt(x^2-a^2),x) --R --R @@ -122,7 +122,7 @@ aa:=integrate(x^2/sqrt(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 10 +--S 10 of 150 bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -133,7 +133,7 @@ bb:=(x*sqrt(x^2-a^2))/2+a^2/2*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 11 +--S 11 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -144,7 +144,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 12 14:211 Schaums and Axiom differ by a constant +--S 12 of 150 14:211 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 2 @@ -164,7 +164,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 150 aa:=integrate(x^3/sqrt(x^2-a^2),x) --R --R @@ -178,7 +178,7 @@ aa:=integrate(x^3/sqrt(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 150 bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2) --R --R +-------+ @@ -189,7 +189,7 @@ bb:=(x^2-a^2)^(3/2)/3+a^2*sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 15 14:212 Schaums and Axiom agree +--S 15 of 150 14:212 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -204,7 +204,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 150 aa:=integrate(1/(x*sqrt(x^2-a^2)),x) --R --R @@ -218,7 +218,7 @@ aa:=integrate(1/(x*sqrt(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 150 bb:=1/a*asec(x/a) --R --R x @@ -229,7 +229,7 @@ bb:=1/a*asec(x/a) --R Type: Expression Integer --E ---S 18 +--S 18 of 150 cc:=aa-bb --R --R +-------+ @@ -242,7 +242,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 19 +--S 19 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -258,7 +258,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 20 +--S 20 of 150 dd:=asecrule cc --R --R +-------+ @@ -274,7 +274,7 @@ dd:=asecrule cc --R Type: Expression Complex Integer --E ---S 21 +--S 21 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -285,7 +285,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 22 +--S 22 of 150 ee:=atanrule dd --R --R +-------+ @@ -303,7 +303,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 23 +--S 23 of 150 ff:=expandLog ee --R --R (8) @@ -322,7 +322,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 24 +--S 24 of 150 gg:=rootSimp ff --R --R (9) @@ -338,7 +338,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 25 14:213 Schaums and Axiom differ by a constant +--S 25 of 150 14:213 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R %pi @@ -356,7 +356,7 @@ $$ <<*>>= )clear all ---S 26 +--S 26 of 150 aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x) --R --R @@ -368,7 +368,7 @@ aa:=integrate(1/(x^2*sqrt(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 27 +--S 27 of 150 bb:=sqrt(x^2-a^2)/(a^2*x) --R --R +-------+ @@ -380,7 +380,7 @@ bb:=sqrt(x^2-a^2)/(a^2*x) --R Type: Expression Integer --E ---S 28 14:214 Schaums and Axiom differ by a constant +--S 28 of 150 14:214 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 1 @@ -399,7 +399,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 150 aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x) --R --R @@ -420,7 +420,7 @@ aa:=integrate(1/(x^3*sqrt(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 150 bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a) --R --R +-------+ @@ -433,7 +433,7 @@ bb:=sqrt(x^2-a^2)/(2*a^2*x^2)+1/(2*a^3)*asec(x/a) --R Type: Expression Integer --E ---S 31 +--S 31 of 150 cc:=aa-bb --R --R @@ -448,7 +448,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 +--S 32 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -459,7 +459,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 33 +--S 33 of 150 dd:=atanrule cc --R --R +-------+ @@ -475,7 +475,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 34 +--S 34 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -491,7 +491,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 35 +--S 35 of 150 ee:=asecrule dd --R --R +-------+ @@ -510,7 +510,7 @@ ee:=asecrule dd --R Type: Expression Complex Integer --E ---S 36 +--S 36 of 150 ff:=expandLog ee --R --R (8) @@ -530,7 +530,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 37 +--S 37 of 150 gg:=rootSimp ff --R --R (9) @@ -547,7 +547,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 38 14:215 Schaums and Axiom differ by a constant +--S 38 of 150 14:215 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R %pi @@ -566,7 +566,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 150 aa:=integrate(sqrt(x^2-a^2),x) --R --R @@ -585,7 +585,7 @@ aa:=integrate(sqrt(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 150 bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -596,7 +596,7 @@ bb:=(x*sqrt(x^2-a^2))/2-a^2/2*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 41 +--S 41 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -607,7 +607,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 42 14:216 Schaums and Axiom differ by a constant +--S 42 of 150 14:216 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 2 @@ -625,7 +625,7 @@ $$ <<*>>= )clear all ---S 43 +--S 43 of 150 aa:=integrate(x*sqrt(x^2-a^2),x) --R --R @@ -639,7 +639,7 @@ aa:=integrate(x*sqrt(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 44 +--S 44 of 150 bb:=(x^2-a^2)^(3/2)/3 --R --R +-------+ @@ -650,7 +650,7 @@ bb:=(x^2-a^2)^(3/2)/3 --R Type: Expression Integer --E ---S 45 14:217 Schaums and Axiom agree +--S 45 of 150 14:217 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -667,7 +667,7 @@ $$ <<*>>= )clear all ---S 46 +--S 46 of 150 aa:=integrate(x^2*sqrt(x^2-a^2),x) --R --R @@ -686,7 +686,7 @@ aa:=integrate(x^2*sqrt(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 47 +--S 47 of 150 bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -697,7 +697,7 @@ bb:=(x*(x^2-a^2)^(3/2))/4+(a^2*x*sqrt(x^2-a^2))/8-a^4/8*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 48 +--S 48 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -708,7 +708,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 49 14:218 Schaums and Axiom differ by a constant +--S 49 of 150 14:218 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 4 2 @@ -727,7 +727,7 @@ $$ <<*>>= )clear all ---S 50 +--S 50 of 150 aa:=integrate(x^3*sqrt(x^2-a^2),x) --R --R @@ -745,7 +745,7 @@ aa:=integrate(x^3*sqrt(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 51 +--S 51 of 150 bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3 --R --R +-------+ @@ -756,7 +756,7 @@ bb:=(x^2-a^2)^(5/2)/5+(a^2*(x^2-a^2)^(3/2))/3 --R Type: Expression Integer --E ---S 52 14:219 Schaums and Axiom agree +--S 52 of 150 14:219 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -772,7 +772,7 @@ $$ <<*>>= )clear all ---S 53 +--S 53 of 150 aa:=integrate(sqrt(x^2-a^2)/x,x) --R --R @@ -788,7 +788,7 @@ aa:=integrate(sqrt(x^2-a^2)/x,x) --R Type: Union(Expression Integer,...) --E ---S 54 +--S 54 of 150 bb:=sqrt(x^2-a^2)-a*asec(x/a) --R --R +-------+ @@ -798,7 +798,7 @@ bb:=sqrt(x^2-a^2)-a*asec(x/a) --R Type: Expression Integer --E ---S 55 +--S 55 of 150 cc:=aa-bb --R --R +-------+ @@ -809,7 +809,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 56 +--S 56 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -820,7 +820,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 57 +--S 57 of 150 dd:=atanrule cc --R --R +-------+ @@ -833,7 +833,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 58 +--S 58 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -849,7 +849,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 59 +--S 59 of 150 ee:=asecrule dd --R --R (7) @@ -868,7 +868,7 @@ ee:=asecrule dd --R Type: Expression Complex Integer --E ---S 60 +--S 60 of 150 ff:=expandLog ee --R --R (8) @@ -887,7 +887,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 61 +--S 61 of 150 gg:=rootSimp ff --R --R (9) @@ -903,7 +903,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 62 14:220 Schaums and Axiom differ by a constant +--S 62 of 150 14:220 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R a %pi @@ -921,7 +921,7 @@ $$ <<*>>= )clear all ---S 63 +--S 63 of 150 aa:=integrate(sqrt(x^2-a^2)/x^2,x) --R --R @@ -935,7 +935,7 @@ aa:=integrate(sqrt(x^2-a^2)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 64 +--S 64 of 150 bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -946,7 +946,7 @@ bb:=-sqrt(x^2-a^2)/x+log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 65 +--S 65 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -955,7 +955,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 66 14:221 Schaums and Axiom differ by a constant +--S 66 of 150 14:221 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 @@ -974,7 +974,7 @@ $$ <<*>>= )clear all ---S 67 +--S 67 of 150 aa:=integrate(sqrt(x^2-a^2)/x^3,x) --R --R @@ -995,7 +995,7 @@ aa:=integrate(sqrt(x^2-a^2)/x^3,x) --R Type: Union(Expression Integer,...) --E ---S 68 +--S 68 of 150 bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a) --R --R +-------+ @@ -1008,7 +1008,7 @@ bb:=-sqrt(x^2-a^2)/(2*x^2)+1/(2*a)*asec(x/a) --R Type: Expression Integer --E ---S 69 +--S 69 of 150 cc:=aa-bb --R --R +-------+ @@ -1021,7 +1021,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 70 +--S 70 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -1037,7 +1037,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 71 +--S 71 of 150 dd:=asecrule cc --R --R +-------+ @@ -1053,7 +1053,7 @@ dd:=asecrule cc --R Type: Expression Complex Integer --E ---S 72 +--S 72 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1064,7 +1064,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 73 +--S 73 of 150 ee:=atanrule dd --R --R +-------+ @@ -1082,7 +1082,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 74 +--S 74 of 150 ff:=expandLog ee --R --R (8) @@ -1101,7 +1101,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 75 +--S 75 of 150 gg:=rootSimp ff --R --R (9) @@ -1117,7 +1117,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 76 14:222 Schaums and Axiom differ by a constant +--S 76 of 150 14:222 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R %pi @@ -1134,7 +1134,7 @@ $$ <<*>>= )clear all ---S 77 +--S 77 of 150 aa:=integrate(1/(x^2-a^2)^(3/2),x) --R --R @@ -1146,7 +1146,7 @@ aa:=integrate(1/(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 78 +--S 78 of 150 bb:=-x/(a^2*sqrt(x^2-a^2)) --R --R x @@ -1157,7 +1157,7 @@ bb:=-x/(a^2*sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 79 14:223 Schaums and Axiom differ by a constant +--S 79 of 150 14:223 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 1 @@ -1176,7 +1176,7 @@ $$ <<*>>= )clear all ---S 80 +--S 80 of 150 aa:=integrate(x/(x^2-a^2)^(3/2),x) --R --R @@ -1190,7 +1190,7 @@ aa:=integrate(x/(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 81 +--S 81 of 150 bb:=-1/sqrt(x^2-a^2) --R --R 1 @@ -1201,7 +1201,7 @@ bb:=-1/sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 82 14:224 Schaums and Axiom agree +--S 82 of 150 14:224 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1217,7 +1217,7 @@ $$ <<*>>= )clear all ---S 83 +--S 83 of 150 aa:=integrate(x^2/(x^2-a^2)^(3/2),x) --R --R @@ -1231,7 +1231,7 @@ aa:=integrate(x^2/(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 84 +--S 84 of 150 bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -1244,7 +1244,7 @@ bb:=-x/sqrt(x^2-a^2)+log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 85 +--S 85 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -1253,7 +1253,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 86 14:225 Schaums and Axiom differ by a constant +--S 86 of 150 14:225 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 @@ -1270,7 +1270,7 @@ $$ <<*>>= )clear all ---S 87 +--S 87 of 150 aa:=integrate(x^3/(x^2-a^2)^(3/2),x) --R --R @@ -1284,7 +1284,7 @@ aa:=integrate(x^3/(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 88 +--S 88 of 150 bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2) --R --R 2 2 @@ -1296,7 +1296,7 @@ bb:=sqrt(x^2-a^2)-a^2/sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 89 14:226 Schaums and Axiom agree +--S 89 of 150 14:226 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1313,7 +1313,7 @@ $$ <<*>>= )clear all ---S 90 +--S 90 of 150 aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x) --R --R @@ -1329,7 +1329,7 @@ aa:=integrate(1/(x*(x^2-a^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 91 +--S 91 of 150 bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a) --R --R +-------+ @@ -1343,7 +1343,7 @@ bb:=-1/(a^2*sqrt(x^2-a^2))-1/a^3*asec(x/a) --R Type: Expression Integer --E ---S 92 +--S 92 of 150 cc:=aa-bb --R --R +-------+ @@ -1357,7 +1357,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 93 +--S 93 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1368,7 +1368,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 94 +--S 94 of 150 dd:=atanrule cc --R --R +-------+ @@ -1384,7 +1384,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 95 +--S 95 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -1400,7 +1400,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 96 +--S 96 of 150 ee:=asecrule dd --R --R +-------+ @@ -1419,7 +1419,7 @@ ee:=asecrule dd --R Type: Expression Complex Integer --E ---S 97 +--S 97 of 150 ff:=expandLog ee --R --R (8) @@ -1439,7 +1439,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 98 +--S 98 of 150 gg:=rootSimp ff --R --R (9) @@ -1456,7 +1456,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 99 14:227 Schaums and Axiom differ by a constant +--S 99 of 150 14:227 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R %pi @@ -1476,7 +1476,7 @@ $$ <<*>>= )clear all ---S 100 +--S 100 of 150 aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x) --R --R @@ -1488,7 +1488,7 @@ aa:=integrate(1/(x^2*(x^2-a^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 101 +--S 101 of 150 bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2)) --R --R 2 2 @@ -1500,7 +1500,7 @@ bb:=-sqrt(x^2-a^2)/(a^4*x)-x/(a^4*sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 102 14:228 Schaums and Axiom differ by a constant +--S 102 of 150 14:228 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 2 @@ -1522,7 +1522,7 @@ $$ <<*>>= )clear all ---S 103 +--S 103 of 150 aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x) --R --R @@ -1543,7 +1543,7 @@ aa:=integrate(1/(x^3*(x^2-a^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 104 +--S 104 of 150 bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a) --R --R +-------+ @@ -1557,7 +1557,7 @@ bb:=1/(2*a^2*x^2*sqrt(x^2-a^2))-3/(2*a^4*sqrt(x^2-a^2))-3/(2*a^5)*asec(x/a) --R Type: Expression Integer --E ---S 105 +--S 105 of 150 cc:=aa-bb --R --R +-------+ @@ -1571,7 +1571,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 106 +--S 106 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1582,7 +1582,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 107 +--S 107 of 150 dd:=atanrule cc --R --R +-------+ @@ -1598,7 +1598,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 108 +--S 108 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -1614,7 +1614,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 109 +--S 109 of 150 ee:=asecrule dd --R --R +-------+ @@ -1633,7 +1633,7 @@ ee:=asecrule dd --R Type: Expression Complex Integer --E ---S 110 +--S 110 of 150 ff:=expandLog ee --R --R (8) @@ -1653,7 +1653,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 111 +--S 111 of 150 gg:=rootSimp ff --R --R (9) @@ -1670,7 +1670,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 112 14:229 Schaums and Axiom differ by a constant +--S 112 of 150 14:229 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R 3%pi @@ -1688,7 +1688,7 @@ $$ <<*>>= )clear all ---S 113 +--S 113 of 150 aa:=integrate((x^2-a^2)^(3/2),x) --R --R @@ -1710,7 +1710,7 @@ aa:=integrate((x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 114 +--S 114 of 150 bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -1721,7 +1721,7 @@ bb:=(x*(x^2-a^2)^(3/2))/4-(3*a^2*x*sqrt(x^2-a^2))/8+3/8*a^4*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 115 +--S 115 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -1732,7 +1732,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 116 14:230 Schaums and Axiom differ by a constant +--S 116 of 150 14:230 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 4 2 @@ -1749,7 +1749,7 @@ $$\int{x(x^2-a^2)^{3/2}}=\frac{(x^2-a^2)^{5/2}}{5}$$ <<*>>= )clear all ---S 117 +--S 117 of 150 aa:=integrate(x*(x^2-a^2)^(3/2),x) --R --R @@ -1767,7 +1767,7 @@ aa:=integrate(x*(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 118 +--S 118 of 150 bb:=(x^2-a^2)^(5/2)/5 --R --R +-------+ @@ -1778,7 +1778,7 @@ bb:=(x^2-a^2)^(5/2)/5 --R Type: Expression Integer --E ---S 119 14:231 Schaums and Axiom agree +--S 119 of 150 14:231 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1795,7 +1795,7 @@ $$ <<*>>= )clear all ---S 120 +--S 120 of 150 aa:=integrate(x^2*(x^2-a^2)^(3/2),x) --R --R @@ -1824,7 +1824,7 @@ aa:=integrate(x^2*(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 121 +--S 121 of 150 bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^6/16*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -1835,7 +1835,7 @@ bb:=(x*(x^2-a^2)^(5/2))/6+(a^2*x*(x^2-a^2)^(3/2))/24-(a^4*x*sqrt(x^2-a^2))/16+a^ --R Type: Expression Integer --E ---S 122 +--S 122 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -1846,7 +1846,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 123 14:232 Schaums and Axiom differ by a constant +--S 123 of 150 14:232 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 6 2 @@ -1864,7 +1864,7 @@ $$ <<*>>= )clear all ---S 124 +--S 124 of 150 aa:=integrate(x^3*(x^2-a^2)^(3/2),x) --R --R @@ -1894,7 +1894,7 @@ aa:=integrate(x^3*(x^2-a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 125 +--S 125 of 150 bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5 --R --R +-------+ @@ -1905,7 +1905,7 @@ bb:=(x^2-a^2)^(7/2)/7+(a^2*(x^2-a^2)^(5/2))/5 --R Type: Expression Integer --E ---S 126 14:233 Schaums and Axiom agree +--S 126 of 150 14:233 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1922,7 +1922,7 @@ $$ <<*>>= )clear all ---S 127 +--S 127 of 150 aa:=integrate((x^2-a^2)^(3/2)/x,x) --R --R @@ -1943,7 +1943,7 @@ aa:=integrate((x^2-a^2)^(3/2)/x,x) --R Type: Union(Expression Integer,...) --E ---S 128 +--S 128 of 150 bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a) --R --R +-------+ @@ -1955,7 +1955,7 @@ bb:=(x^2-a^2)^(3/2)/3-a^2*sqrt(x^2-a^2)+a^3*asec(x/a) --R Type: Expression Integer --E ---S 129 +--S 129 of 150 cc:=aa-bb --R --R +-------+ @@ -1966,7 +1966,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 130 +--S 130 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -1982,7 +1982,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 131 +--S 131 of 150 dd:=asecrule cc --R --R +-------+ @@ -1998,7 +1998,7 @@ dd:=asecrule cc --R Type: Expression Complex Integer --E ---S 132 +--S 132 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2009,7 +2009,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 133 +--S 133 of 150 ee:=atanrule dd --R --R (7) @@ -2028,7 +2028,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 134 +--S 134 of 150 ff:=expandLog ee --R --R (8) @@ -2047,7 +2047,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 135 +--S 135 of 150 gg:=rootSimp ff --R --R (9) @@ -2063,7 +2063,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 136 14:234 Schaums and Axiom differ by a constant +--S 136 of 150 14:234 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R 3 @@ -2083,7 +2083,7 @@ $$ <<*>>= )clear all ---S 137 +--S 137 of 150 aa:=integrate((x^2-a^2)^{3/2}/x^2,x) --R --R @@ -2102,7 +2102,7 @@ aa:=integrate((x^2-a^2)^{3/2}/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 138 +--S 138 of 150 bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -2113,7 +2113,7 @@ bb:=-(x^2-a^2)^(3/2)/x+3*x*sqrt(x^2-a^2)/2-3/2*a^2*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 139 +--S 139 of 150 cc:=aa-bb --R --R +-------+ +-------+ @@ -2124,7 +2124,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 140 14:235 Schaums and Axiom differ by a constant +--S 140 of 150 14:235 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 2 2 @@ -2145,7 +2145,7 @@ $$ <<*>>= )clear all ---S 141 +--S 141 of 150 aa:=integrate((x^2-a^2)^(3/2)/x^3,x) --R --R @@ -2166,7 +2166,7 @@ aa:=integrate((x^2-a^2)^(3/2)/x^3,x) --R Type: Union(Expression Integer,...) --E ---S 142 +--S 142 of 150 bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a) --R --R +-------+ @@ -2179,7 +2179,7 @@ bb:=-(x^2-a^2)^(3/2)/(2*x^2)+(3*sqrt(x^2-a^2))/2-3/2*a*asec(x/a) --R Type: Expression Integer --E ---S 143 +--S 143 of 150 cc:=aa-bb --R --R +-------+ @@ -2192,7 +2192,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 144 +--S 144 of 150 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2203,7 +2203,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 145 +--S 145 of 150 dd:=atanrule cc --R --R +-------+ @@ -2218,7 +2218,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 146 +--S 146 of 150 asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R --R +------+ @@ -2234,7 +2234,7 @@ asecrule:=rule(asec(x) == 1/2*%pi+%i*log(sqrt(1-1/x^2)+%i/x)) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 147 +--S 147 of 150 ee:=asecrule dd --R --R (7) @@ -2253,7 +2253,7 @@ ee:=asecrule dd --R Type: Expression Complex Integer --E ---S 148 +--S 148 of 150 ff:=expandLog ee --R --R (8) @@ -2272,7 +2272,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 149 +--S 149 of 150 gg:=rootSimp ff --R --R (9) @@ -2288,7 +2288,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 150 14:236 Schaums and Axiom differ by a constant +--S 150 of 150 14:236 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R 3a %pi diff --git a/src/input/schaum11.input.pamphlet b/src/input/schaum11.input.pamphlet index fc3117e..84bc9ab 100644 --- a/src/input/schaum11.input.pamphlet +++ b/src/input/schaum11.input.pamphlet @@ -15,7 +15,7 @@ $$\int{\frac{1}{\sqrt{a^2-x^2}}}=\ln\left(x+\sqrt{a^2-x^2}\right)$$ )set message auto off )clear all ---S 1 +--S 1 of 170 aa:=integrate(1/(sqrt(a^2-x^2)),x) --R --R @@ -27,7 +27,7 @@ aa:=integrate(1/(sqrt(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 170 bb:=asin(x/a) --R --R x @@ -36,7 +36,7 @@ bb:=asin(x/a) --R Type: Expression Integer --E ---S 3 +--S 3 of 170 cc:=aa-bb --R --R +---------+ @@ -47,7 +47,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -58,7 +58,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 5 +--S 5 of 170 dd:=atanrule cc --R --R +---------+ @@ -71,7 +71,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 6 +--S 6 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -80,7 +80,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 7 +--S 7 of 170 ee:=asinrule dd --R --R +---------+ @@ -96,7 +96,7 @@ ee:=asinrule dd --R Type: Expression Complex Integer --E ---S 8 +--S 8 of 170 ff:=rootSimp ee --R --R +-------+ +-------+ @@ -109,7 +109,7 @@ ff:=rootSimp ee --R Type: Expression Complex Integer --E ---S 9 14:238 Schaums and Axiom agree +--S 9 of 170 14:238 Schaums and Axiom agree gg:=complexNormalize ff --R --R (9) 0 @@ -123,7 +123,7 @@ $$\int{\frac{x}{\sqrt{a^2-x^2}}}=\sqrt{a^2-x^2}$$ <<*>>= )clear all ---S 10 +--S 10 of 170 aa:=integrate(x/(sqrt(a^2-x^2)),x) --R --R @@ -136,7 +136,7 @@ aa:=integrate(x/(sqrt(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 170 bb:=-sqrt(a^2-x^2) --R --R +---------+ @@ -145,7 +145,7 @@ bb:=-sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 12 14:238 Schaums and Axiom differ by a constant +--S 12 of 170 14:238 Schaums and Axiom differ by a constant cc:=aa-bb --R --R (3) - a @@ -161,7 +161,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 170 aa:=integrate(x^2/sqrt(a^2-x^2),x) --R --R @@ -182,7 +182,7 @@ aa:=integrate(x^2/sqrt(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 170 bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a) --R --R +---------+ @@ -194,7 +194,7 @@ bb:=-(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a) --R Type: Expression Integer --E ---S 15 +--S 15 of 170 cc:=aa-bb --R --R +---------+ @@ -207,7 +207,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 16 +--S 16 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -218,7 +218,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 17 +--S 17 of 170 dd:=atanrule cc --R --R +---------+ @@ -233,7 +233,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 18 +--S 18 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -242,7 +242,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 19 +--S 19 of 170 ee:=asinrule dd --R --R +---------+ @@ -260,7 +260,7 @@ ee:=asinrule dd --R Type: Expression Complex Integer --E ---S 20 +--S 20 of 170 ff:=expandLog ee --R --R (8) @@ -279,7 +279,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 21 +--S 21 of 170 gg:=rootSimp ff --R --R (9) @@ -295,7 +295,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 22 14:239 Schaums and Axiom agree +--S 22 of 170 14:239 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -312,7 +312,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 170 aa:=integrate(x^3/sqrt(a^2-x^2),x) --R --R @@ -326,7 +326,7 @@ aa:=integrate(x^3/sqrt(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 170 bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2) --R --R +---------+ @@ -337,7 +337,7 @@ bb:=(a^2-x^2)^(3/2)/3-a^2*sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 25 14:240 Schaums and Axiom differ by a constant +--S 25 of 170 14:240 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 3 @@ -355,7 +355,7 @@ $$ <<*>>= )clear all ---S 26 +--S 26 of 170 aa:=integrate(1/(x*sqrt(a^2-x^2)),x) --R --R @@ -369,7 +369,7 @@ aa:=integrate(1/(x*sqrt(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 27 +--S 27 of 170 bb:=-1/a*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -382,7 +382,7 @@ bb:=-1/a*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 28 +--S 28 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -395,7 +395,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 29 +--S 29 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -406,7 +406,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 30 +--S 30 of 170 ee:=complexNormalize dd --R --R x @@ -419,7 +419,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 31 14:241 Schaums and Axiom differ by a constant +--S 31 of 170 14:241 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ @@ -438,7 +438,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 170 aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x) --R --R @@ -452,7 +452,7 @@ aa:=integrate(1/(x^2*sqrt(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 170 bb:=-sqrt(a^2-x^2)/(a^2*x) --R --R +---------+ @@ -464,7 +464,7 @@ bb:=-sqrt(a^2-x^2)/(a^2*x) --R Type: Expression Integer --E ---S 34 14:242 Schaums and Axiom agree +--S 34 of 170 14:242 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -480,7 +480,7 @@ $$ <<*>>= )clear all ---S 35 +--S 35 of 170 aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x) --R --R @@ -501,7 +501,7 @@ aa:=integrate(1/(x^3*sqrt(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 36 +--S 36 of 170 bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -515,7 +515,7 @@ bb:=-sqrt(a^2-x^2)/(2*a^2*x^2)-1/(2*a^3)*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 37 +--S 37 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -529,7 +529,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 38 +--S 38 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -541,7 +541,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 39 +--S 39 of 170 ee:=complexNormalize dd --R --R x @@ -555,7 +555,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 40 14:243 Schaums and Axiom differ by a constant +--S 40 of 170 14:243 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ @@ -574,7 +574,7 @@ $$ <<*>>= )clear all ---S 41 +--S 41 of 170 aa:=integrate(sqrt(a^2-x^2),x) --R --R @@ -595,7 +595,7 @@ aa:=integrate(sqrt(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 170 bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a) --R --R +---------+ @@ -607,7 +607,7 @@ bb:=(x*sqrt(a^2-x^2))/2+a^2/2*asin(x/a) --R Type: Expression Integer --E ---S 43 +--S 43 of 170 cc:=aa-bb --R --R +---------+ @@ -620,7 +620,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 44 +--S 44 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -629,7 +629,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 45 +--S 45 of 170 dd:=asinrule cc --R --R +---------+ @@ -645,7 +645,7 @@ dd:=asinrule cc --R Type: Expression Complex Integer --E ---S 46 +--S 46 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -656,7 +656,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 47 +--S 47 of 170 ee:=atanrule dd --R --R +---------+ @@ -674,7 +674,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 48 +--S 48 of 170 ff:=expandLog ee --R --R (8) @@ -693,7 +693,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 49 +--S 49 of 170 gg:=rootSimp ff --R --R (9) @@ -709,7 +709,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 50 14:244 Schaums and Axiom agree +--S 50 of 170 14:244 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -724,7 +724,7 @@ $$ <<*>>= )clear all ---S 51 +--S 51 of 170 aa:=integrate(x*sqrt(a^2-x^2),x) --R --R @@ -738,7 +738,7 @@ aa:=integrate(x*sqrt(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 52 +--S 52 of 170 bb:=-(a^2-x^2)^(3/2)/3 --R --R +---------+ @@ -749,7 +749,7 @@ bb:=-(a^2-x^2)^(3/2)/3 --R Type: Expression Integer --E ---S 53 14:245 Schaums and Axiom differ by a constant +--S 53 of 170 14:245 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 3 @@ -769,7 +769,7 @@ $$ <<*>>= )clear all ---S 54 +--S 54 of 170 aa:=integrate(x^2*sqrt(a^2-x^2),x) --R --R @@ -794,7 +794,7 @@ aa:=integrate(x^2*sqrt(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 55 +--S 55 of 170 bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a) --R --R +---------+ @@ -806,7 +806,7 @@ bb:=-(x*(a^2-x^2)^(3/2))/4+(a^2*x*sqrt(a^2-x^2))/8+a^4/8*asin(x/a) --R Type: Expression Integer --E ---S 56 +--S 56 of 170 cc:=aa-bb --R --R +---------+ @@ -819,7 +819,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 57 +--S 57 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -830,7 +830,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 58 +--S 58 of 170 dd:=atanrule cc --R --R +---------+ @@ -845,7 +845,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 59 +--S 59 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -854,7 +854,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 60 +--S 60 of 170 ee:=asinrule dd --R --R +---------+ @@ -872,7 +872,7 @@ ee:=asinrule dd --R Type: Expression Complex Integer --E ---S 61 +--S 61 of 170 ff:=expandLog ee --R --R (8) @@ -891,7 +891,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 62 +--S 62 of 170 gg:=rootSimp ff --R --R (9) @@ -907,7 +907,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 63 14:246 Schaums and Axiom agree +--S 63 of 170 14:246 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -923,7 +923,7 @@ $$ <<*>>= )clear all ---S 64 +--S 64 of 170 aa:=integrate(x^3*sqrt(a^2-x^2),x) --R --R @@ -938,7 +938,7 @@ aa:=integrate(x^3*sqrt(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 65 +--S 65 of 170 bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3 --R --R +---------+ @@ -949,7 +949,7 @@ bb:=(a^2-x^2)^(5/2)/5-(a^2*(a^2-x^2)^(3/2))/3 --R Type: Expression Integer --E ---S 66 14:247 Schaums and Axiom differ by a constant +--S 66 of 170 14:247 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 5 @@ -968,7 +968,7 @@ $$ <<*>>= )clear all ---S 67 +--S 67 of 170 aa:=integrate(sqrt(a^2-x^2)/x,x) --R --R @@ -984,7 +984,7 @@ aa:=integrate(sqrt(a^2-x^2)/x,x) --R Type: Union(Expression Integer,...) --E ---S 68 +--S 68 of 170 bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -995,7 +995,7 @@ bb:=sqrt(a^2-x^2)-a*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 69 +--S 69 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -1006,7 +1006,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 70 +--S 70 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -1015,7 +1015,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 71 +--S 71 of 170 ee:=complexNormalize dd --R --R x @@ -1026,7 +1026,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 72 14:248 Schaums and Axiom differ by a constant +--S 72 of 170 14:248 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ @@ -1043,7 +1043,7 @@ $$ <<*>>= )clear all ---S 73 +--S 73 of 170 aa:=integrate(sqrt(a^2-x^2)/x^2,x) --R --R @@ -1060,7 +1060,7 @@ aa:=integrate(sqrt(a^2-x^2)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 74 +--S 74 of 170 bb:=-sqrt(a^2-x^2)/x-asin(x/a) --R --R +---------+ @@ -1072,7 +1072,7 @@ bb:=-sqrt(a^2-x^2)/x-asin(x/a) --R Type: Expression Integer --E ---S 75 +--S 75 of 170 cc:=aa-bb --R --R +---------+ @@ -1083,7 +1083,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 76 +--S 76 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -1092,7 +1092,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 77 +--S 77 of 170 dd:=asinrule cc --R --R +---------+ @@ -1106,7 +1106,7 @@ dd:=asinrule cc --R Type: Expression Complex Integer --E ---S 78 +--S 78 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1117,7 +1117,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 79 +--S 79 of 170 ee:=atanrule dd --R --R +---------+ @@ -1133,7 +1133,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 80 +--S 80 of 170 ff:=expandLog ee --R --R (8) @@ -1150,7 +1150,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 81 +--S 81 of 170 gg:=rootSimp ff --R --R (9) @@ -1164,7 +1164,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 82 14:249 Schaums and Axiom agree +--S 82 of 170 14:249 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -1181,7 +1181,7 @@ $$ <<*>>= )clear all ---S 83 +--S 83 of 170 aa:=integrate(sqrt(a^2-x^2)/x^3,x) --R --R @@ -1202,7 +1202,7 @@ aa:=integrate(sqrt(a^2-x^2)/x^3,x) --R Type: Union(Expression Integer,...) --E ---S 84 +--S 84 of 170 bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -1216,7 +1216,7 @@ bb:=-sqrt(a^2-x^2)/(2*x^2)+1/(2*a)*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 85 +--S 85 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -1229,7 +1229,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 86 +--S 86 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -1240,7 +1240,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 87 +--S 87 of 170 ee:=complexNormalize dd --R --R x @@ -1253,7 +1253,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 88 14:250 Schaums and Axiom differ by a constant +--S 88 of 170 14:250 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ @@ -1271,7 +1271,7 @@ $$ <<*>>= )clear all ---S 89 +--S 89 of 170 aa:=integrate(1/(a^2-x^2)^(3/2),x) --R --R @@ -1285,7 +1285,7 @@ aa:=integrate(1/(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 90 +--S 90 of 170 bb:=x/(a^2*sqrt(a^2-x^2)) --R --R x @@ -1296,7 +1296,7 @@ bb:=x/(a^2*sqrt(a^2-x^2)) --R Type: Expression Integer --E ---S 91 14:251 Schaums and Axiom agree +--S 91 of 170 14:251 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1312,7 +1312,7 @@ $$ <<*>>= )clear all ---S 92 +--S 92 of 170 aa:=integrate(x/(a^2-x^2)^(3/2),x) --R --R @@ -1325,7 +1325,7 @@ aa:=integrate(x/(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 93 +--S 93 of 170 bb:=1/sqrt(a^2-x^2) --R --R 1 @@ -1336,7 +1336,7 @@ bb:=1/sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 94 14:252 Schaums and Axiom differ by a constant +--S 94 of 170 14:252 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 1 @@ -1354,7 +1354,7 @@ $$ <<*>>= )clear all ---S 95 +--S 95 of 170 aa:=integrate(x^2/(a^2-x^2)^(3/2),x) --R --R @@ -1371,7 +1371,7 @@ aa:=integrate(x^2/(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 96 +--S 96 of 170 bb:=x/sqrt(a^2-x^2)-asin(x/a) --R --R +---------+ @@ -1385,7 +1385,7 @@ bb:=x/sqrt(a^2-x^2)-asin(x/a) --R Type: Expression Integer --E ---S 97 +--S 97 of 170 cc:=aa-bb --R --R +---------+ @@ -1396,7 +1396,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 98 +--S 98 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1407,7 +1407,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 99 +--S 99 of 170 dd:=atanrule cc --R --R +---------+ @@ -1420,7 +1420,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 100 +--S 100 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -1429,7 +1429,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 101 +--S 101 of 170 ee:=asinrule dd --R --R +---------+ @@ -1445,7 +1445,7 @@ ee:=asinrule dd --R Type: Expression Complex Integer --E ---S 102 +--S 102 of 170 ff:=expandLog ee --R --R (8) @@ -1462,7 +1462,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 103 +--S 103 of 170 gg:=rootSimp ff --R --R (9) @@ -1476,7 +1476,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 104 14:253 Schaums and Axiom agree +--S 104 of 170 14:253 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -1492,7 +1492,7 @@ $$ <<*>>= )clear all ---S 105 +--S 105 of 170 aa:=integrate(x^3/(a^2-x^2)^(3/2),x) --R --R @@ -1505,7 +1505,7 @@ aa:=integrate(x^3/(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 106 +--S 106 of 170 bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2) --R --R 2 2 @@ -1517,7 +1517,7 @@ bb:=sqrt(a^2-x^2)+a^2/sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 107 14:254 Schaums and Axiom differ by a constant +--S 107 of 170 14:254 Schaums and Axiom differ by a constant cc:=aa-bb --R --R (3) 2a @@ -1534,7 +1534,7 @@ $$ <<*>>= )clear all ---S 108 +--S 108 of 170 aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x) --R --R @@ -1550,7 +1550,7 @@ aa:=integrate(1/(x*(a^2-x^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 109 +--S 109 of 170 bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -1565,7 +1565,7 @@ bb:=1/(a^2*sqrt(a^2-x^2))-1/a^3*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 110 +--S 110 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -1579,7 +1579,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 111 +--S 111 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -1591,7 +1591,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 112 +--S 112 of 170 ee:=complexNormalize dd --R --R x @@ -1605,7 +1605,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 113 14:255 Schaums and Axiom differ by a constant +--S 113 of 170 14:255 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ @@ -1625,7 +1625,7 @@ $$ <<*>>= )clear all ---S 114 +--S 114 of 170 aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x) --R --R @@ -1639,7 +1639,7 @@ aa:=integrate(1/(x^2*(a^2-x^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 115 +--S 115 of 170 bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2)) --R --R 2 2 @@ -1651,7 +1651,7 @@ bb:=-sqrt(a^2-x^2)/(a^4*x)+x/(a^4*sqrt(a^2-x^2)) --R Type: Expression Integer --E ---S 116 14:256 Schaums and Axiom agree +--S 116 of 170 14:256 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1669,7 +1669,7 @@ $$ <<*>>= )clear all ---S 117 +--S 117 of 170 aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x) --R --R @@ -1694,7 +1694,7 @@ aa:=integrate(1/(x^3*(a^2-x^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 118 +--S 118 of 170 bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -1709,7 +1709,7 @@ bb:=-1/(2*a^2*x^2*sqrt(a^2-x^2))+3/(2*a^4*sqrt(a^2-x^2))-3/(2*a^5)*log((a+sqrt(a --R Type: Expression Integer --E ---S 119 +--S 119 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -1723,7 +1723,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 120 +--S 120 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -1735,7 +1735,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 121 +--S 121 of 170 ee:=complexNormalize dd --R --R x @@ -1749,7 +1749,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 122 14:257 Schaums and Axiom differ by a constant +--S 122 of 170 14:257 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ @@ -1769,7 +1769,7 @@ $$ <<*>>= )clear all ---S 123 +--S 123 of 170 aa:=integrate((a^2-x^2)^(3/2),x) --R --R @@ -1797,7 +1797,7 @@ aa:=integrate((a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 124 +--S 124 of 170 bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a) --R --R +---------+ @@ -1809,7 +1809,7 @@ bb:=(x*(a^2-x^2)^(3/2))/4+(3*a^2*x*sqrt(a^2-x^2))/8+3/8*a^4*asin(x/a) --R Type: Expression Integer --E ---S 125 +--S 125 of 170 cc:=aa-bb --R --R +---------+ @@ -1822,7 +1822,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 126 +--S 126 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -1831,7 +1831,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 127 +--S 127 of 170 ee:=asinrule cc --R --R +---------+ @@ -1847,7 +1847,7 @@ ee:=asinrule cc --R Type: Expression Complex Integer --E ---S 128 +--S 128 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1858,7 +1858,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 129 +--S 129 of 170 ff:=atanrule ee --R --R (7) @@ -1877,7 +1877,7 @@ ff:=atanrule ee --R Type: Expression Complex Integer --E ---S 130 +--S 130 of 170 gg:=expandLog ff --R --R (8) @@ -1896,7 +1896,7 @@ gg:=expandLog ff --R Type: Expression Complex Integer --E ---S 131 +--S 131 of 170 hh:=rootSimp gg --R --R (9) @@ -1912,7 +1912,7 @@ hh:=rootSimp gg --R Type: Expression Complex Integer --E ---S 132 14:258 Schaums and Axiom agree +--S 132 of 170 14:258 Schaums and Axiom agree ii:=complexNormalize hh --R --R (10) 0 @@ -1925,7 +1925,7 @@ $$\int{x(a^2-x^2)^{3/2}}=\frac{(a^2-x^2)^{5/2}}{5}$$ <<*>>= )clear all ---S 133 +--S 133 of 170 aa:=integrate(x*(a^2-x^2)^(3/2),x) --R --R @@ -1943,7 +1943,7 @@ aa:=integrate(x*(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 134 +--S 134 of 170 bb:=-(a^2-x^2)^(5/2)/5 --R --R +---------+ @@ -1954,7 +1954,7 @@ bb:=-(a^2-x^2)^(5/2)/5 --R Type: Expression Integer --E ---S 135 14:259 Schaums and Axiom differ by a constant +--S 135 of 170 14:259 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 5 @@ -1974,7 +1974,7 @@ $$ <<*>>= )clear all ---S 136 +--S 136 of 170 aa:=integrate(x^2*(a^2-x^2)^(3/2),x) --R --R @@ -2008,7 +2008,7 @@ aa:=integrate(x^2*(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 137 +--S 137 of 170 bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a^6/16*asin(x/a) --R --R +---------+ @@ -2020,7 +2020,7 @@ bb:=-(x*(a^2-x^2)^(5/2))/6+(a^2*x*(a^2-x^2)^(3/2))/24+(a^4*x*sqrt(a^2-x^2))/16+a --R Type: Expression Integer --E ---S 138 +--S 138 of 170 cc:=aa-bb --R --R +---------+ @@ -2033,7 +2033,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 139 +--S 139 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2044,7 +2044,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 140 +--S 140 of 170 dd:=atanrule cc --R --R +---------+ @@ -2059,7 +2059,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 141 +--S 141 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -2068,7 +2068,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 142 +--S 142 of 170 ee:=asinrule dd --R --R +---------+ @@ -2086,7 +2086,7 @@ ee:=asinrule dd --R Type: Expression Complex Integer --E ---S 143 +--S 143 of 170 ff:=expandLog ee --R --R (8) @@ -2105,7 +2105,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 144 +--S 144 of 170 gg:=rootSimp ff --R --R (9) @@ -2121,7 +2121,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 145 14:260 Schaums and Axiom agree +--S 145 of 170 14:260 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -2136,7 +2136,7 @@ $$ <<*>>= )clear all ---S 146 +--S 146 of 170 aa:=integrate(x^3*(a^2-x^2)^(3/2),x) --R --R @@ -2157,7 +2157,7 @@ aa:=integrate(x^3*(a^2-x^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 147 +--S 147 of 170 bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5 --R --R +---------+ @@ -2168,7 +2168,7 @@ bb:=(a^2-x^2)^(7/2)/7-(a^2*(a^2-x^2)^(5/2))/5 --R Type: Expression Integer --E ---S 148 14:261 Schaums and Axiom differ by a constant +--S 148 of 170 14:261 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 7 @@ -2188,7 +2188,7 @@ $$ <<*>>= )clear all ---S 149 +--S 149 of 170 aa:=integrate((a^2-x^2)^(3/2)/x,x) --R --R @@ -2209,7 +2209,7 @@ aa:=integrate((a^2-x^2)^(3/2)/x,x) --R Type: Union(Expression Integer,...) --E ---S 150 +--S 150 of 170 bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -2222,7 +2222,7 @@ bb:=(a^2-x^2)^(3/2)/3+a^2*sqrt(a^2-x^2)-a^3*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 151 +--S 151 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -2235,7 +2235,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 152 +--S 152 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -2246,7 +2246,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 153 +--S 153 of 170 ee:=complexNormalize dd --R --R 3 x 3 @@ -2259,7 +2259,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 154 14:262 Schaums and Axiom differ by a constant +--S 154 of 170 14:262 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R 3 +---+ 3 @@ -2279,7 +2279,7 @@ $$ <<*>>= )clear all ---S 155 +--S 155 of 170 aa:=integrate((a^2-x^2)^{3/2}/x^2,x) --R --R @@ -2300,7 +2300,7 @@ aa:=integrate((a^2-x^2)^{3/2}/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 156 +--S 156 of 170 bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a) --R --R +---------+ @@ -2312,7 +2312,7 @@ bb:=-(a^2-x^2)^(3/2)/x-(3*x*sqrt(a^2-x^2))/2-3/2*a^2*asin(x/a) --R Type: Expression Integer --E ---S 157 +--S 157 of 170 cc:=aa-bb --R --R +---------+ @@ -2325,7 +2325,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 158 +--S 158 of 170 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -2334,7 +2334,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 159 +--S 159 of 170 dd:=asinrule cc --R --R +---------+ @@ -2350,7 +2350,7 @@ dd:=asinrule cc --R Type: Expression Complex Integer --E ---S 160 +--S 160 of 170 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2361,7 +2361,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 161 +--S 161 of 170 ee:=atanrule dd --R --R +---------+ @@ -2379,7 +2379,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 162 +--S 162 of 170 ff:=expandLog ee --R --R (8) @@ -2398,7 +2398,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 163 +--S 163 of 170 gg:=rootSimp ff --R --R (9) @@ -2414,7 +2414,7 @@ gg:=rootSimp ff --R Type: Expression Complex Integer --E ---S 164 14:263 Schaums and Axiom agree +--S 164 of 170 14:263 Schaums and Axiom agree hh:=complexNormalize gg --R --R (10) 0 @@ -2431,7 +2431,7 @@ $$ <<*>>= )clear all ---S 165 +--S 165 of 170 aa:=integrate((a^2-x^2)^(3/2)/x^3,x) --R --R @@ -2452,7 +2452,7 @@ aa:=integrate((a^2-x^2)^(3/2)/x^3,x) --R Type: Union(Expression Integer,...) --E ---S 166 +--S 166 of 170 bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -2466,7 +2466,7 @@ bb:=-(a^2-x^2)^(3/2)/(2*x^2)-(3*sqrt(a^2-x^2))/2+3/2*a*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 167 +--S 167 of 170 cc:=aa-bb --R --R +---------+ +---------+ @@ -2479,7 +2479,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 168 +--S 168 of 170 dd:=expandLog cc --R --R +---------+ +---------+ @@ -2490,7 +2490,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 169 +--S 169 of 170 ee:=complexNormalize dd --R --R x @@ -2501,7 +2501,7 @@ ee:=complexNormalize dd --R Type: Expression Integer --E ---S 170 14:264 Schaums and Axiom differ by a constant +--S 170 of 170 14:264 Schaums and Axiom differ by a constant ff:=rootSimp ee --R --R +---+ diff --git a/src/input/schaum12.input.pamphlet b/src/input/schaum12.input.pamphlet index 7d5d77a..5bd9dc9 100644 --- a/src/input/schaum12.input.pamphlet +++ b/src/input/schaum12.input.pamphlet @@ -24,7 +24,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 84 aa:=integrate(1/(a*x^2+b*x+c),x) --R --R (1) @@ -57,7 +57,7 @@ aa:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 2 +--S 2 of 84 bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2)) --R --R @@ -73,7 +73,7 @@ bb1:=2/sqrt(4*a*c-b^2)*atan((2*a*x+b)/sqrt(4*a*c-b^2)) --R Type: Expression Integer --E ---S 3 +--S 3 of 84 bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c))) --R --R @@ -91,7 +91,7 @@ bb2:=1/sqrt(b^2-4*a*c)*log((2*a*x+b-sqrt(b^2-4*a*c))/(2*a*x+b+sqrt(b^2-4*a*c))) --R Type: Expression Integer --E ---S 4 +--S 4 of 84 cc1:=aa.1-bb1 --R --R (4) @@ -123,7 +123,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 5 +--S 5 of 84 cc2:=aa.1-bb2 --R --R (5) @@ -152,7 +152,7 @@ cc2:=aa.1-bb2 --R Type: Expression Integer --E ---S 6 +--S 6 of 84 cc3:=aa.2-bb1 --R --R +---------+ @@ -169,7 +169,7 @@ cc3:=aa.2-bb1 --R Type: Expression Integer --E ---S 7 +--S 7 of 84 cc4:=aa.2-bb2 --R --R (7) @@ -194,7 +194,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 8 +--S 8 of 84 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -205,7 +205,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 9 +--S 9 of 84 dd3:=atanrule cc3 --R --R (9) @@ -231,7 +231,7 @@ dd3:=atanrule cc3 --R Type: Expression Complex Integer --E ---S 10 +--S 10 of 84 ee3:=expandLog dd3 --R --R (10) @@ -257,7 +257,7 @@ ee3:=expandLog dd3 --R Type: Expression Complex Integer --E ---S 11 14:265 Schaums and Axiom agree +--S 11 of 84 14:265 Schaums and Axiom agree ff3:=complexNormalize ee3 --R --R (11) 0 @@ -273,7 +273,7 @@ $$ <<*>>= )clear all ---S 12 +--S 12 of 84 aa:=integrate(x/(a*x^2+b*x+c),x) --R --R (1) @@ -312,7 +312,7 @@ aa:=integrate(x/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 13 +--S 13 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -346,7 +346,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 14 +--S 14 of 84 bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1 --R --R @@ -375,7 +375,7 @@ bb1:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.1 --R Type: Expression Integer --E ---S 15 +--S 15 of 84 bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2 --R --R @@ -392,7 +392,7 @@ bb2:=1/(2*a)*log(a*x^2+b*x+c)-b/(2*a)*t1.2 --R Type: Expression Integer --E ---S 16 +--S 16 of 84 cc1:=aa.1-bb1 --R --R (5) @@ -428,7 +428,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 17 +--S 17 of 84 cc2:=aa.2-bb1 --R --R (6) @@ -460,7 +460,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 18 +--S 18 of 84 cc3:=aa.2-bb1 --R --R (7) @@ -492,7 +492,7 @@ cc3:=aa.2-bb1 --R Type: Expression Integer --E ---S 19 14:266 Schaums and Axiom agree +--S 19 of 84 14:266 Schaums and Axiom agree cc4:=aa.2-bb2 --R --R (8) 0 @@ -510,7 +510,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 84 aa:=integrate(x^2/(a*x^2+b*x+c),x) --R --R @@ -557,7 +557,7 @@ aa:=integrate(x^2/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 21 +--S 21 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -591,7 +591,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 22 +--S 22 of 84 bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1 --R --R @@ -620,7 +620,7 @@ bb1:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.1 --R Type: Expression Integer --E ---S 23 +--S 23 of 84 bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2 --R --R @@ -642,7 +642,7 @@ bb2:=x/a-b/(2*a^2)*log(a*x^2+b*x+c)+(b^2-2*a*c)/(2*a^2)*t1.2 --R Type: Expression Integer --E ---S 24 +--S 24 of 84 cc1:=bb1-aa.1 --R --R (5) @@ -680,7 +680,7 @@ cc1:=bb1-aa.1 --R Type: Expression Integer --E ---S 25 14:267 Schaums and Axiom differ by a constant +--S 25 of 84 14:267 Schaums and Axiom differ by a constant dd1:=complexNormalize cc1 --R --R 2 3 2 2 @@ -702,7 +702,7 @@ $$ <<*>>= )clear all ---S 26 14:268 Axiom cannot compute this integral +--S 26 of 84 14:268 Axiom cannot compute this integral aa:=integrate(x^m/(a*x^2+b*x+c),x) --R --R @@ -725,7 +725,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 84 aa:=integrate(1/(x*(a*x^2+b*x+c)),x) --R --R @@ -771,7 +771,7 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)),x) --R Type: Union(List Expression Integer,...) --E ---S 28 +--S 28 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -805,7 +805,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 29 +--S 29 of 84 bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1 --R --R @@ -836,7 +836,7 @@ bb1:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.1 --R Type: Expression Integer --E ---S 30 +--S 30 of 84 bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2 --R --R @@ -853,7 +853,7 @@ bb2:=1/(2*c)*log(x^2/(a*x^2+b*x+c))-b/(2*c)*t1.2 --R Type: Expression Integer --E ---S 31 +--S 31 of 84 cc1:=bb1-aa.1 --R --R (5) @@ -897,7 +897,7 @@ cc1:=bb1-aa.1 --R Type: Expression Integer --E ---S 32 +--S 32 of 84 dd1:=expandLog cc1 --R --R (6) @@ -932,7 +932,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 33 14:269 Schaums and Axiom differ by a constant +--S 33 of 84 14:269 Schaums and Axiom differ by a constant ee1:=complexNormalize dd1 --R --R 3 2 2 @@ -954,7 +954,7 @@ $$ <<*>>= )clear all ---S 34 +--S 34 of 84 aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x) --R --R @@ -1001,7 +1001,7 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)),x) --R Type: Union(List Expression Integer,...) --E ---S 35 +--S 35 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -1035,7 +1035,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 36 +--S 36 of 84 bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1 --R --R @@ -1066,7 +1066,7 @@ bb1:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.1 --R Type: Expression Integer --E ---S 37 +--S 37 of 84 bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2 --R --R @@ -1090,7 +1090,7 @@ bb2:=b/(2*c^2)*log((a*x^2+b*x+c)/x^2)-1/(c*x)+(b^2-2*a*c)/(2*c^2)*t1.2 --R Type: Expression Integer --E ---S 38 +--S 38 of 84 cc1:=bb1-aa.1 --R --R (5) @@ -1134,7 +1134,7 @@ cc1:=bb1-aa.1 --R Type: Expression Integer --E ---S 39 +--S 39 of 84 dd1:=expandLog cc1 --R --R (6) @@ -1169,7 +1169,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 40 14:270 Schaums and Axiom differ by a constant +--S 40 of 84 14:270 Schaums and Axiom differ by a constant ee1:=complexNormalize dd1 --R --R 2 3 2 2 @@ -1192,7 +1192,7 @@ $$ <<*>>= )clear all ---S 41 14:271 Axiom cannot compute this integral +--S 41 of 84 14:271 Axiom cannot compute this integral aa:=integrate(1/(x^n*(a*x^2+b*x+c)),x) --R --R @@ -1215,7 +1215,7 @@ $$ <<*>>= )clear all ---S 42 +--S 42 of 84 aa:=integrate(1/(a*x^2+b*x+c)^2,x) --R --R @@ -1257,7 +1257,7 @@ aa:=integrate(1/(a*x^2+b*x+c)^2,x) --R Type: Union(List Expression Integer,...) --E ---S 43 +--S 43 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -1291,7 +1291,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 44 +--S 44 of 84 bb1:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.1 --R --R (3) @@ -1319,7 +1319,7 @@ bb1:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.1 --R Type: Expression Integer --E ---S 45 +--S 45 of 84 bb2:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.2 --R --R (4) @@ -1336,14 +1336,14 @@ bb2:=(2*a*x+b)/((4*a*c-b^2)*(a*x^2+b*x+c))+(2*a)/(4*a*c-b^2)*t1.2 --R Type: Expression Integer --E ---S 46 +--S 46 of 84 cc1:=aa.1-bb1 --R --R (5) 0 --R Type: Expression Integer --E ---S 47 +--S 47 of 84 cc2:=aa.2-bb1 --R --R (6) @@ -1376,7 +1376,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 48 +--S 48 of 84 cc3:=aa.1-bb2 --R --R (7) @@ -1408,7 +1408,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 49 14:272 Schaums and Axiom agree +--S 49 of 84 14:272 Schaums and Axiom agree cc4:=aa.2-bb2 --R --R (8) 0 @@ -1426,7 +1426,7 @@ $$ <<*>>= )clear all ---S 50 +--S 50 of 84 aa:=integrate(x/(a*x^2+b*x+c)^2,x) --R --R @@ -1473,7 +1473,7 @@ aa:=integrate(x/(a*x^2+b*x+c)^2,x) --R Type: Union(List Expression Integer,...) --E ---S 51 +--S 51 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -1507,7 +1507,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 52 +--S 52 of 84 bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1 --R --R @@ -1536,7 +1536,7 @@ bb1:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.1 --R Type: Expression Integer --E ---S 53 +--S 53 of 84 bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2 --R --R @@ -1558,7 +1558,7 @@ bb2:=-(b*x+2*c)/((4*a*c-b^2)*(a*x^2+b*x+c))-b/(4*a*c-b^2)*t1.2 --R Type: Expression Integer --E ---S 54 +--S 54 of 84 cc1:=bb1-aa.1 --R --R (5) @@ -1596,7 +1596,7 @@ cc1:=bb1-aa.1 --R Type: Expression Integer --E ---S 55 +--S 55 of 84 dd1:=expandLog cc1 --R --R (6) @@ -1631,7 +1631,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 56 14:273 Schaums and Axiom differ by a constant +--S 56 of 84 14:273 Schaums and Axiom differ by a constant ee1:=complexNormalize dd1 --R --R 3 2 2 @@ -1654,7 +1654,7 @@ $$ <<*>>= )clear all ---S 57 +--S 57 of 84 aa:=integrate(x^2/(a*x^2+b*x+c)^2,x) --R --R @@ -1701,7 +1701,7 @@ aa:=integrate(x^2/(a*x^2+b*x+c)^2,x) --R Type: Union(List Expression Integer,...) --E ---S 58 +--S 58 of 84 t1:=integrate(1/(a*x^2+b*x+c),x) --R --R @@ -1735,7 +1735,7 @@ t1:=integrate(1/(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 59 +--S 59 of 84 bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1 --R --R (3) @@ -1763,7 +1763,7 @@ bb1:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.1 --R Type: Expression Integer --E ---S 60 +--S 60 of 84 bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2 --R --R (4) @@ -1784,7 +1784,7 @@ bb2:=((b^2-2*a*c)*x+b*c)/(a*(4*a*c-b^2)*(a*x^2+b*x+c))+(2*c)/(4*a*c-b^2)*t1.2 --R Type: Expression Integer --E ---S 61 14:274 Schaums and Axiom agree +--S 61 of 84 14:274 Schaums and Axiom agree cc1:=aa.1-bb1 --R --R (5) 0 @@ -1807,7 +1807,7 @@ $$ <<*>>= )clear all ---S 62 14:275 Axiom cannot compute this integral +--S 62 of 84 14:275 Axiom cannot compute this integral aa:=integrate(x^m/(a*x^2+b*x+c)^n,x) --R --R @@ -1835,7 +1835,7 @@ $$ <<*>>= )clear all ---S 63 14:276 Axiom cannot compute this integral +--S 63 of 84 14:276 Axiom cannot compute this integral aa:=integrate(x^(2*n-1)/(a*x^2+b*x+c)^n,x) --R --R @@ -1863,7 +1863,7 @@ $$ <<*>>= )clear all ---S 64 +--S 64 of 84 aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x) --R --R @@ -1937,7 +1937,7 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 65 +--S 65 of 84 t1:=integrate(1/(a*x^2+b*x+c)^2,x) --R --R @@ -1979,7 +1979,7 @@ t1:=integrate(1/(a*x^2+b*x+c)^2,x) --R Type: Union(List Expression Integer,...) --E ---S 66 +--S 66 of 84 t2:=integrate(1/(x*(a*x^2+b*x+c)),x) --R --R @@ -2025,7 +2025,7 @@ t2:=integrate(1/(x*(a*x^2+b*x+c)),x) --R Type: Union(List Expression Integer,...) --E ---S 67 +--S 67 of 84 bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1 --R --R @@ -2080,7 +2080,7 @@ bb1:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.1 --R Type: Expression Integer --E ---S 68 +--S 68 of 84 bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1 --R --R @@ -2137,7 +2137,7 @@ bb2:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.1 --R Type: Expression Integer --E ---S 69 +--S 69 of 84 bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2 --R --R @@ -2193,7 +2193,7 @@ bb3:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.1+1/c*t2.2 --R Type: Expression Integer --E ---S 70 +--S 70 of 84 bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2 --R --R @@ -2230,7 +2230,7 @@ bb4:=1/(2*c*(a*x^2+b*x+c))-b/(2*c)*t1.2+1/c*t2.2 --R Type: Expression Integer --E ---S 71 +--S 71 of 84 cc1:=aa.1-bb1 --R --R (8) @@ -2266,7 +2266,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 72 +--S 72 of 84 dd1:=expandLog cc1 --R --R (9) @@ -2299,7 +2299,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 73 14:277 Schaums and Axiom differ by a constant +--S 73 of 84 14:277 Schaums and Axiom differ by a constant ee1:=complexNormalize dd1 --R --R 3 2 2 @@ -2326,7 +2326,7 @@ $$ <<*>>= )clear all ---S 74 +--S 74 of 84 aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x) --R --R @@ -2410,7 +2410,7 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 75 +--S 75 of 84 t1:=integrate(1/(a*x^2+b*x+c)^2,x) --R --R @@ -2452,7 +2452,7 @@ t1:=integrate(1/(a*x^2+b*x+c)^2,x) --R Type: Union(List Expression Integer,...) --E ---S 76 +--S 76 of 84 t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x) --R --R @@ -2526,7 +2526,7 @@ t2:=integrate(1/(x*(a*x^2+b*x+c)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 77 +--S 77 of 84 bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1 --R --R @@ -2583,7 +2583,7 @@ bb1:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.1 --R Type: Expression Integer --E ---S 78 +--S 78 of 84 bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1 --R --R @@ -2645,7 +2645,7 @@ bb2:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.1 --R Type: Expression Integer --E ---S 79 +--S 79 of 84 bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2 --R --R @@ -2703,7 +2703,7 @@ bb3:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.1-(2*b)/c*t2.2 --R Type: Expression Integer --E ---S 80 +--S 80 of 84 bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2 --R --R @@ -2745,7 +2745,7 @@ bb4:=-1/(c*x*(a*x^2+b*x+c))-((3*a)/c)*t1.2-(2*b)/c*t2.2 --R Type: Expression Integer --E ---S 81 +--S 81 of 84 cc1:=aa.1-bb1 --R --R (8) @@ -2783,7 +2783,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 82 +--S 82 of 84 dd1:=expandLog cc1 --R --R (9) @@ -2818,7 +2818,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 83 14:278 Schaums and Axiom differ by a constant +--S 83 of 84 14:278 Schaums and Axiom differ by a constant ee1:=complexNormalize dd1 --R --R 2 3 2 2 @@ -2845,7 +2845,7 @@ $$ <<*>>= )clear all ---S 84 14:279 Axiom cannot compute this integral +--S 84 of 84 14:279 Axiom cannot compute this integral aa:=integrate(1/(x^m*(a*x^2+b*x+c)^n),x) --R --R diff --git a/src/input/schaum13.input.pamphlet b/src/input/schaum13.input.pamphlet index 678e41c..5df3793 100644 --- a/src/input/schaum13.input.pamphlet +++ b/src/input/schaum13.input.pamphlet @@ -29,7 +29,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 131 aa:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (1) @@ -60,7 +60,7 @@ aa:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 2 +--S 2 of 131 bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)+2*a*x+b) --R --R +--------------+ @@ -72,7 +72,7 @@ bb1:=1/sqrt(a)*log(2*sqrt(a)*sqrt(a*x^2+b*x+c)+2*a*x+b) --R Type: Expression Integer --E ---S 3 +--S 3 of 131 bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c)) --R --R 2a x + b @@ -86,7 +86,7 @@ bb2:=-1/sqrt(-a)*asin((2*a*x+b)/sqrt(b^2-4*a*c)) --R Type: Expression Integer --E ---S 4 +--S 4 of 131 bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2)) --R --R 2a x + b @@ -100,7 +100,7 @@ bb3:=1/sqrt(a)*asinh((2*a*x+b)/sqrt(4*a*c-b^2)) --R Type: Expression Integer --E ---S 5 +--S 5 of 131 cc1:=bb1-aa.1 --R --R (5) @@ -126,7 +126,7 @@ cc1:=bb1-aa.1 --R Type: Expression Integer --E ---S 6 +--S 6 of 131 cc2:=bb1-aa.2 --R --R (6) @@ -145,7 +145,7 @@ cc2:=bb1-aa.2 --R Type: Expression Integer --E ---S 7 +--S 7 of 131 cc3:=bb2-aa.1 --R --R (7) @@ -176,7 +176,7 @@ cc3:=bb2-aa.1 --R Type: Expression Integer --E ---S 8 +--S 8 of 131 cc4:=bb2-aa.2 --R --R +--------------+ @@ -192,7 +192,7 @@ cc4:=bb2-aa.2 --R Type: Expression Integer --E ---S 9 +--S 9 of 131 cc5:=bb3-aa.1 --R --R (9) @@ -220,7 +220,7 @@ cc5:=bb3-aa.1 --R Type: Expression Integer --E ---S 10 +--S 10 of 131 cc6:=bb3-aa.2 --R --R (10) @@ -237,7 +237,7 @@ cc6:=bb3-aa.2 --R Type: Expression Integer --E ---S 11 +--S 11 of 131 dd1:=simplifyLog cc1 --R --R (11) @@ -261,7 +261,7 @@ dd1:=simplifyLog cc1 --R Type: Expression Integer --E ---S 12 14:280 Schaums and Axiom differ by a constant +--S 12 of 131 14:280 Schaums and Axiom differ by a constant ee1:=ratDenom dd1 --R --R +-+ +-+ @@ -282,7 +282,7 @@ $$ <<*>>= )clear all ---S 11 +--S 11 of 131 aa:=integrate(x/sqrt(a*x^2+b*x+c),x) --R --R @@ -334,7 +334,7 @@ aa:=integrate(x/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 12 +--S 12 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -365,7 +365,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 13 +--S 13 of 131 bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1 --R --R (3) @@ -393,7 +393,7 @@ bb1:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.1 --R Type: Expression Integer --E ---S 14 +--S 14 of 131 bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2 --R --R (4) @@ -408,7 +408,7 @@ bb2:=sqrt(a*x^2+b*x+c)/a-b/(2*a)*t1.2 --R Type: Expression Integer --E ---S 15 +--S 15 of 131 cc1:=bb1-aa.1 --R --R (5) @@ -454,7 +454,7 @@ cc1:=bb1-aa.1 --R Type: Expression Integer --E ---S 16 +--S 16 of 131 cc2:=bb1-aa.2 --R --R (6) @@ -494,7 +494,7 @@ cc2:=bb1-aa.2 --R Type: Expression Integer --E ---S 17 +--S 17 of 131 cc3:=bb2-aa.1 --R --R (7) @@ -534,7 +534,7 @@ cc3:=bb2-aa.1 --R Type: Expression Integer --E ---S 18 +--S 18 of 131 cc4:=bb2-aa.2 --R --R +--------------+ @@ -547,7 +547,7 @@ cc4:=bb2-aa.2 --R Type: Expression Integer --E ---S 19 14:281 Schaums and Axiom differ by a constant +--S 19 of 131 14:281 Schaums and Axiom differ by a constant dd1:=ratDenom cc4 --R --R +-+ @@ -567,7 +567,7 @@ $$ <<*>>= )clear all ---S 19 +--S 19 of 131 aa:=integrate(x^2/sqrt(a*x^2+b*x+c),x) --R --R (1) @@ -651,7 +651,7 @@ aa:=integrate(x^2/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 20 +--S 20 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -682,7 +682,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 21 +--S 21 of 131 bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1 --R --R (3) @@ -710,7 +710,7 @@ bb1:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.1 --R Type: Expression Integer --E ---S 22 +--S 22 of 131 bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2 --R --R (4) @@ -729,7 +729,7 @@ bb2:=(2*a*x-3*b)/(4*a^2)*sqrt(a*x^2+b*x+c)+(3*b^2-4*a*c)/(8*a^2)*t1.2 --R Type: Expression Integer --E ---S 23 +--S 23 of 131 cc1:=aa.1-bb1 --R --R (5) @@ -787,7 +787,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 24 +--S 24 of 131 cc2:=aa.2-bb1 --R --R (6) @@ -851,7 +851,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 25 +--S 25 of 131 cc3:=aa.2-bb1 --R --R (7) @@ -915,7 +915,7 @@ cc3:=aa.2-bb1 --R Type: Expression Integer --E ---S 26 +--S 26 of 131 cc4:=aa.2-bb2 --R --R (8) @@ -935,7 +935,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 27 14:282 Schaums and Axiom differ by a constant +--S 27 of 131 14:282 Schaums and Axiom differ by a constant dd4:=ratDenom cc4 --R --R +-+ @@ -967,7 +967,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 131 aa:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R --R +--------------+ @@ -981,7 +981,7 @@ aa:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 28 +--S 28 of 131 bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x) --R --R +--------------+ @@ -995,7 +995,7 @@ bb1:=-1/sqrt(c)*log((2*sqrt(c)*sqrt(a*x^2+b*x+c)+b*x+2*c)/x) --R Type: Expression Integer --E ---S 29 +--S 29 of 131 bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c))) --R --R b x + 2c @@ -1009,7 +1009,7 @@ bb2:=1/sqrt(-c)*asin((b*x+2*c)/(x*sqrt(b^2-4*a*c))) --R Type: Expression Integer --E ---S 30 +--S 30 of 131 bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(4*a*c-b^2))) --R --R b x + 2c @@ -1023,7 +1023,7 @@ bb3:=-1/sqrt(c)*asinh((b*x+2*c)/(x*sqrt(4*a*c-b^2))) --R Type: Expression Integer --E ---S 31 +--S 31 of 131 cc1:=aa-bb1 --R --R (5) @@ -1044,7 +1044,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 32 +--S 32 of 131 cc2:=aa-bb2 --R --R (6) @@ -1061,7 +1061,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 33 +--S 33 of 131 cc3:=aa-bb3 --R --R +--------------+ @@ -1077,7 +1077,7 @@ cc3:=aa-bb3 --R Type: Expression Integer --E ---S 34 +--S 34 of 131 dd1:=expandLog cc1 --R --R (8) @@ -1094,7 +1094,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 35 +--S 35 of 131 ee1:=ratDenom dd1 --R --R (9) @@ -1110,7 +1110,7 @@ ee1:=ratDenom dd1 --R Type: Expression Integer --E ---S 36 14:283 Schaums and Axiom differ by a constant +--S 36 of 131 14:283 Schaums and Axiom differ by a constant ff1:=complexNormalize ee1 --R --R 2 +-+ @@ -1129,7 +1129,7 @@ $$ <<*>>= )clear all ---S 37 +--S 37 of 131 aa:=integrate(1/(x^2*sqrt(a*x^2+b*x+c)),x) --R --R (1) @@ -1153,7 +1153,7 @@ aa:=integrate(1/(x^2*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 38 +--S 38 of 131 t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R --R +--------------+ @@ -1167,7 +1167,7 @@ t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 39 +--S 39 of 131 bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*c)*t1 --R --R +--------------+ @@ -1181,7 +1181,7 @@ bb:=-sqrt(a*x^2+b*x+c)/(c*x)-b/(2*c)*t1 --R Type: Expression Integer --E ---S 40 +--S 40 of 131 cc:=aa-bb --R --R (4) @@ -1215,7 +1215,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 41 +--S 41 of 131 dd:=expandLog cc --R --R (5) @@ -1248,7 +1248,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 42 +--S 42 of 131 ee:=ratDenom dd --R --R (6) @@ -1268,7 +1268,7 @@ ee:=ratDenom dd --R Type: Expression Integer --E ---S 43 14:284 Schaums and Axiom differ by a constant +--S 43 of 131 14:284 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R +-+ @@ -1290,7 +1290,7 @@ $$ <<*>>= )clear all ---S 44 +--S 44 of 131 aa:=integrate(sqrt(a*x^2+b*x+c),x) --R --R @@ -1375,7 +1375,7 @@ aa:=integrate(sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 45 +--S 45 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -1406,7 +1406,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 46 +--S 46 of 131 bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1 --R --R (3) @@ -1434,7 +1434,7 @@ bb1:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.1 --R Type: Expression Integer --E ---S 47 +--S 47 of 131 bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2 --R --R (4) @@ -1453,7 +1453,7 @@ bb2:=((2*a*x+b)*sqrt(a*x^2+b*x+c))/(4*a)+(4*a*c-b^2)/(8*a)*t1.2 --R Type: Expression Integer --E ---S 48 +--S 48 of 131 cc1:=aa.1-bb1 --R --R (5) @@ -1473,7 +1473,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 49 +--S 49 of 131 cc2:=aa.2-bb1 --R --R (6) @@ -1525,7 +1525,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 50 +--S 50 of 131 cc3:=aa.1-bb2 --R --R (7) @@ -1577,7 +1577,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 51 +--S 51 of 131 cc4:=aa.2-bb2 --R --R (8) @@ -1597,7 +1597,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 52 14:285 Schaums and Axiom differ by a constant +--S 52 of 131 14:285 Schaums and Axiom differ by a constant dd4:=ratDenom cc4 --R --R +-+ @@ -1623,7 +1623,7 @@ $$ <<*>>= )clear all ---S 53 +--S 53 of 131 aa:=integrate(x*sqrt(a*x^2+b*x+c),x) --R --R @@ -1768,7 +1768,7 @@ aa:=integrate(x*sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 54 +--S 54 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -1799,7 +1799,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 55 +--S 55 of 131 bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.1 --R --R (3) @@ -1827,7 +1827,7 @@ bb1:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c --R Type: Expression Integer --E ---S 56 +--S 56 of 131 bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c-b^2))/(16*a^2)*t1.2 --R --R (4) @@ -1846,7 +1846,7 @@ bb2:=(a*x^2+b*x+c)^(3/2)/(3*a)-(b*(2*a*x+b))/(8*a^2)*sqrt(a*x^2+b*x+c)-(b*(4*a*c --R Type: Expression Integer --E ---S 57 +--S 57 of 131 cc1:=aa.1-bb1 --R --R (5) @@ -1940,7 +1940,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 58 +--S 58 of 131 cc2:=aa.2-bb1 --R --R (6) @@ -2043,7 +2043,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 59 +--S 59 of 131 cc3:=aa.1-bb2 --R --R (7) @@ -2146,7 +2146,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 60 +--S 60 of 131 cc4:=aa.2-bb2 --R --R (8) @@ -2178,7 +2178,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 61 14:286 Schaums and Axiom differ by a constant +--S 61 of 131 14:286 Schaums and Axiom differ by a constant dd4:=ratDenom cc4 --R --R 2 +-+ @@ -2199,7 +2199,7 @@ $$ <<*>>= )clear all ---S 62 +--S 62 of 131 aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x) --R --R @@ -2431,7 +2431,7 @@ aa:=integrate(x^2*sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 63 +--S 63 of 131 t1:=integrate(sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -2515,7 +2515,7 @@ t1:=integrate(sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 64 +--S 64 of 131 bb1:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.1 --R --R (3) @@ -2578,7 +2578,7 @@ bb1:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.1 --R Type: Expression Integer --E ---S 65 +--S 65 of 131 bb2:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.2 --R --R (4) @@ -2635,7 +2635,7 @@ bb2:=(6*a*x-5*b)/(24*a^2)*(a*x^2+b*x+c)^(3/2)+(5*b^2-4*a*c)/(16*a^2)*t1.2 --R Type: Expression Integer --E ---S 66 +--S 66 of 131 cc1:=aa.1-bb1 --R --R (5) @@ -2831,7 +2831,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 67 +--S 67 of 131 cc2:=aa.2-bb1 --R --R (6) @@ -3039,7 +3039,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 68 +--S 68 of 131 cc3:=aa.1-bb2 --R --R (7) @@ -3247,7 +3247,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 69 +--S 69 of 131 cc4:=aa.2-bb2 --R --R (8) @@ -3315,7 +3315,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 70 14:287 Schaums and Axiom differ by a constant +--S 70 of 131 14:287 Schaums and Axiom differ by a constant dd4:=ratDenom cc4 --R --R +-+ @@ -3336,7 +3336,7 @@ $$ <<*>>= )clear all ---S 71 +--S 71 of 131 aa:=integrate(sqrt(a*x^2+b*x+c)/x,x) --R --R @@ -3420,7 +3420,7 @@ aa:=integrate(sqrt(a*x^2+b*x+c)/x,x) --R Type: Union(List Expression Integer,...) --E ---S 72 +--S 72 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -3451,7 +3451,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 73 +--S 73 of 131 t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R --R +--------------+ @@ -3465,7 +3465,7 @@ t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 74 +--S 74 of 131 bb1:=sqrt(a*x^2+b*x+c)+b/2*t1.1+c*t2 --R --R (4) @@ -3499,7 +3499,7 @@ bb1:=sqrt(a*x^2+b*x+c)+b/2*t1.1+c*t2 --R Type: Expression Integer --E ---S 75 +--S 75 of 131 bb2:=sqrt(a*x^2+b*x+c)+b/2*t1.2+c*t2 --R --R (5) @@ -3524,7 +3524,7 @@ bb2:=sqrt(a*x^2+b*x+c)+b/2*t1.2+c*t2 --R Type: Expression Integer --E ---S 76 +--S 76 of 131 cc1:=aa.1-bb1 --R --R (6) @@ -3589,7 +3589,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 77 +--S 77 of 131 cc2:=aa.2-bb1 --R --R (7) @@ -3634,7 +3634,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 78 +--S 78 of 131 cc3:=aa.1-bb2 --R --R (8) @@ -3686,7 +3686,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 79 +--S 79 of 131 cc4:=aa.2-bb2 --R --R (9) @@ -3721,7 +3721,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 80 +--S 80 of 131 dd4:=ratDenom cc4 --R --R (10) @@ -3739,7 +3739,7 @@ dd4:=ratDenom cc4 --R Type: Expression Integer --E ---S 81 +--S 81 of 131 ee4:=expandLog dd4 --R --R (11) @@ -3753,7 +3753,7 @@ ee4:=expandLog dd4 --R Type: Expression Integer --E ---S 82 14:288 Schaums and Axiom differ by a constant +--S 82 of 131 14:288 Schaums and Axiom differ by a constant ff4:=complexNormalize ee4 --R --R +-+ @@ -3774,7 +3774,7 @@ $$ <<*>>= )clear all ---S 83 +--S 83 of 131 aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x) --R --R @@ -3843,7 +3843,7 @@ aa:=integrate(sqrt(a*x^2+b*x+c)/x^2,x) --R Type: Union(List Expression Integer,...) --E ---S 84 +--S 84 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -3874,7 +3874,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 85 +--S 85 of 131 t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R --R +--------------+ @@ -3888,7 +3888,7 @@ t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 86 +--S 86 of 131 bb1:=-sqrt(a*x^2+b*x+c)/x+a*t1.1+b/2*t2 --R --R (4) @@ -3922,7 +3922,7 @@ bb1:=-sqrt(a*x^2+b*x+c)/x+a*t1.1+b/2*t2 --R Type: Expression Integer --E ---S 87 +--S 87 of 131 bb2:=-sqrt(a*x^2+b*x+c)/x+a*t1.2+b/2*t2 --R --R (5) @@ -3947,7 +3947,7 @@ bb2:=-sqrt(a*x^2+b*x+c)/x+a*t1.2+b/2*t2 --R Type: Expression Integer --E ---S 88 +--S 88 of 131 cc1:=aa.1-bb1 --R --R (6) @@ -4009,7 +4009,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 89 +--S 89 of 131 cc2:=aa.2-bb1 --R --R (7) @@ -4070,7 +4070,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 90 +--S 90 of 131 cc3:=aa.1-bb2 --R --R (8) @@ -4126,7 +4126,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 91 +--S 91 of 131 cc4:=aa.2-bb2 --R --R (9) @@ -4181,7 +4181,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 92 +--S 92 of 131 dd4:=ratDenom cc4 --R --R (10) @@ -4201,7 +4201,7 @@ dd4:=ratDenom cc4 --R Type: Expression Integer --E ---S 93 +--S 93 of 131 ee4:=expandLog dd4 --R --R (11) @@ -4220,7 +4220,7 @@ ee4:=expandLog dd4 --R Type: Expression Integer --E ---S 94 14:289 Schaums and Axiom differ by a constant +--S 94 of 131 14:289 Schaums and Axiom differ by a constant ff4:=complexNormalize ee4 --R --R +-+ @@ -4240,7 +4240,7 @@ $$ <<*>>= )clear all ---S 95 +--S 95 of 131 aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x) --R --R @@ -4254,7 +4254,7 @@ aa:=integrate(1/(a*x^2+b*x+c)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 96 +--S 96 of 131 bb:=(2*(2*a*x+b))/((4*a*c-b^2)*sqrt(a*x^2+b*x+c)) --R --R 4a x + 2b @@ -4265,7 +4265,7 @@ bb:=(2*(2*a*x+b))/((4*a*c-b^2)*sqrt(a*x^2+b*x+c)) --R Type: Expression Integer --E ---S 97 +--S 97 of 131 cc:=aa-bb --R --R (3) @@ -4279,7 +4279,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 98 14:290 Schaums and Axiom differ by a constant +--S 98 of 131 14:290 Schaums and Axiom differ by a constant dd:=ratDenom cc --R --R +-+ @@ -4299,7 +4299,7 @@ $$ <<*>>= )clear all ---S 99 +--S 99 of 131 aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x) --R --R @@ -4312,7 +4312,7 @@ aa:=integrate(x/(a*x^2+b*x+c)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 100 +--S 100 of 131 bb:=(2*(b*x+2*c))/((b^2-4*a*c)*sqrt(a*x^2+b*x+c)) --R --R - 2b x - 4c @@ -4323,7 +4323,7 @@ bb:=(2*(b*x+2*c))/((b^2-4*a*c)*sqrt(a*x^2+b*x+c)) --R Type: Expression Integer --E ---S 101 +--S 101 of 131 cc:=aa-bb --R --R (3) @@ -4337,7 +4337,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 102 14:291 Schaums and Axiom differ by a constant +--S 102 of 131 14:291 Schaums and Axiom differ by a constant dd:=ratDenom cc --R --R +-+ @@ -4358,7 +4358,7 @@ $$ <<*>>= )clear all ---S 103 +--S 103 of 131 aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x) --R --R @@ -4416,7 +4416,7 @@ aa:=integrate(x^2/(a*x^2+b*x+c)^(3/2),x) --R Type: Union(List Expression Integer,...) --E ---S 104 +--S 104 of 131 t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R --R (2) @@ -4447,7 +4447,7 @@ t1:=integrate(1/sqrt(a*x^2+b*x+c),x) --R Type: Union(List Expression Integer,...) --E ---S 105 +--S 105 of 131 bb1:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.1 --R --R (3) @@ -4476,7 +4476,7 @@ bb1:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.1 --R Type: Expression Integer --E ---S 106 +--S 106 of 131 bb2:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.2 --R --R (4) @@ -4495,7 +4495,7 @@ bb2:=((2*b^2-4*a*c)*x+2*b*c)/(a*(4*a*c-b^2)*sqrt(a*x^2+b*x+c))+1/a*t1.2 --R Type: Expression Integer --E ---S 107 +--S 107 of 131 cc1:=aa.1-bb1 --R --R (5) @@ -4509,7 +4509,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 108 +--S 108 of 131 cc2:=aa.2-bb1 --R --R (6) @@ -4558,7 +4558,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 109 +--S 109 of 131 cc3:=aa.1-bb2 --R --R (7) @@ -4607,7 +4607,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 110 +--S 110 of 131 cc4:=aa.2-bb2 --R --R (8) @@ -4621,7 +4621,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 111 14:292 Schaums and Axiom differ by a constant +--S 111 of 131 14:292 Schaums and Axiom differ by a constant dd4:=ratDenom cc4 --R --R +-+ @@ -4643,7 +4643,7 @@ $$ <<*>>= )clear all ---S 112 +--S 112 of 131 aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x) --R --R @@ -4669,7 +4669,7 @@ aa:=integrate(1/(x*(a*x^2+b*x+c)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 113 +--S 113 of 131 t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R --R +--------------+ @@ -4683,7 +4683,7 @@ t1:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 114 +--S 114 of 131 t2:=integrate(1/(a*x^2+b*x+c)^(3/2),x) --R --R +--------------+ @@ -4696,7 +4696,7 @@ t2:=integrate(1/(a*x^2+b*x+c)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 115 +--S 115 of 131 bb:=1/(c*sqrt(a*x^2+b*x+c))+1/c*t1-b/(2*c)*t2 --R --R (4) @@ -4726,7 +4726,7 @@ bb:=1/(c*sqrt(a*x^2+b*x+c))+1/c*t1-b/(2*c)*t2 --R Type: Expression Integer --E ---S 116 +--S 116 of 131 cc:=aa-bb --R --R (5) @@ -4773,7 +4773,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 117 +--S 117 of 131 dd:=ratDenom cc --R --R (6) @@ -4794,7 +4794,7 @@ dd:=ratDenom cc --R Type: Expression Integer --E ---S 118 +--S 118 of 131 ee:=expandLog dd --R --R (7) @@ -4814,7 +4814,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 119 14:293 Schaums and Axiom differ by a constant +--S 119 of 131 14:293 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R +-+ @@ -4840,7 +4840,7 @@ $$ <<*>>= )clear all ---S 120 +--S 120 of 131 aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x) --R --R @@ -4881,7 +4881,7 @@ aa:=integrate(1/(x^2*(a*x^2+b*x+c)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 121 +--S 121 of 131 t1:=integrate(1/(a*x^2+b*x+c)^(3/2),x) --R --R +--------------+ @@ -4894,7 +4894,7 @@ t1:=integrate(1/(a*x^2+b*x+c)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 122 +--S 122 of 131 t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R --R +--------------+ @@ -4908,7 +4908,7 @@ t2:=integrate(1/(x*sqrt(a*x^2+b*x+c)),x) --R Type: Union(Expression Integer,...) --E ---S 123 +--S 123 of 131 bb:=-(a*x^2+2*b*x+c)/(c^2*x*sqrt(a*x^2+b*x+c))+(b^2-2*a*c)/(2*c^2)*t1-(3*b)/(2*c^2)*t2 --R --R (4) @@ -4947,7 +4947,7 @@ bb:=-(a*x^2+2*b*x+c)/(c^2*x*sqrt(a*x^2+b*x+c))+(b^2-2*a*c)/(2*c^2)*t1-(3*b)/(2*c --R Type: Expression Integer --E ---S 124 +--S 124 of 131 cc:=aa-bb --R --R (5) @@ -5024,7 +5024,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 125 +--S 125 of 131 dd:=ratDenom cc --R --R (6) @@ -5045,7 +5045,7 @@ dd:=ratDenom cc --R Type: Expression Integer --E ---S 126 +--S 126 of 131 ee:=expandLog dd --R --R (7) @@ -5065,7 +5065,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 127 14:294 Schaums and Axiom differ by a constant +--S 127 of 131 14:294 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R +-+ @@ -5090,7 +5090,7 @@ $$ <<*>>= )clear all ---S 128 14:295 Axiom cannot compute this integral +--S 128 of 131 14:295 Axiom cannot compute this integral aa:=integrate((a*x^2+b*x+c)^(n+1/2),x) --R --R @@ -5112,7 +5112,7 @@ $$ <<*>>= )clear all ---S 129 14:296 Axiom cannot compute this integral +--S 129 of 131 14:296 Axiom cannot compute this integral aa:=integrate(x*(a*x^2+b*x+c)^(n+1/2),x) --R --R @@ -5138,7 +5138,7 @@ $$ <<*>>= )clear all ---S 130 14:297 Axiom cannot compute this integral +--S 130 of 131 14:297 Axiom cannot compute this integral aa:=integrate(1/(a*x^2+b*x+c)^(n+1/2),x) --R --R @@ -5169,7 +5169,7 @@ $$ <<*>>= )clear all ---S 131 14:298 Axiom cannot compute this integral +--S 131 of 131 14:298 Axiom cannot compute this integral aa:=integrate(1/(x*(a*x^2+b*x+c)^(n+1/2)),x) --R --R diff --git a/src/input/schaum14.input.pamphlet b/src/input/schaum14.input.pamphlet index 3452b30..dacd0ee 100644 --- a/src/input/schaum14.input.pamphlet +++ b/src/input/schaum14.input.pamphlet @@ -19,7 +19,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 39 aa:=integrate(1/(x^3+a^3),x) --R --R @@ -33,7 +33,7 @@ aa:=integrate(1/(x^3+a^3),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 39 bb:=1/(6*a^2)*log((x+a)^2/(x^2-a*x+a^2))+1/(a^2*sqrt(3))*atan((2*x-a)/(a*sqrt(3))) --R --R 2 2 +-+ @@ -47,7 +47,7 @@ bb:=1/(6*a^2)*log((x+a)^2/(x^2-a*x+a^2))+1/(a^2*sqrt(3))*atan((2*x-a)/(a*sqrt(3) --R Type: Expression Integer --E ---S 3 +--S 3 of 39 cc:=aa-bb --R --R 2 2 @@ -61,7 +61,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 14:299 Schaums and Axiom agree +--S 4 of 39 14:299 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -78,7 +78,7 @@ $$ <<*>>= )clear all ---S 5 +--S 5 of 39 aa:=integrate(x/(x^3+a^3),x) --R --R @@ -92,7 +92,7 @@ aa:=integrate(x/(x^3+a^3),x) --R Type: Union(Expression Integer,...) --E ---S 6 +--S 6 of 39 bb:=1/(6*a)*log((x^2-a*x+a^2)/(x+a)^2)+1/(a*sqrt(3))*atan((2*x-a)/(a*sqrt(3))) --R --R 2 2 +-+ @@ -105,7 +105,7 @@ bb:=1/(6*a)*log((x^2-a*x+a^2)/(x+a)^2)+1/(a*sqrt(3))*atan((2*x-a)/(a*sqrt(3))) --R Type: Expression Integer --E ---S 7 +--S 7 of 39 cc:=aa-bb --R --R 2 2 @@ -118,7 +118,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 8 14:300 Schaums and Axiom agree +--S 8 of 39 14:300 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -134,7 +134,7 @@ $$ <<*>>= )clear all ---S 9 +--S 9 of 39 aa:=integrate(x^2/(x^3+a^3),x) --R --R @@ -145,7 +145,7 @@ aa:=integrate(x^2/(x^3+a^3),x) --R Type: Union(Expression Integer,...) --E ---S 10 +--S 10 of 39 bb:=1/3*log(x^3+a^3) --R --R 3 3 @@ -155,7 +155,7 @@ bb:=1/3*log(x^3+a^3) --R Type: Expression Integer --E ---S 11 14:301 Schaums and Axiom agree +--S 11 of 39 14:301 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -171,7 +171,7 @@ $$ <<*>>= )clear all ---S 12 +--S 12 of 39 aa:=integrate(1/(x*(x^3+a^3)),x) --R --R @@ -183,7 +183,7 @@ aa:=integrate(1/(x*(x^3+a^3)),x) --R Type: Union(Expression Integer,...) --E ---S 13 +--S 13 of 39 bb:=1/(3*a^3)*log(x^3/(x^3+a^3)) --R --R 3 @@ -197,7 +197,7 @@ bb:=1/(3*a^3)*log(x^3/(x^3+a^3)) --R Type: Expression Integer --E ---S 14 +--S 14 of 39 cc:=aa-bb --R --R 3 @@ -211,7 +211,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 15 14:302 Schaums and Axiom agree +--S 15 of 39 14:302 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -228,7 +228,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 39 aa:=integrate(1/(x^2*(x^3+a^3)),x) --R --R @@ -243,7 +243,7 @@ aa:=integrate(1/(x^2*(x^3+a^3)),x) --R Type: Union(Expression Integer,...) --E ---S 16 +--S 16 of 39 bb:=-1/(a^3*x)-1/(6*a^4)*log((x^2-a*x+a^2)/(x+a)^2)-1/(a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3))) --R --R 2 2 +-+ @@ -257,7 +257,7 @@ bb:=-1/(a^3*x)-1/(6*a^4)*log((x^2-a*x+a^2)/(x+a)^2)-1/(a^4*sqrt(3))*atan((2*x-a) --R Type: Expression Integer --E ---S 17 +--S 17 of 39 cc:=aa-bb --R --R 2 2 @@ -271,7 +271,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 18 14:303 Schaums and Axiom agree +--S 18 of 39 14:303 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -289,7 +289,7 @@ $$ <<*>>= )clear all ---S 19 +--S 19 of 39 aa:=integrate(1/(x^3+a^3)^2,x) --R --R @@ -307,7 +307,7 @@ aa:=integrate(1/(x^3+a^3)^2,x) --R Type: Union(Expression Integer,...) --E ---S 20 +--S 20 of 39 bb:=x/(3*a^3*(x^3+a^3))+1/(9*a^5)*log((x+a)^2/(x^2-a*x+a^2))+2/(3*a^5*sqrt(3))*atan((2*x-a)/(a*sqrt(3))) --R --R (2) @@ -322,7 +322,7 @@ bb:=x/(3*a^3*(x^3+a^3))+1/(9*a^5)*log((x+a)^2/(x^2-a*x+a^2))+2/(3*a^5*sqrt(3))*a --R Type: Expression Integer --E ---S 21 +--S 21 of 39 cc:=aa-bb --R --R 2 2 @@ -336,7 +336,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 22 14:304 Schaums and Axiom agree +--S 22 of 39 14:304 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -354,7 +354,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 39 aa:=integrate(x/(x^3+a^3)^2,x) --R --R @@ -372,7 +372,7 @@ aa:=integrate(x/(x^3+a^3)^2,x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 39 bb:=x^2/(3*a^3*(x^3+a^3))+1/(18*a^4)*log((x^2-a*x+a^2)/(x+a)^2)+1/(3*a^4*sqrt(3))*atan((2*x-a)/(a*sqrt(3))) --R --R (2) @@ -387,7 +387,7 @@ bb:=x^2/(3*a^3*(x^3+a^3))+1/(18*a^4)*log((x^2-a*x+a^2)/(x+a)^2)+1/(3*a^4*sqrt(3) --R Type: Expression Integer --E ---S 25 +--S 25 of 39 cc:=aa-bb --R --R 2 2 @@ -401,7 +401,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 26 14:305 Schaums and Axiom agree +--S 26 of 39 14:305 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -417,7 +417,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 39 aa:=integrate(x^2/(x^3+a^3)^2,x) --R --R @@ -428,7 +428,7 @@ aa:=integrate(x^2/(x^3+a^3)^2,x) --R Type: Union(Expression Integer,...) --E ---S 28 +--S 28 of 39 bb:=-1/(3*(x^3+a^3)) --R --R 1 @@ -438,7 +438,7 @@ bb:=-1/(3*(x^3+a^3)) --R Type: Fraction Polynomial Integer --E ---S 29 14:306 Schaums and Axiom agree +--S 29 of 39 14:306 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -454,7 +454,7 @@ $$ <<*>>= )clear all ---S 30 +--S 30 of 39 aa:=integrate(1/(x*(x^3+a^3)^2),x) --R --R @@ -466,7 +466,7 @@ aa:=integrate(1/(x*(x^3+a^3)^2),x) --R Type: Union(Expression Integer,...) --E ---S 31 +--S 31 of 39 bb:=1/(3*a^3*(x^3+a^3))+1/(3*a^6)*log(x^3/(x^3+a^3)) --R --R 3 @@ -480,7 +480,7 @@ bb:=1/(3*a^3*(x^3+a^3))+1/(3*a^6)*log(x^3/(x^3+a^3)) --R Type: Expression Integer --E ---S 32 +--S 32 of 39 cc:=aa-bb --R --R 3 @@ -494,7 +494,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 33 14:307 Schaums and Axiom agree +--S 33 of 39 14:307 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -511,7 +511,7 @@ $$ <<*>>= )clear all ---S 34 +--S 34 of 39 aa:=integrate(1/(x^2*(x^3+a^3)^2),x) --R --R @@ -529,7 +529,7 @@ aa:=integrate(1/(x^2*(x^3+a^3)^2),x) --R Type: Union(Expression Integer,...) --E ---S 35 +--S 35 of 39 t1:=integrate(x/(x^3+a^3),x) --R --R +-+ @@ -542,7 +542,7 @@ t1:=integrate(x/(x^3+a^3),x) --R Type: Union(Expression Integer,...) --E ---S 36 +--S 36 of 39 bb:=-1/(a^6*x)-x^2/(3*a^6*(x^3+a^3))-4/(3*a^6)*t1 --R --R (3) @@ -559,7 +559,7 @@ bb:=-1/(a^6*x)-x^2/(3*a^6*(x^3+a^3))-4/(3*a^6)*t1 --R Type: Expression Integer --E ---S 37 14:308 Schaums and Axiom agree +--S 37 of 39 14:308 Schaums and Axiom agree cc:=aa-bb --R --R (4) 0 @@ -575,7 +575,7 @@ $$ <<*>>= )clear all ---S 38 14:309 Axiom cannot compute this integral +--S 38 of 39 14:309 Axiom cannot compute this integral aa:=integrate(x^m/(x^3+a^3),x) --R --R @@ -596,7 +596,7 @@ $$ <<*>>= )clear all ---S 39 14:310 Axiom cannot compute this integral +--S 39 of 39 14:310 Axiom cannot compute this integral aa:=integrate(1/(x^n*(x^3+a^3)),x) --R --R diff --git a/src/input/schaum15.input.pamphlet b/src/input/schaum15.input.pamphlet index 0c01fbb..3a02bf0 100644 --- a/src/input/schaum15.input.pamphlet +++ b/src/input/schaum15.input.pamphlet @@ -20,7 +20,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 65 aa:=integrate(1/(x^4+a^4),x) --R --R @@ -54,7 +54,7 @@ aa:=integrate(1/(x^4+a^4),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 65 bb:=1/(4*a^3*sqrt(2))*log((x^2+a*x*sqrt(2)+a^2)/(x^2-a*x*sqrt(2)+a^2))-1/(2*a^3*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2)) --R --R +-+ 2 2 +-+ @@ -68,7 +68,7 @@ bb:=1/(4*a^3*sqrt(2))*log((x^2+a*x*sqrt(2)+a^2)/(x^2-a*x*sqrt(2)+a^2))-1/(2*a^3* --R Type: Expression Integer --E ---S 3 +--S 3 of 65 cc:=aa-bb --R --R (3) @@ -119,7 +119,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 65 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -130,7 +130,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 5 +--S 5 of 65 dd:=atanrule cc --R --R (5) @@ -181,7 +181,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 6 +--S 6 of 65 ee:=rootSimp dd --R --R (6) @@ -208,7 +208,7 @@ ee:=rootSimp dd --R Type: Expression Complex Integer --E ---S 7 +--S 7 of 65 ff:=expandLog ee --R --R (7) @@ -228,7 +228,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 8 +--S 8 of 65 gg:=complexNormalize ff --R --R %i %i @@ -240,7 +240,7 @@ gg:=complexNormalize ff --R Type: Expression Complex Integer --E ---S 9 14:311 Schaums and Axiom differ by a constant +--S 9 of 65 14:311 Schaums and Axiom differ by a constant hh:=expandLog gg --R --R %i log(%i) - %i log(- %i) + (- 2 - %i)log(- 1) @@ -259,7 +259,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 65 aa:=integrate(x/(x^4+a^4),x) --R --R @@ -274,7 +274,7 @@ aa:=integrate(x/(x^4+a^4),x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 65 bb:=1/(2*a^2)*atan(x^2/a^2) --R --R 2 @@ -288,7 +288,7 @@ bb:=1/(2*a^2)*atan(x^2/a^2) --R Type: Expression Integer --E ---S 12 14:312 Schaums and Axiom agree +--S 12 of 65 14:312 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -306,7 +306,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 65 aa:=integrate(x^2/(x^4+a^4),x) --R --R @@ -340,7 +340,7 @@ aa:=integrate(x^2/(x^4+a^4),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 65 bb:=1/(4*a*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))-1/(2*a*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2)) --R --R +-+ 2 2 +-+ @@ -353,7 +353,7 @@ bb:=1/(4*a*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))-1/(2*a*sqrt --R Type: Expression Integer --E ---S 15 +--S 15 of 65 cc:=aa-bb --R --R (3) @@ -404,7 +404,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 16 +--S 16 of 65 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -415,7 +415,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 17 +--S 17 of 65 dd:=atanrule cc --R --R (5) @@ -466,7 +466,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 18 +--S 18 of 65 ee:=expandLog dd --R --R (6) @@ -519,7 +519,7 @@ ee:=expandLog dd --R Type: Expression Complex Integer --E ---S 19 +--S 19 of 65 ff:=rootSimp ee --R --R (7) @@ -537,7 +537,7 @@ ff:=rootSimp ee --R Type: Expression Complex Integer --E ---S 20 14:313 Schaums and Axiom differ by a constant +--S 20 of 65 14:313 Schaums and Axiom differ by a constant gg:=complexNormalize ff --R --R %i log(2) - %i log(- 1) - %i log(- 2) @@ -556,7 +556,7 @@ $$ <<*>>= )clear all ---S 21 +--S 21 of 65 aa:=integrate(x^3/(x^4+a^4),x) --R --R @@ -567,7 +567,7 @@ aa:=integrate(x^3/(x^4+a^4),x) --R Type: Union(Expression Integer,...) --E ---S 22 +--S 22 of 65 bb:=1/4*log(x^4+a^4) --R --R 4 4 @@ -577,7 +577,7 @@ bb:=1/4*log(x^4+a^4) --R Type: Expression Integer --E ---S 23 14:314 Schaums and Axiom agree +--S 23 of 65 14:314 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -593,7 +593,7 @@ $$ <<*>>= )clear all ---S 24 +--S 24 of 65 aa:=integrate(1/(x*(x^4+a^4)),x) --R --R @@ -605,7 +605,7 @@ aa:=integrate(1/(x*(x^4+a^4)),x) --R Type: Union(Expression Integer,...) --E ---S 25 +--S 25 of 65 bb:=1/(4*a^4)*log(x^4/(x^4+a^4)) --R --R 4 @@ -619,7 +619,7 @@ bb:=1/(4*a^4)*log(x^4/(x^4+a^4)) --R Type: Expression Integer --E ---S 26 +--S 26 of 65 cc:=aa-bb --R --R 4 @@ -633,7 +633,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 27 14:315 Schaums and Axiom agree +--S 27 of 65 14:315 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -651,7 +651,7 @@ $$ <<*>>= )clear all ---S 28 +--S 28 of 65 aa:=integrate(1/(x^2*(x^4+a^4)),x) --R --R @@ -697,7 +697,7 @@ aa:=integrate(1/(x^2*(x^4+a^4)),x) --R Type: Union(Expression Integer,...) --E ---S 29 +--S 29 of 65 bb:=-1/(a^4*x)-1/(4*a^5*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2))+1/(2*a^5*sqrt(2))*atan((a*x*sqrt(2))/(x^2-a^2)) --R --R +-+ 2 2 +-+ @@ -711,7 +711,7 @@ bb:=-1/(a^4*x)-1/(4*a^5*sqrt(2))*log((x^2-a*x*sqrt(2)+a^2)/(x^2+a*x*sqrt(2)+a^2) --R Type: Expression Integer --E ---S 30 +--S 30 of 65 cc:=aa-bb --R --R (3) @@ -762,7 +762,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 31 +--S 31 of 65 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -773,7 +773,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 32 +--S 32 of 65 dd:=atanrule cc --R --R (5) @@ -824,7 +824,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 33 +--S 33 of 65 ee:=expandLog dd --R --R (6) @@ -881,7 +881,7 @@ ee:=expandLog dd --R Type: Expression Complex Integer --E ---S 34 +--S 34 of 65 ff:=rootSimp ee --R --R (7) @@ -901,7 +901,7 @@ ff:=rootSimp ee --R Type: Expression Complex Integer --E ---S 35 14:316 Schaums and Axiom differ by a constant +--S 35 of 65 14:316 Schaums and Axiom differ by a constant gg:=complexNormalize ff --R --R - %i log(2) + %i log(- 1) + %i log(- 2) @@ -920,7 +920,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 65 aa:=integrate(1/(x^3*(x^4+a^4)),x) --R --R @@ -935,7 +935,7 @@ aa:=integrate(1/(x^3*(x^4+a^4)),x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 65 bb:=-1/(2*a^4*x^2)-1/(2*a^6)*atan(x^2/a^2) --R --R 2 @@ -949,7 +949,7 @@ bb:=-1/(2*a^4*x^2)-1/(2*a^6)*atan(x^2/a^2) --R Type: Expression Integer --E ---S 38 14:317 Schaums and Axiom agree +--S 38 of 65 14:317 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -966,7 +966,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 65 aa:=integrate(1/(x^4-a^4),x) --R --R @@ -979,7 +979,7 @@ aa:=integrate(1/(x^4-a^4),x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 65 bb:=1/(4*a^3)*log((x-a)/(x+a))-1/(2*a^3)*atan(x/a) --R --R x - a x @@ -991,7 +991,7 @@ bb:=1/(4*a^3)*log((x-a)/(x+a))-1/(2*a^3)*atan(x/a) --R Type: Expression Integer --E ---S 41 +--S 41 of 65 cc:=aa-bb --R --R x - a @@ -1003,7 +1003,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 42 14:318 Schaums and Axiom agree +--S 42 of 65 14:318 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1019,7 +1019,7 @@ $$ <<*>>= )clear all ---S 43 +--S 43 of 65 aa:=integrate(x/(x^4-a^4),x) --R --R @@ -1031,7 +1031,7 @@ aa:=integrate(x/(x^4-a^4),x) --R Type: Union(Expression Integer,...) --E ---S 44 +--S 44 of 65 bb:=1/(4*a^2)*log((x^2-a^2)/(x^2+a^2)) --R --R 2 2 @@ -1045,7 +1045,7 @@ bb:=1/(4*a^2)*log((x^2-a^2)/(x^2+a^2)) --R Type: Expression Integer --E ---S 45 +--S 45 of 65 cc:=aa-bb --R --R 2 2 @@ -1059,7 +1059,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 46 14:319 Schaums and Axiom agree +--S 46 of 65 14:319 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1076,7 +1076,7 @@ $$ <<*>>= )clear all ---S 47 +--S 47 of 65 aa:=integrate(x^2/(x^4-a^4),x) --R --R @@ -1088,7 +1088,7 @@ aa:=integrate(x^2/(x^4-a^4),x) --R Type: Union(Expression Integer,...) --E ---S 48 +--S 48 of 65 bb:=1/(4*a)*log((x-a)/(x+a))+1/(2*a)*atan(x/a) --R --R x - a x @@ -1099,7 +1099,7 @@ bb:=1/(4*a)*log((x-a)/(x+a))+1/(2*a)*atan(x/a) --R Type: Expression Integer --E ---S 49 +--S 49 of 65 cc:=aa-bb --R --R x - a @@ -1110,7 +1110,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 50 14:320 Schaums and Axiom agree +--S 50 of 65 14:320 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1126,7 +1126,7 @@ $$ <<*>>= )clear all ---S 51 +--S 51 of 65 aa:=integrate(x^3/(x^4-a^4),x) --R --R @@ -1137,7 +1137,7 @@ aa:=integrate(x^3/(x^4-a^4),x) --R Type: Union(Expression Integer,...) --E ---S 52 +--S 52 of 65 bb:=1/4*log(x^4-a^4) --R --R 4 4 @@ -1147,7 +1147,7 @@ bb:=1/4*log(x^4-a^4) --R Type: Expression Integer --E ---S 53 14:321 Schaums and Axiom agree +--S 53 of 65 14:321 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1163,7 +1163,7 @@ $$ <<*>>= )clear all ---S 54 +--S 54 of 65 aa:=integrate(1/(x*(x^4-a^4)),x) --R --R @@ -1175,7 +1175,7 @@ aa:=integrate(1/(x*(x^4-a^4)),x) --R Type: Union(Expression Integer,...) --E ---S 55 +--S 55 of 65 bb:=1/(4*a^4)*log((x^4-a^4)/x^4) --R --R 4 4 @@ -1189,7 +1189,7 @@ bb:=1/(4*a^4)*log((x^4-a^4)/x^4) --R Type: Expression Integer --E ---S 56 +--S 56 of 65 cc:=aa-bb --R --R 4 4 @@ -1203,7 +1203,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 57 14:322 Schaums and Axiom agree +--S 57 of 65 14:322 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1220,7 +1220,7 @@ $$ <<*>>= )clear all ---S 58 +--S 58 of 65 aa:=integrate(1/(x^2*(x^4-a^4)),x) --R --R @@ -1233,7 +1233,7 @@ aa:=integrate(1/(x^2*(x^4-a^4)),x) --R Type: Union(Expression Integer,...) --E ---S 59 +--S 59 of 65 bb:=1/(a^4*x)+1/(4*a^5)*log((x-a)/(x+a))+1/(2*a^5)*atan(x/a) --R --R x - a x @@ -1245,7 +1245,7 @@ bb:=1/(a^4*x)+1/(4*a^5)*log((x-a)/(x+a))+1/(2*a^5)*atan(x/a) --R Type: Expression Integer --E ---S 60 +--S 60 of 65 cc:=aa-bb --R --R x - a @@ -1257,7 +1257,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 61 14:323 Schaums and Axiom agree +--S 61 of 65 14:323 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1273,7 +1273,7 @@ $$ <<*>>= )clear all ---S 62 +--S 62 of 65 aa:=integrate(1/(x^3*(x^4-a^4)),x) --R --R @@ -1285,7 +1285,7 @@ aa:=integrate(1/(x^3*(x^4-a^4)),x) --R Type: Union(Expression Integer,...) --E ---S 63 +--S 63 of 65 bb:=1/(2*a^4*x^2)+1/(4*a^6)*log((x^2-a^2)/(x^2+a^2)) --R --R 2 2 @@ -1299,7 +1299,7 @@ bb:=1/(2*a^4*x^2)+1/(4*a^6)*log((x^2-a^2)/(x^2+a^2)) --R Type: Expression Integer --E ---S 64 +--S 64 of 65 cc:=aa-bb --R --R 2 2 @@ -1313,7 +1313,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 65 14:324 Schaums and Axiom agree +--S 65 of 65 14:324 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 diff --git a/src/input/schaum16.input.pamphlet b/src/input/schaum16.input.pamphlet index caf8bfd..4288115 100644 --- a/src/input/schaum16.input.pamphlet +++ b/src/input/schaum16.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 45 aa:=integrate(1/(x*(x^n+a^n)),x) --R --R n log(x) n @@ -29,7 +29,7 @@ aa:=integrate(1/(x*(x^n+a^n)),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 45 bb:=1/(n*a^n)*log(x^n/(x^n+a^n)) --R --R n @@ -43,7 +43,7 @@ bb:=1/(n*a^n)*log(x^n/(x^n+a^n)) --R Type: Expression Integer --E ---S 3 +--S 3 of 45 cc:=aa-bb --R --R n @@ -57,7 +57,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 45 dd:=expandLog cc --R --R n log(x) n n n n @@ -68,7 +68,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 5 14:325 Schaums and Axiom agree +--S 5 of 45 14:325 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -84,7 +84,7 @@ $$ <<*>>= )clear all ---S 8 +--S 8 of 45 aa:=integrate(x^(n-1)/(x^n+a^n),x) --R --R @@ -95,7 +95,7 @@ aa:=integrate(x^(n-1)/(x^n+a^n),x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 45 bb:=1/n*log(x^n+a^n) --R --R n n @@ -105,7 +105,7 @@ bb:=1/n*log(x^n+a^n) --R Type: Expression Integer --E ---S 10 +--S 10 of 45 cc:=aa-bb --R --R n log(x) n n n @@ -115,7 +115,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 11 +--S 11 of 45 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -123,7 +123,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 12 14:326 Schaums and Axiom agree +--S 12 of 45 14:326 Schaums and Axiom agree dd:=explog cc --R --R (5) 0 @@ -140,7 +140,7 @@ $$ <<*>>= )clear all ---S 13 14:327 Axiom cannot compute this integral +--S 13 of 45 14:327 Axiom cannot compute this integral aa:=integrate(x^m/(x^n+a^n)^r,x) --R --R @@ -162,7 +162,7 @@ $$ <<*>>= )clear all ---S 14 14:328 Axiom cannot compute this integral +--S 14 of 45 14:328 Axiom cannot compute this integral aa:=integrate(1/(x^m*(x^n+a^n)^r),x) --R --R @@ -184,7 +184,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 45 aa:=integrate(1/(x*sqrt(x^n+a^n)),x) --R --R @@ -212,7 +212,7 @@ aa:=integrate(1/(x*sqrt(x^n+a^n)),x) --R Type: Union(List Expression Integer,...) --E ---S 16 +--S 16 of 45 bb:=1/(n*sqrt(a^n))*log((sqrt(x^n+a^n)-sqrt(a^n))/(sqrt(x^n+a^n)+sqrt(a^n))) --R --R +-------+ +--+ @@ -229,7 +229,7 @@ bb:=1/(n*sqrt(a^n))*log((sqrt(x^n+a^n)-sqrt(a^n))/(sqrt(x^n+a^n)+sqrt(a^n))) --R Type: Expression Integer --E ---S 17 +--S 17 of 45 cc1:=aa.1-bb --R --R (3) @@ -254,7 +254,7 @@ cc1:=aa.1-bb --R Type: Expression Integer --E ---S 18 +--S 18 of 45 dd1:=expandLog cc1 --R --R (4) @@ -272,7 +272,7 @@ dd1:=expandLog cc1 --R Type: Expression Integer --E ---S 19 +--S 19 of 45 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -280,7 +280,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 20 +--S 20 of 45 ee1:=explog dd1 --R --R (6) @@ -298,7 +298,7 @@ ee1:=explog dd1 --R Type: Expression Integer --E ---S 21 +--S 21 of 45 ff1:=complexNormalize ee1 --R --R n log(a) + 4log(- 1) @@ -309,7 +309,7 @@ ff1:=complexNormalize ee1 --R Type: Expression Integer --E ---S 22 14:329 Schaums and Axiom differ by a constant +--S 22 of 45 14:329 Schaums and Axiom differ by a constant gg1:=explog ff1 --R --R n log(a) + 4log(- 1) @@ -329,7 +329,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 45 aa:=integrate(1/(x*(x^n-a^n)),x) --R --R @@ -341,7 +341,7 @@ aa:=integrate(1/(x*(x^n-a^n)),x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 45 bb:=1/(n*a^n)*log((x^n-a^n)/x^n) --R --R n n @@ -355,7 +355,7 @@ bb:=1/(n*a^n)*log((x^n-a^n)/x^n) --R Type: Expression Integer --E ---S 25 +--S 25 of 45 cc:=aa-bb --R --R n n @@ -369,7 +369,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 26 +--S 26 of 45 dd:=expandLog cc --R --R n log(x) n n n n @@ -380,7 +380,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 27 +--S 27 of 45 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -388,7 +388,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 28 +--S 28 of 45 ee:=explog dd --R --R n @@ -399,7 +399,7 @@ ee:=explog dd --R Type: Expression Integer --E ---S 29 +--S 29 of 45 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -407,7 +407,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 30 14:330 Schaums and Axiom agree +--S 30 of 45 14:330 Schaums and Axiom agree ff:=logpow ee --R --R (8) 0 @@ -423,7 +423,7 @@ $$ <<*>>= )clear all ---S 31 +--S 31 of 45 aa:=integrate(x^(n-1)/(x^n-a^n),x) --R --R @@ -434,7 +434,7 @@ aa:=integrate(x^(n-1)/(x^n-a^n),x) --R Type: Union(Expression Integer,...) --E ---S 32 +--S 32 of 45 bb:=1/n*log(x^n-a^n) --R --R n n @@ -444,7 +444,7 @@ bb:=1/n*log(x^n-a^n) --R Type: Expression Integer --E ---S 33 +--S 33 of 45 cc:=aa-bb --R --R n log(x) n n n @@ -454,7 +454,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 34 +--S 34 of 45 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -462,7 +462,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 35 14:331 Schaums and Axiom agree +--S 35 of 45 14:331 Schaums and Axiom agree dd:=explog cc --R --R (5) 0 @@ -480,7 +480,7 @@ $$ <<*>>= )clear all ---S 36 14:332 Axiom cannot compute this integral +--S 36 of 45 14:332 Axiom cannot compute this integral aa:=integrate(x^m/(x^n-a^n)^r,x) --R --R @@ -502,7 +502,7 @@ $$ <<*>>= )clear all ---S 37 14:333 Axiom cannot compute this integral +--S 37 of 45 14:333 Axiom cannot compute this integral aa:=integrate(1/(x^m*(x^n-a^n)^r),x) --R --R @@ -523,7 +523,7 @@ $$ <<*>>= )clear all ---S 38 +--S 38 of 45 aa:=integrate(1/(x*sqrt(x^n-a^n)),x) --R --R @@ -551,7 +551,7 @@ aa:=integrate(1/(x*sqrt(x^n-a^n)),x) --R Type: Union(List Expression Integer,...) --E ---S 39 +--S 39 of 45 bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n)) --R --R +--+ @@ -567,7 +567,7 @@ bb:=2/(n*sqrt(a^n))*acos(sqrt(a^n/x^n)) --R Type: Expression Integer --E ---S 40 +--S 40 of 45 cc1:=aa.1-bb --R --R (3) @@ -591,7 +591,7 @@ cc1:=aa.1-bb --R Type: Expression Integer --E ---S 41 14:334 Axiom cannot simplify this expression +--S 41 of 45 14:334 Axiom cannot simplify this expression cc2:=aa.2-bb --R --R +--+ +---------------+ +--+ @@ -623,7 +623,7 @@ $$ <<*>>= )clear all ---S 42 14:335 Axiom cannot compute this integral +--S 42 of 45 14:335 Axiom cannot compute this integral aa:=integrate(x^(p-1)/(x^(2*m)+a^(2*m)),x) --R --R @@ -653,7 +653,7 @@ $$ <<*>>= )clear all ---S 43 14:336 Axiom cannot compute this integral +--S 43 of 45 14:336 Axiom cannot compute this integral aa:=integrate(x^(p-1)/(x^(2*m)-a^(2*m)),x) --R --R @@ -687,7 +687,7 @@ $$ <<*>>= )clear all ---S 44 14:337 Axiom cannot compute this integral +--S 44 of 45 14:337 Axiom cannot compute this integral aa:=integrate(x^(p-1)/(x^(2*m+1)+a^(2*m+1)),x) --R --R @@ -723,7 +723,7 @@ $$ <<*>>= )clear all ---S 45 14:338 Axiom cannot compute this integral +--S 45 of 45 14:338 Axiom cannot compute this integral aa:=integrate(x^(p-1)/(x^(2*m+1)-a^(2*m+1)),x) --R --R diff --git a/src/input/schaum17.input.pamphlet b/src/input/schaum17.input.pamphlet index 6939c30..d9d7ac1 100644 --- a/src/input/schaum17.input.pamphlet +++ b/src/input/schaum17.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 136 aa:=integrate(sin(a*x),x) --R --R @@ -28,7 +28,7 @@ aa:=integrate(sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 136 bb:=-cos(a*x)/a --R --R cos(a x) @@ -37,7 +37,7 @@ bb:=-cos(a*x)/a --R Type: Expression Integer --E ---S 3 14:339 Schaums and Axiom agree +--S 3 of 136 14:339 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -53,7 +53,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 136 aa:=integrate(x*sin(a*x),x) --R --R @@ -64,7 +64,7 @@ aa:=integrate(x*sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 136 bb:=sin(a*x)/a^2-(x*cos(a*x))/a --R --R sin(a x) - a x cos(a x) @@ -74,7 +74,7 @@ bb:=sin(a*x)/a^2-(x*cos(a*x))/a --R Type: Expression Integer --E ---S 6 14:340 Schaums and Axiom agree +--S 6 of 136 14:340 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -90,7 +90,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 136 aa:=integrate(x^2*sin(a*x),x) --R --R @@ -102,7 +102,7 @@ aa:=integrate(x^2*sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 136 bb:=(2*x)/a^2*sin(a*x)+(2/a^3-x^2/a)*cos(a*x) --R --R 2 2 @@ -113,7 +113,7 @@ bb:=(2*x)/a^2*sin(a*x)+(2/a^3-x^2/a)*cos(a*x) --R Type: Expression Integer --E ---S 9 14:341 Schaums and Axiom agree +--S 9 of 136 14:341 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -130,7 +130,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 136 aa:=integrate(x^3*sin(a*x),x) --R --R @@ -142,7 +142,7 @@ aa:=integrate(x^3*sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 136 bb:=((3*x^2)/a^2-6/a^4)*sin(a*x)+(6*x/a^3-x^3/a)*cos(a*x) --R --R 2 2 3 3 @@ -153,7 +153,7 @@ bb:=((3*x^2)/a^2-6/a^4)*sin(a*x)+(6*x/a^3-x^3/a)*cos(a*x) --R Type: Expression Integer --E ---S 12 14:342 Schaums and Axiom agree +--S 12 of 136 14:342 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -169,7 +169,7 @@ $$ <<*>>= )clear all ---S 13 14:343 Schaums and Axiom agree by definition +--S 13 of 136 14:343 Schaums and Axiom agree by definition aa:=integrate(sin(x)/x,x) --R --R @@ -186,7 +186,7 @@ $$ <<*>>= )clear all ---S 14 14:344 Axiom cannot compute this integral +--S 14 of 136 14:344 Axiom cannot compute this integral aa:=integrate(sin(a*x)/x^2,x) --R --R @@ -208,7 +208,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 136 aa:=integrate(1/sin(a*x),x) --R --R @@ -220,7 +220,7 @@ aa:=integrate(1/sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 16 +--S 16 of 136 bb:=1/a*log(tan((a*x)/2)) --R --R a x @@ -231,7 +231,7 @@ bb:=1/a*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 17 +--S 17 of 136 cc:=aa-bb --R --R a x sin(a x) @@ -242,7 +242,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 18 14:345 Schaums and Axiom agree +--S 18 of 136 14:345 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -260,7 +260,7 @@ $$ <<*>>= )clear all ---S 19 14:346 Axiom cannot compute this integral +--S 19 of 136 14:346 Axiom cannot compute this integral aa:=integrate(x/sin(a*x),x) --R --R @@ -280,7 +280,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 136 aa:=integrate(sin(a*x)^2,x) --R --R @@ -290,7 +290,7 @@ aa:=integrate(sin(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 136 bb:=x/2-sin(2*a*x)/(4*a) --R --R - sin(2a x) + 2a x @@ -299,7 +299,7 @@ bb:=x/2-sin(2*a*x)/(4*a) --R Type: Expression Integer --E ---S 22 +--S 22 of 136 cc:=aa-bb --R --R sin(2a x) - 2cos(a x)sin(a x) @@ -308,7 +308,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 23 14:347 Schaums and Axiom agreee +--S 23 of 136 14:347 Schaums and Axiom agreee dd:=complexNormalize cc --R --R (4) 0 @@ -324,7 +324,7 @@ $$ <<*>>= )clear all ---S 24 +--S 24 of 136 aa:=integrate(x*sin(a*x)^2,x) --R --R @@ -336,7 +336,7 @@ aa:=integrate(x*sin(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 25 +--S 25 of 136 bb:=x^2/4-(x*sin(2*a*x))/(4*a)-cos(2*a*x)/(8*a^2) --R --R 2 2 @@ -347,7 +347,7 @@ bb:=x^2/4-(x*sin(2*a*x))/(4*a)-cos(2*a*x)/(8*a^2) --R Type: Expression Integer --E ---S 26 +--S 26 of 136 cc:=aa-bb --R --R 2 @@ -358,7 +358,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 27 14:348 Schaums and Axiom differ by a constant +--S 27 of 136 14:348 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 1 @@ -377,7 +377,7 @@ $$ <<*>>= )clear all ---S 28 +--S 28 of 136 aa:=integrate(sin(a*x)^3,x) --R --R @@ -388,7 +388,7 @@ aa:=integrate(sin(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 29 +--S 29 of 136 bb:=-cos(a*x)/a+cos(a*x)^3/(3*a) --R --R 3 @@ -398,7 +398,7 @@ bb:=-cos(a*x)/a+cos(a*x)^3/(3*a) --R Type: Expression Integer --E ---S 30 14:349 Schaums and Axiom agree +--S 30 of 136 14:349 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -414,7 +414,7 @@ $$ <<*>>= )clear all ---S 31 +--S 31 of 136 aa:=integrate(sin(a*x)^4,x) --R --R @@ -425,7 +425,7 @@ aa:=integrate(sin(a*x)^4,x) --R Type: Union(Expression Integer,...) --E ---S 32 +--S 32 of 136 bb:=(3*x)/8-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a) --R --R sin(4a x) - 8sin(2a x) + 12a x @@ -434,7 +434,7 @@ bb:=(3*x)/8-sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a) --R Type: Expression Integer --E ---S 33 +--S 33 of 136 cc:=aa-bb --R --R 3 @@ -444,7 +444,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 34 14:350 Schaums and Axiom agree +--S 34 of 136 14:350 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -460,7 +460,7 @@ $$ <<*>>= )clear all ---S 35 +--S 35 of 136 aa:=integrate(1/sin(a*x)^2,x) --R --R @@ -470,7 +470,7 @@ aa:=integrate(1/sin(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 36 +--S 36 of 136 bb:=-1/a*cot(a*x) --R --R cot(a x) @@ -479,7 +479,7 @@ bb:=-1/a*cot(a*x) --R Type: Expression Integer --E ---S 37 +--S 37 of 136 cc:=aa-bb --R --R cot(a x)sin(a x) - cos(a x) @@ -488,7 +488,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 38 14:351 Schaums and Axiom agree +--S 38 of 136 14:351 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -504,7 +504,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 136 aa:=integrate(1/sin(a*x)^3,x) --R --R @@ -517,7 +517,7 @@ aa:=integrate(1/sin(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 136 bb:=-cos(a*x)/(2*a*sin(a*x)^2)+1/(2*a)*log(tan((a*x)/2)) --R --R 2 a x @@ -529,7 +529,7 @@ bb:=-cos(a*x)/(2*a*sin(a*x)^2)+1/(2*a)*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 41 +--S 41 of 136 cc:=aa-bb --R --R (3) @@ -548,7 +548,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 42 +--S 42 of 136 dd:=expandLog cc --R --R (4) @@ -570,7 +570,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 43 14:352 Schaums and Axiom agree +--S 43 of 136 14:352 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -586,7 +586,7 @@ $$ <<*>>= )clear all ---S 44 +--S 44 of 136 aa:=integrate(sin(p*x)*sin(q*x),x) --R --R @@ -597,7 +597,7 @@ aa:=integrate(sin(p*x)*sin(q*x),x) --R Type: Union(Expression Integer,...) --E ---S 45 +--S 45 of 136 bb:=sin((p-q)*x)/(2*(p-q))-sin((p+q)*x)/(2*(p+q)) --R --R (- q + p)sin((q + p)x) + (q + p)sin((q - p)x) @@ -607,7 +607,7 @@ bb:=sin((p-q)*x)/(2*(p-q))-sin((p+q)*x)/(2*(p+q)) --R Type: Expression Integer --E ---S 46 +--S 46 of 136 cc:=aa-bb --R --R (3) @@ -620,7 +620,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 47 14:353 Schams and Axiom agree +--S 47 of 136 14:353 Schams and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -636,7 +636,7 @@ $$ <<*>>= )clear all ---S 48 +--S 48 of 136 aa:=integrate(1/(1-sin(a*x)),x) --R --R @@ -646,7 +646,7 @@ aa:=integrate(1/(1-sin(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 49 +--S 49 of 136 bb:=1/a*tan(%pi/4+(a*x)/2) --R --R 2a x + %pi @@ -657,7 +657,7 @@ bb:=1/a*tan(%pi/4+(a*x)/2) --R Type: Expression Integer --E ---S 50 +--S 50 of 136 cc:=aa-bb --R --R 2a x + %pi @@ -668,7 +668,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 51 14:354 Schaums and Axiom differ by a constant +--S 51 of 136 14:354 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 1 @@ -687,7 +687,7 @@ $$ <<*>>= )clear all ---S 52 +--S 52 of 136 aa:=integrate(x/(1-sin(ax)),x) --R --R @@ -698,7 +698,7 @@ aa:=integrate(x/(1-sin(ax)),x) --R Type: Union(Expression Integer,...) --E ---S 53 +--S 53 of 136 bb:=x/a*tan(%pi/4+(a*x)/2)+2/a^2*log(sin(%pi/4-(a*x)/2)) --R --R 2a x - %pi 2a x + %pi @@ -710,7 +710,7 @@ bb:=x/a*tan(%pi/4+(a*x)/2)+2/a^2*log(sin(%pi/4-(a*x)/2)) --R Type: Expression Integer --E ---S 54 14:355 Axiom cannot simplify this expression +--S 54 of 136 14:355 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -736,7 +736,7 @@ $$ <<*>>= )clear all ---S 55 +--S 55 of 136 aa:=integrate(1/(1+sin(ax)),x) --R --R @@ -746,7 +746,7 @@ aa:=integrate(1/(1+sin(ax)),x) --R Type: Union(Expression Integer,...) --E ---S 56 +--S 56 of 136 bb:=-1/a*tan(%pi/4-(a*x)/2) --R --R 2a x - %pi @@ -757,7 +757,7 @@ bb:=-1/a*tan(%pi/4-(a*x)/2) --R Type: Expression Integer --E ---S 57 +--S 57 of 136 cc:=aa-bb --R --R 2a x - %pi @@ -768,7 +768,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 58 +--S 58 of 136 tanrule:=rule(tan(a/b) == sin(a)/cos(b)) --R --R a sin(a) @@ -777,7 +777,7 @@ tanrule:=rule(tan(a/b) == sin(a)/cos(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 59 14:356 Axiom cannot simplify this expression +--S 59 of 136 14:356 Axiom cannot simplify this expression dd:=tanrule cc --R --R (- sin(ax) - 1)sin(2a x - %pi) + a x cos(4) @@ -796,7 +796,7 @@ $$ <<*>>= )clear all ---S 60 +--S 60 of 136 aa:=integrate(x/(1+sin(a*x)),x) --R --R @@ -816,7 +816,7 @@ aa:=integrate(x/(1+sin(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 61 +--S 61 of 136 bb:=-x/a*tan(%pi/4-(a*x)/2)+2/a^2*log(sin(%pi/4+(a*x)/2)) --R --R 2a x + %pi 2a x - %pi @@ -828,7 +828,7 @@ bb:=-x/a*tan(%pi/4-(a*x)/2)+2/a^2*log(sin(%pi/4+(a*x)/2)) --R Type: Expression Integer --E ---S 62 14:257 Axiom cannot simplify this expression +--S 62 of 136 14:257 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -866,7 +866,7 @@ $$ <<*>>= )clear all ---S 63 +--S 63 of 136 aa:=integrate(1/(1-sin(a*x))^2,x) --R --R 2 @@ -877,7 +877,7 @@ aa:=integrate(1/(1-sin(a*x))^2,x) --R Type: Union(Expression Integer,...) --E ---S 64 +--S 64 of 136 bb:=1/(2*a)*tan(%pi/4+(a*x)/2)+1/(6*a)*tan(%pi/4+(a*x)/2)^3 --R --R 2a x + %pi 3 2a x + %pi @@ -888,7 +888,7 @@ bb:=1/(2*a)*tan(%pi/4+(a*x)/2)+1/(6*a)*tan(%pi/4+(a*x)/2)^3 --R Type: Expression Integer --E ---S 65 +--S 65 of 136 cc:=aa-bb --R --R (3) @@ -908,7 +908,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 66 +--S 66 of 136 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -917,7 +917,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 67 +--S 67 of 136 dd:=tanrule cc --R --R (5) @@ -969,7 +969,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 68 +--S 68 of 136 sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4)) --R --R b - a a b b a @@ -978,7 +978,7 @@ sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 69 +--S 69 of 136 ee:=sindiffrule2 dd --R --R (7) @@ -1030,7 +1030,7 @@ ee:=sindiffrule2 dd --R Type: Expression Integer --E ---S 70 +--S 70 of 136 sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a)) --R --R 3 - sin(3a) + 3sin(a) @@ -1039,7 +1039,7 @@ sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 71 +--S 71 of 136 ff:=sincuberule ee --R --R (9) @@ -1095,7 +1095,7 @@ ff:=sincuberule ee --R Type: Expression Integer --E ---S 72 14:358 Schaums and Axiom differ by a constant +--S 72 of 136 14:358 Schaums and Axiom differ by a constant complexNormalize % --R --R 2 @@ -1114,7 +1114,7 @@ $$ <<*>>= )clear all ---S 73 +--S 73 of 136 aa:=integrate(1/(1+sin(a*x))^2,x) --R --R 2 @@ -1125,7 +1125,7 @@ aa:=integrate(1/(1+sin(a*x))^2,x) --R Type: Union(Expression Integer,...) --E ---S 74 +--S 74 of 136 bb:=-1/(2*a)*tan(%pi/4-(a*x)/2)-1/(6*a)*tan(%pi/4-(a*x)/2)^3 --R --R 2a x - %pi 3 2a x - %pi @@ -1136,7 +1136,7 @@ bb:=-1/(2*a)*tan(%pi/4-(a*x)/2)-1/(6*a)*tan(%pi/4-(a*x)/2)^3 --R Type: Expression Integer --E ---S 75 +--S 75 of 136 cc:=aa-bb --R --R (3) @@ -1156,7 +1156,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 76 +--S 76 of 136 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -1165,7 +1165,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 77 +--S 77 of 136 dd:=tanrule cc --R --R (5) @@ -1217,7 +1217,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 78 +--S 78 of 136 sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4)) --R --R @@ -1227,7 +1227,7 @@ sindiffrule2:=rule(sin((a-b)/4) == sin(a/4)*cos(b/4)-cos(a/4)*sin(b/4)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 79 +--S 79 of 136 ee:=sindiffrule2 dd --R --R (7) @@ -1283,7 +1283,7 @@ ee:=sindiffrule2 dd --R Type: Expression Integer --E ---S 80 +--S 80 of 136 sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a)) --R --R 3 - sin(3a) + 3sin(a) @@ -1292,7 +1292,7 @@ sincuberule:=rule(sin(a)^3 == 3/4*sin(a)-1/4*sin(3*a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 81 +--S 81 of 136 ff:=sincuberule ee --R --R (9) @@ -1352,7 +1352,7 @@ ff:=sincuberule ee --R Type: Expression Integer --E ---S 82 14:359 Schaums and Axiom differ by a constant +--S 82 of 136 14:359 Schaums and Axiom differ by a constant complexNormalize % --R --R 2 @@ -1380,7 +1380,7 @@ $$ <<*>>= )clear all ---S 83 +--S 83 of 136 aa:=integrate(1/(p+q*sin(a*x)),x) --R --R (1) @@ -1412,7 +1412,7 @@ aa:=integrate(1/(p+q*sin(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 84 +--S 84 of 136 bb1:=2/(a*sqrt(p^2-q^2))*atan((p*tan(a*x/2)+q)/sqrt(p^2-q^2)) --R --R a x @@ -1429,7 +1429,7 @@ bb1:=2/(a*sqrt(p^2-q^2))*atan((p*tan(a*x/2)+q)/sqrt(p^2-q^2)) --R Type: Expression Integer --E ---S 85 +--S 85 of 136 bb2:=1/(a*sqrt(q^2-p^2))*log((p*tan((a*x)/2)+q-sqrt(q^2-p^2))/(p*tan((a*x)/2)+q+sqrt(q^2-p^2))) --R --R +-------+ @@ -1448,7 +1448,7 @@ bb2:=1/(a*sqrt(q^2-p^2))*log((p*tan((a*x)/2)+q-sqrt(q^2-p^2))/(p*tan((a*x)/2)+q+ --R Type: Expression Integer --E ---S 86 +--S 86 of 136 cc1:=aa.1-bb1 --R --R (4) @@ -1480,7 +1480,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 87 +--S 87 of 136 cc2:=aa.2-bb1 --R --R (5) @@ -1498,7 +1498,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 88 +--S 88 of 136 cc3:=aa.1-bb2 --R --R (6) @@ -1528,7 +1528,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 89 +--S 89 of 136 cc4:=aa.2-bb2 --R --R (7) @@ -1555,7 +1555,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 90 +--S 90 of 136 dd2:=ratDenom cc2 --R --R (8) @@ -1579,7 +1579,7 @@ dd2:=ratDenom cc2 --R Type: Expression Integer --E ---S 91 +--S 91 of 136 atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x))) --R --R 1 1 @@ -1588,7 +1588,7 @@ atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x))) --RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer) --E ---S 92 +--S 92 of 136 ee2:=atanrule2 dd2 --R --R (10) @@ -1644,7 +1644,7 @@ ee2:=atanrule2 dd2 --R Type: Expression Complex Fraction Integer --E ---S 93 +--S 93 of 136 ff2:=expandLog ee2 --R --R (11) @@ -1688,7 +1688,7 @@ ff2:=expandLog ee2 --R Type: Expression Complex Fraction Integer --E ---S 94 +--S 94 of 136 gg2:=numer(ff2)/denom(ff2) --R --R (12) @@ -1732,7 +1732,7 @@ gg2:=numer(ff2)/denom(ff2) --RType: Fraction SparseMultivariatePolynomial(Complex Fraction Integer,Kernel Expression Complex Fraction Integer) --E ---S 95 +--S 95 of 136 hh2:=gg2::Expression Complex Fraction Integer --R --R (13) @@ -1776,7 +1776,7 @@ hh2:=gg2::Expression Complex Fraction Integer --R Type: Expression Complex Fraction Integer --E ---S 96 14:360 Schaums and Axiom agree +--S 96 of 136 14:360 Schaums and Axiom agree complexNormalize hh2 --R --R (14) 0 @@ -1793,7 +1793,7 @@ $$ <<*>>= )clear all ---S 97 +--S 97 of 136 aa:=integrate(1/(p+q*sin(a*x))^2,x) --R --R @@ -1839,7 +1839,7 @@ aa:=integrate(1/(p+q*sin(a*x))^2,x) --R Type: Union(List Expression Integer,...) --E ---S 98 +--S 98 of 136 t1:=integrate(1/(p+q*sin(a*x)),x) --R --R (2) @@ -1871,7 +1871,7 @@ t1:=integrate(1/(p+q*sin(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 99 +--S 99 of 136 bb1:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.1 --R --R (3) @@ -1898,7 +1898,7 @@ bb1:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.1 --R Type: Expression Integer --E ---S 100 +--S 100 of 136 bb2:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.2 --R --R (4) @@ -1919,7 +1919,7 @@ bb2:=(q*cos(a*x))/(a*(p^2-q^2)*(p+q*sin(a*x)))+p/(p^2-q^2)*t1.2 --R Type: Expression Integer --E ---S 101 +--S 101 of 136 cc1:=aa.1-bb1 --R --R (5) @@ -1959,7 +1959,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 102 +--S 102 of 136 cc2:=aa.2-bb1 --R --R (6) @@ -1994,7 +1994,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 103 +--S 103 of 136 cc3:=aa.1-bb2 --R --R (7) @@ -2029,7 +2029,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 104 14:361 Schaums and Axiom differ by a constant +--S 104 of 136 14:361 Schaums and Axiom differ by a constant cc4:=aa.2-bb2 --R --R q @@ -2048,7 +2048,7 @@ $$ <<*>>= )clear all ---S 105 +--S 105 of 136 aa:=integrate(1/(p^2+q^2*sin(a*x)^2),x) --R --R (1) @@ -2072,7 +2072,7 @@ aa:=integrate(1/(p^2+q^2*sin(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 106 +--S 106 of 136 bb:=1/(a*p*sqrt(p^2+q^2))*atan((sqrt(p^2+q^2)*tan(a*x))/p) --R --R +-------+ @@ -2087,7 +2087,7 @@ bb:=1/(a*p*sqrt(p^2+q^2))*atan((sqrt(p^2+q^2)*tan(a*x))/p) --R Type: Expression Integer --E ---S 107 +--S 107 of 136 cc:=aa-bb --R --R (3) @@ -2111,7 +2111,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 108 +--S 108 of 136 dd:=ratDenom cc --R --R (4) @@ -2140,7 +2140,7 @@ dd:=ratDenom cc --R Type: Expression Integer --E ---S 109 +--S 109 of 136 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2151,7 +2151,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 110 +--S 110 of 136 ee:=atanrule dd --R --R (6) @@ -2214,7 +2214,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 111 +--S 111 of 136 ff:=expandLog ee --R --R (7) @@ -2287,7 +2287,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 112 +--S 112 of 136 tanrule2:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -2296,7 +2296,7 @@ tanrule2:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(tan(a) == sin(a) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 113 +--S 113 of 136 gg:=tanrule2 ff --R --R (9) @@ -2369,7 +2369,7 @@ gg:=tanrule2 ff --R Type: Expression Complex Integer --E ---S 114 +--S 114 of 136 hh:=expandLog gg --R --R (10) @@ -2438,7 +2438,7 @@ hh:=expandLog gg --R Type: Expression Complex Integer --E ---S 115 14:362 Schaums and Axiom differ by a constant +--S 115 of 136 14:362 Schaums and Axiom differ by a constant ii:=complexNormalize hh --R --R +-------+ @@ -2468,7 +2468,7 @@ $$ <<*>>= )clear all ---S 116 +--S 116 of 136 aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x) --R --R (1) @@ -2510,7 +2510,7 @@ aa:=integrate(1/(p^2-q^2*sin(a*x)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 117 +--S 117 of 136 bb1:=1/(a*p*sqrt(p^2-q^2))*atan((sqrt(p^2-q^2)*tan(a*x))/p) --R --R +---------+ @@ -2525,7 +2525,7 @@ bb1:=1/(a*p*sqrt(p^2-q^2))*atan((sqrt(p^2-q^2)*tan(a*x))/p) --R Type: Expression Integer --E ---S 118 +--S 118 of 136 bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((sqrt(q^2-p^2)*tan(a*x)+p)/(sqrt(q^2-p^2)*tan(a*x)-p)) --R --R +-------+ @@ -2542,7 +2542,7 @@ bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((sqrt(q^2-p^2)*tan(a*x)+p)/(sqrt(q^2-p^2)*tan(a --R Type: Expression Integer --E ---S 119 +--S 119 of 136 cc1:=aa.1-bb1 --R --R (4) @@ -2573,7 +2573,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 120 +--S 120 of 136 cc2:=aa.2-bb1 --R --R (5) @@ -2597,7 +2597,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 121 +--S 121 of 136 cc3:=aa.1-bb2 --R --R (6) @@ -2626,7 +2626,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 122 +--S 122 of 136 cc4:=aa.2-bb2 --R --R (7) @@ -2658,7 +2658,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 123 +--S 123 of 136 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -2667,7 +2667,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 124 +--S 124 of 136 dd2:=tanrule cc2 --R --R (9) @@ -2691,7 +2691,7 @@ dd2:=tanrule cc2 --R Type: Expression Integer --E ---S 125 +--S 125 of 136 ee2:=ratDenom dd2 --R --R (10) @@ -2725,7 +2725,7 @@ ee2:=ratDenom dd2 --R Type: Expression Integer --E ---S 126 +--S 126 of 136 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2736,7 +2736,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 127 +--S 127 of 136 ff2:=atanrule ee2 --R --R (12) @@ -2798,7 +2798,7 @@ ff2:=atanrule ee2 --R Type: Expression Complex Integer --E ---S 128 +--S 128 of 136 gg2:=expandLog ff2 --R --R (13) @@ -2871,7 +2871,7 @@ gg2:=expandLog ff2 --R Type: Expression Complex Integer --E ---S 129 +--S 129 of 136 rootrule4a:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(sqrt(p^2-q^2)==sqrt(p-q)*sqrt(q+p)) --R --R +---------+ @@ -2880,7 +2880,7 @@ rootrule4a:RewriteRule(INT,COMPLEX(INT),EXPR(COMPLEX(INT))):=rule(sqrt(p^2-q^2)= --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 130 +--S 130 of 136 hh2:=rootrule4a gg2 --R --R (15) @@ -2946,7 +2946,7 @@ hh2:=rootrule4a gg2 --R Type: Expression Complex Integer --E ---S 131 14:363 Schaums and Axiom differ by a constant +--S 131 of 136 14:363 Schaums and Axiom differ by a constant ii2:=complexNormalize hh2 --R --R +-------+ +-----+ @@ -2967,7 +2967,7 @@ $$ <<*>>= )clear all ---S 132 14:364 Axiom cannot compute this integral +--S 132 of 136 14:364 Axiom cannot compute this integral aa:=integrate(x^m*sin(a*x),x) --R --R @@ -2987,7 +2987,7 @@ $$ <<*>>= )clear all ---S 133 14:365 Axiom cannot compute this integral +--S 133 of 136 14:365 Axiom cannot compute this integral aa:=integrate(sin(a*x)/x^n,x) --R --R @@ -3008,7 +3008,7 @@ $$ <<*>>= )clear all ---S 134 14:366 Axiom cannot compute this integral +--S 134 of 136 14:366 Axiom cannot compute this integral aa:=integrate(sin(a*x)^n,x) --R --R @@ -3029,7 +3029,7 @@ $$ <<*>>= )clear all ---S 135 14:367 Axiom cannot compute this integral +--S 135 of 136 14:367 Axiom cannot compute this integral aa:=integrate(1/(sin(a*x))^n,x) --R --R @@ -3052,7 +3052,7 @@ $$ <<*>>= )clear all ---S 136 14:368 Axiom cannot compute this integral +--S 136 of 136 14:368 Axiom cannot compute this integral aa:=integrate(x/sin(a*x)^n,x) --R --R diff --git a/src/input/schaum18.input.pamphlet b/src/input/schaum18.input.pamphlet index 62de8d7..2626bfb 100644 --- a/src/input/schaum18.input.pamphlet +++ b/src/input/schaum18.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 127 aa:=integrate(cos(a*x),x) --R --R @@ -28,7 +28,7 @@ aa:=integrate(cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 127 bb:=sin(a*x)/a --R --R sin(a x) @@ -37,7 +37,7 @@ bb:=sin(a*x)/a --R Type: Expression Integer --E ---S 3 14:369 Schaums and Axiom agree +--S 3 of 127 14:369 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -53,7 +53,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 127 aa:=integrate(x*cos(a*x),x) --R --R @@ -64,7 +64,7 @@ aa:=integrate(x*cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 127 bb:=cos(a*x)/a^2+(x*sin(a*x))/a --R --R a x sin(a x) + cos(a x) @@ -74,7 +74,7 @@ bb:=cos(a*x)/a^2+(x*sin(a*x))/a --R Type: Expression Integer --E ---S 6 14:370 Schaums and Axiom agree +--S 6 of 127 14:370 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -90,7 +90,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 127 aa:=integrate(x^2*cos(a*x),x) --R --R @@ -102,7 +102,7 @@ aa:=integrate(x^2*cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 127 bb:=(2*x)/a^2*cos(a*x)+(x^2/a-2/a^3)*sin(a*x) --R --R 2 2 @@ -113,7 +113,7 @@ bb:=(2*x)/a^2*cos(a*x)+(x^2/a-2/a^3)*sin(a*x) --R Type: Expression Integer --E ---S 9 14:371 Schaums and Axiom agree +--S 9 of 127 14:371 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -130,7 +130,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 127 aa:=integrate(x^3*cos(a*x),x) --R --R @@ -142,7 +142,7 @@ aa:=integrate(x^3*cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 127 bb:=((3*x^2)/a^2-6/a^4)*cos(a*x)+(x^3/a-(6*x)/a^3)*sin(a*x) --R --R 3 3 2 2 @@ -153,7 +153,7 @@ bb:=((3*x^2)/a^2-6/a^4)*cos(a*x)+(x^3/a-(6*x)/a^3)*sin(a*x) --R Type: Expression Integer --E ---S 12 14:372 Schaums and Axiom agree +--S 12 of 127 14:372 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -170,7 +170,7 @@ $$ <<*>>= )clear all ---S 13 14:373 Schaums and Axiom agree by definition +--S 13 of 127 14:373 Schaums and Axiom agree by definition aa:=integrate(cos(x)/x,x) --R --R @@ -187,7 +187,7 @@ $$ <<*>>= )clear all ---S 14 14:374 Axiom cannot compute this integral +--S 14 of 127 14:374 Axiom cannot compute this integral aa:=integrate(cos(a*x)/x^2,x) --R --R @@ -209,7 +209,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 127 aa:=integrate(1/cos(a*x),x) --R --R @@ -221,7 +221,7 @@ aa:=integrate(1/cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 16 +--S 16 of 127 bb1:=1/a*log(sec(a*x)+tan(a*x)) --R --R log(tan(a x) + sec(a x)) @@ -230,7 +230,7 @@ bb1:=1/a*log(sec(a*x)+tan(a*x)) --R Type: Expression Integer --E ---S 17 +--S 17 of 127 bb2:=1/a*log(tan(%pi/4+(a*x)/2)) --R --R 2a x + %pi @@ -241,7 +241,7 @@ bb2:=1/a*log(tan(%pi/4+(a*x)/2)) --R Type: Expression Integer --E ---S 18 +--S 18 of 127 cc1:=aa-bb1 --R --R (4) @@ -257,7 +257,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 19 +--S 19 of 127 cc2:=aa-bb2 --R --R (5) @@ -273,7 +273,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 20 14:375 Schaums and Axiom differ by a constant +--S 20 of 127 14:375 Schaums and Axiom differ by a constant complexNormalize cc1 --R --R log(- 1) @@ -295,7 +295,7 @@ $$ <<*>>= )clear all ---S 21 14:376 Axiom cannot compute this integral +--S 21 of 127 14:376 Axiom cannot compute this integral aa:=integrate(x/cos(a*x),x) --R --R @@ -315,7 +315,7 @@ $$ <<*>>= )clear all ---S 22 +--S 22 of 127 aa:=integrate(cos(a*x)^2,x) --R --R @@ -325,7 +325,7 @@ aa:=integrate(cos(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 23 +--S 23 of 127 bb:=x/2+sin(2*a*x)/(4*a) --R --R sin(2a x) + 2a x @@ -334,7 +334,7 @@ bb:=x/2+sin(2*a*x)/(4*a) --R Type: Expression Integer --E ---S 24 +--S 24 of 127 cc:=aa-bb --R --R - sin(2a x) + 2cos(a x)sin(a x) @@ -343,7 +343,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 25 +--S 25 of 127 cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b))) --R --R @@ -353,7 +353,7 @@ cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 26 14:377 Schaums and Axiom agree +--S 26 of 127 14:377 Schaums and Axiom agree dd:=cossinrule cc --R --R (5) 0 @@ -369,7 +369,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 127 aa:=integrate(x*cos(a*x)^2,x) --R --R @@ -381,7 +381,7 @@ aa:=integrate(x*cos(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 28 +--S 28 of 127 bb:=x^2/4+(x*sin(2*a*x))/(4*a)+cos(2*a*x)/(8*a^2) --R --R 2 2 @@ -392,7 +392,7 @@ bb:=x^2/4+(x*sin(2*a*x))/(4*a)+cos(2*a*x)/(8*a^2) --R Type: Expression Integer --E ---S 29 +--S 29 of 127 cc:=aa-bb --R --R 2 @@ -403,7 +403,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 30 +--S 30 of 127 cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b))) --R --R @@ -413,7 +413,7 @@ cossinrule:=rule(cos(b)*sin(a) == 1/2*(sin(a-b)+sin(a+b))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 31 +--S 31 of 127 dd:=cossinrule cc --R --R 2 @@ -424,7 +424,7 @@ dd:=cossinrule cc --R Type: Expression Integer --E ---S 32 +--S 32 of 127 coscosrule:=rule(cos(a)*cos(b) == 1/2*(cos(a-b)+cos(a+b))) --R --R @@ -434,7 +434,7 @@ coscosrule:=rule(cos(a)*cos(b) == 1/2*(cos(a-b)+cos(a+b))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 33 +--S 33 of 127 ee:=coscosrule dd --R --R 2 @@ -445,7 +445,7 @@ ee:=coscosrule dd --R Type: Expression Integer --E ---S 34 +--S 34 of 127 cossqrrule1:=rule(cos(a)^2 == 1/2+1/2*cos(2*a)) --R --R 2 cos(2a) + 1 @@ -454,7 +454,7 @@ cossqrrule1:=rule(cos(a)^2 == 1/2+1/2*cos(2*a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 35 14:378 Schaums and Axiom differ by a constant +--S 35 of 127 14:378 Schaums and Axiom differ by a constant ff:=cossqrrule1 ee --R --R 1 @@ -473,7 +473,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 127 aa:=integrate(cos(a*x)^3,x) --R --R @@ -484,7 +484,7 @@ aa:=integrate(cos(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 127 bb:=sin(a*x)/a-sin(a*x)^3/(3*a) --R --R 3 @@ -494,7 +494,7 @@ bb:=sin(a*x)/a-sin(a*x)^3/(3*a) --R Type: Expression Integer --E ---S 38 +--S 38 of 127 cc:=aa-bb --R --R 3 2 @@ -504,7 +504,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 39 +--S 39 of 127 cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2) --R --R 2 2 @@ -512,7 +512,7 @@ cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 40 14:379 Schaums and Axiom agree +--S 40 of 127 14:379 Schaums and Axiom agree dd:=cossqrrule cc --R --R (5) 0 @@ -528,7 +528,7 @@ $$ <<*>>= )clear all ---S 41 +--S 41 of 127 aa:=integrate(cos(a*x)^4,x) --R --R @@ -539,7 +539,7 @@ aa:=integrate(cos(a*x)^4,x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 127 bb:=(3*x)/8+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a) --R --R sin(4a x) + 8sin(2a x) + 12a x @@ -548,7 +548,7 @@ bb:=(3*x)/8+sin(2*a*x)/(4*a)+sin(4*a*x)/(32*a) --R Type: Expression Integer --E ---S 43 +--S 43 of 127 cc:=aa-bb --R --R 3 @@ -558,7 +558,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 44 14:380 Schaums and Axiom agree +--S 44 of 127 14:380 Schaums and Axiom agree complexNormalize cc --R --R (4) 0 @@ -574,7 +574,7 @@ $$ <<*>>= )clear all ---S 45 +--S 45 of 127 aa:=integrate(1/cos(a*x)^2,x) --R --R @@ -584,7 +584,7 @@ aa:=integrate(1/cos(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 46 +--S 46 of 127 bb:=tan(a*x)/a --R --R tan(a x) @@ -593,7 +593,7 @@ bb:=tan(a*x)/a --R Type: Expression Integer --E ---S 47 +--S 47 of 127 cc:=aa-bb --R --R - cos(a x)tan(a x) + sin(a x) @@ -602,7 +602,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 48 +--S 48 of 127 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -611,7 +611,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 49 14:381 Schaums and Axiom agree +--S 49 of 127 14:381 Schaums and Axiom agree dd:=tanrule cc --R --R (5) 0 @@ -628,7 +628,7 @@ $$ <<*>>= )clear all ---S 50 +--S 50 of 127 aa:=integrate(1/cos(a*x)^3,x) --R --R @@ -646,7 +646,7 @@ aa:=integrate(1/cos(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 51 +--S 51 of 127 bb:=sin(a*x)/(2*a*cos(a*x)^2)+1/(2*a)*log(tan(%pi/4+(a*x)/2)) --R --R 2 2a x + %pi @@ -658,7 +658,7 @@ bb:=sin(a*x)/(2*a*cos(a*x)^2)+1/(2*a)*log(tan(%pi/4+(a*x)/2)) --R Type: Expression Integer --E ---S 52 +--S 52 of 127 cc:=aa-bb --R --R (3) @@ -674,7 +674,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 53 14:382 Schaums and Axiom differ by a constant +--S 53 of 127 14:382 Schaums and Axiom differ by a constant complexNormalize cc --R --R log(- 1) @@ -692,7 +692,7 @@ $$ <<*>>= )clear all ---S 54 +--S 54 of 127 aa:=integrate(cos(a*x)*cos(p*x),x) --R --R p cos(a x)sin(p x) - a cos(p x)sin(a x) @@ -702,7 +702,7 @@ aa:=integrate(cos(a*x)*cos(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 55 +--S 55 of 127 bb:=(sin((a-p)*x))/(2*(a-p))+(sin((a+p)*x))/(2*(a+p)) --R --R (p - a)sin((p + a)x) + (p + a)sin((p - a)x) @@ -712,7 +712,7 @@ bb:=(sin((a-p)*x))/(2*(a-p))+(sin((a+p)*x))/(2*(a+p)) --R Type: Expression Integer --E ---S 56 +--S 56 of 127 cc:=aa-bb --R --R (3) @@ -725,7 +725,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 57 14:383 Schaums and Axiom agree +--S 57 of 127 14:383 Schaums and Axiom agree complexNormalize cc --R --R (4) 0 @@ -741,7 +741,7 @@ $$ <<*>>= )clear all ---S 58 +--S 58 of 127 aa:=integrate(1/(1-cos(a*x)),x) --R --R @@ -751,7 +751,7 @@ aa:=integrate(1/(1-cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 59 +--S 59 of 127 bb:=-1/a*cot((a*x)/2) --R --R a x @@ -762,7 +762,7 @@ bb:=-1/a*cot((a*x)/2) --R Type: Expression Integer --E ---S 60 +--S 60 of 127 cc:=aa-bb --R --R a x @@ -773,7 +773,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 61 14:384 Schaums and Axiom agree +--S 61 of 127 14:384 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -790,7 +790,7 @@ $$ <<*>>= )clear all ---S 62 +--S 62 of 127 aa:=integrate(x/(1-cos(a*x)),x) --R --R (1) @@ -803,7 +803,7 @@ aa:=integrate(x/(1-cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 63 +--S 63 of 127 bb:=-x/a*cot((a*x)/2)+2/a^2*log(sin((a*x)/2)) --R --R a x a x @@ -815,7 +815,7 @@ bb:=-x/a*cot((a*x)/2)+2/a^2*log(sin((a*x)/2)) --R Type: Expression Integer --E ---S 64 +--S 64 of 127 cc:=aa-bb --R --R (3) @@ -832,7 +832,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 65 +--S 65 of 127 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -841,7 +841,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 66 +--S 66 of 127 dd:=cotrule cc --R --R (5) @@ -863,7 +863,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 67 +--S 67 of 127 ee:=expandLog dd --R --R (6) @@ -885,7 +885,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 68 14:385 Schaums and Axiom agree +--S 68 of 127 14:385 Schaums and Axiom agree complexNormalize ee --R --R (7) 0 @@ -901,7 +901,7 @@ $$ <<*>>= )clear all ---S 69 +--S 69 of 127 aa:=integrate(1/(1+cos(a*x)),x) --R --R sin(a x) @@ -910,7 +910,7 @@ aa:=integrate(1/(1+cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 70 +--S 70 of 127 bb:=1/a*tan((a*x)/2) --R --R a x @@ -921,7 +921,7 @@ bb:=1/a*tan((a*x)/2) --R Type: Expression Integer --E ---S 71 +--S 71 of 127 cc:=aa-bb --R --R a x @@ -932,7 +932,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 72 14:386 Schaums and Axiom agree +--S 72 of 127 14:386 Schaums and Axiom agree complexNormalize cc --R --R (4) 0 @@ -949,7 +949,7 @@ $$ <<*>>= )clear all ---S 73 +--S 73 of 127 aa:=integrate(x/(1+cos(a*x)),x) --R --R @@ -962,7 +962,7 @@ aa:=integrate(x/(1+cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 74 +--S 74 of 127 bb:=x/a*tan((a*x)/2)+2/a^2*log(cos((a*x)/2)) --R --R a x a x @@ -974,7 +974,7 @@ bb:=x/a*tan((a*x)/2)+2/a^2*log(cos((a*x)/2)) --R Type: Expression Integer --E ---S 75 +--S 75 of 127 cc:=aa-bb --R --R (3) @@ -991,7 +991,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 76 +--S 76 of 127 dd:=expandLog cc --R --R (4) @@ -1008,7 +1008,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 77 14:387 Schaums and Axiom agree +--S 77 of 127 14:387 Schaums and Axiom agree complexNormalize dd --R --R (5) 0 @@ -1025,7 +1025,7 @@ $$ <<*>>= )clear all ---S 78 +--S 78 of 127 aa:=integrate(1/(1-cos(a*x))^2,x) --R --R @@ -1036,7 +1036,7 @@ aa:=integrate(1/(1-cos(a*x))^2,x) --R Type: Union(Expression Integer,...) --E ---S 79 +--S 79 of 127 bb:=-1/(2*a)*cot((a*x)/2)-1/(6*a)*cot((a*x)/2)^3 --R --R a x 3 a x @@ -1047,7 +1047,7 @@ bb:=-1/(2*a)*cot((a*x)/2)-1/(6*a)*cot((a*x)/2)^3 --R Type: Expression Integer --E ---S 80 +--S 80 of 127 cc:=aa-bb --R --R (3) @@ -1061,7 +1061,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 81 14:388 Schaums and Axiom agree +--S 81 of 127 14:388 Schaums and Axiom agree complexNormalize cc --R --R (4) 0 @@ -1078,7 +1078,7 @@ $$ <<*>>= )clear all ---S 82 +--S 82 of 127 aa:=integrate(1/(1+cos(a*x))^2,x) --R --R @@ -1089,7 +1089,7 @@ aa:=integrate(1/(1+cos(a*x))^2,x) --R Type: Union(Expression Integer,...) --E ---S 83 +--S 83 of 127 bb:=1/(2*a)*tan((a*x)/2)+1/(6*a)*tan((a*x)/2)^3 --R --R a x 3 a x @@ -1100,7 +1100,7 @@ bb:=1/(2*a)*tan((a*x)/2)+1/(6*a)*tan((a*x)/2)^3 --R Type: Expression Integer --E ---S 84 +--S 84 of 127 cc:=aa-bb --R --R (3) @@ -1117,7 +1117,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 85 14:389 Schaums and Axiom agree +--S 85 of 127 14:389 Schaums and Axiom agree complexNormalize cc --R --R (4) 0 @@ -1144,7 +1144,7 @@ $$ <<*>>= )clear all ---S 86 +--S 86 of 127 aa:=integrate(1/(p+q*cos(a*x)),x) --R --R (1) @@ -1169,7 +1169,7 @@ aa:=integrate(1/(p+q*cos(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 87 +--S 87 of 127 bb1:=2/(a*sqrt(p^2-q^2))*atan(sqrt((p-q)/(p+q))*tan(1/2*a*x)) --R --R @@ -1184,7 +1184,7 @@ bb1:=2/(a*sqrt(p^2-q^2))*atan(sqrt((p-q)/(p+q))*tan(1/2*a*x)) --R Type: Expression Integer --E ---S 88 +--S 88 of 127 bb2:=1/(a*sqrt(q^2-p^2))*log((tan(1/2*a*x)+sqrt((q+p)/(q-p)))/(tan(1/2*a*x)-sqrt((q+p)/(q-p)))) --R --R +-----+ @@ -1203,7 +1203,7 @@ bb2:=1/(a*sqrt(q^2-p^2))*log((tan(1/2*a*x)+sqrt((q+p)/(q-p)))/(tan(1/2*a*x)-sqrt --R Type: Expression Integer --E ---S 89 +--S 89 of 127 cc1:=aa.1-bb1 --R --R @@ -1225,7 +1225,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 90 +--S 90 of 127 cc2:=aa.2-bb1 --R --R @@ -1241,7 +1241,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 91 +--S 91 of 127 cc3:=aa.1-bb2 --R --R (6) @@ -1267,7 +1267,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 92 14:390 Axiom cannot simplify these expressions +--S 92 of 127 14:390 Axiom cannot simplify these expressions cc4:=aa.2-bb2 --R --R (7) @@ -1304,7 +1304,7 @@ $$ <<*>>= )clear all ---S 93 +--S 93 of 127 aa:=integrate(1/(p+q*cos(a*x))^2,x) --R --R @@ -1345,7 +1345,7 @@ aa:=integrate(1/(p+q*cos(a*x))^2,x) --R Type: Union(List Expression Integer,...) --E ---S 94 +--S 94 of 127 t1:=integrate(1/(p+q*cos(a*x)),x) --R --R (2) @@ -1370,7 +1370,7 @@ t1:=integrate(1/(p+q*cos(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 95 +--S 95 of 127 bb1:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.1 --R --R (3) @@ -1393,7 +1393,7 @@ bb1:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.1 --R Type: Expression Integer --E ---S 96 +--S 96 of 127 bb2:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.2 --R --R (4) @@ -1409,7 +1409,7 @@ bb2:=(q*sin(a*x))/(a*(q^2-p^2)*(p+q*cos(a*x)))-p/(q^2-p^2)*t1.2 --R Type: Expression Integer --E ---S 97 +--S 97 of 127 cc1:=aa.1-bb1 --R --R (5) @@ -1431,7 +1431,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 98 +--S 98 of 127 cc2:=aa.2-bb1 --R --R (6) @@ -1453,7 +1453,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 99 +--S 99 of 127 cc3:=aa.1-bb2 --R --R (7) @@ -1475,7 +1475,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 100 14:391 Schaums and Axiom agree +--S 100 of 127 14:391 Schaums and Axiom agree cc4:=aa.2-bb2 --R --R (8) 0 @@ -1491,7 +1491,7 @@ $$ <<*>>= )clear all ---S 101 +--S 101 of 127 aa:=integrate(1/(p^2+q^2*cos(a*x)^2),x) --R --R @@ -1510,7 +1510,7 @@ aa:=integrate(1/(p^2+q^2*cos(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 102 +--S 102 of 127 bb:=1/(a*p*sqrt(p^2+q^2))*atan((p*tan(a*x))/sqrt(p^2+q^2)) --R --R p tan(a x) @@ -1525,7 +1525,7 @@ bb:=1/(a*p*sqrt(p^2+q^2))*atan((p*tan(a*x))/sqrt(p^2+q^2)) --R Type: Expression Integer --E ---S 103 +--S 103 of 127 cc:=aa-bb --R --R (3) @@ -1550,7 +1550,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 104 +--S 104 of 127 dd:=ratDenom cc --R --R (4) @@ -1584,7 +1584,7 @@ dd:=ratDenom cc --R Type: Expression Integer --E ---S 105 +--S 105 of 127 atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x))) --R --R 1 1 @@ -1593,7 +1593,7 @@ atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x))) --RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer) --E ---S 106 +--S 106 of 127 ee:=atanrule2 dd --R --R (6) @@ -1663,7 +1663,7 @@ ee:=atanrule2 dd --R Type: Expression Complex Fraction Integer --E ---S 107 +--S 107 of 127 ff:=expandLog ee --R --R (7) @@ -1730,7 +1730,7 @@ ff:=expandLog ee --R Type: Expression Complex Fraction Integer --E ---S 108 14:392 Schaums and Axiom differ by a constant +--S 108 of 127 14:392 Schaums and Axiom differ by a constant complexNormalize ff --R --R (8) @@ -1770,7 +1770,7 @@ $$ <<*>>= )clear all ---S 109 +--S 109 of 127 aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x) --R --R @@ -1806,7 +1806,7 @@ aa:=integrate(1/(p^2-q^2*cos(a*x)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 110 +--S 110 of 127 bb1:=1/(a*p*sqrt(p^2-q^2))*atan((p*tan(a*x))/sqrt(p^2-q^2)) --R --R p tan(a x) @@ -1821,7 +1821,7 @@ bb1:=1/(a*p*sqrt(p^2-q^2))*atan((p*tan(a*x))/sqrt(p^2-q^2)) --R Type: Expression Integer --E ---S 111 +--S 111 of 127 bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((p*tan(a*x)-sqrt(q^2-p^2))/(p*tan(a*x)+sqrt(q^2-p^2))) --R --R +-------+ @@ -1838,7 +1838,7 @@ bb2:=1/(2*a*p*sqrt(q^2-p^2))*log((p*tan(a*x)-sqrt(q^2-p^2))/(p*tan(a*x)+sqrt(q^2 --R Type: Expression Integer --E ---S 112 +--S 112 of 127 cc1:=aa.1-bb1 --R --R (4) @@ -1870,7 +1870,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 113 +--S 113 of 127 cc2:=aa.2-bb1 --R --R (5) @@ -1895,7 +1895,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 114 +--S 114 of 127 cc3:=aa.1-bb2 --R --R (6) @@ -1921,7 +1921,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 115 +--S 115 of 127 cc4:=aa.2-bb2 --R --R (7) @@ -1952,7 +1952,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 116 +--S 116 of 127 dd2:=ratDenom cc2 --R --R (8) @@ -1985,7 +1985,7 @@ dd2:=ratDenom cc2 --R Type: Expression Integer --E ---S 117 +--S 117 of 127 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -1994,7 +1994,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 118 +--S 118 of 127 ee2:=tanrule dd2 --R --R (10) @@ -2027,7 +2027,7 @@ ee2:=tanrule dd2 --R Type: Expression Integer --E ---S 119 +--S 119 of 127 atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x))) --R --R 1 1 @@ -2036,7 +2036,7 @@ atanrule2:=rule(atan(x) == 1/2*%i*(log(1-%i*x)-log(1+%i*x))) --RType: RewriteRule(Integer,Complex Fraction Integer,Expression Complex Fraction Integer) --E ---S 120 +--S 120 of 127 ff2:=atanrule2 ee2 --R --R (12) @@ -2106,7 +2106,7 @@ ff2:=atanrule2 ee2 --R Type: Expression Complex Fraction Integer --E ---S 121 +--S 121 of 127 gg2:=expandLog ff2 --R --R (13) @@ -2173,7 +2173,7 @@ gg2:=expandLog ff2 --R Type: Expression Complex Fraction Integer --E ---S 122 14:393 Schaums and Axiom differ by a constant +--S 122 of 127 14:393 Schaums and Axiom differ by a constant hh2:=complexNormalize gg2 --R --R (14) @@ -2200,7 +2200,7 @@ $$ <<*>>= )clear all ---S 123 14:394 Axiom cannot compute this integral +--S 123 of 127 14:394 Axiom cannot compute this integral aa:=integrate(x^m*cos(a*x),x) --R --R @@ -2220,7 +2220,7 @@ $$ <<*>>= )clear all ---S 124 14:395 Axiom cannot compute this integral +--S 124 of 127 14:395 Axiom cannot compute this integral aa:=integrate(cos(a*x)/x^n,x) --R --R @@ -2241,7 +2241,7 @@ $$ <<*>>= )clear all ---S 125 14:396 Axiom cannot compute this integral +--S 125 of 127 14:396 Axiom cannot compute this integral aa:=integrate(cos(a*x)^n,x) --R --R @@ -2262,7 +2262,7 @@ $$ <<*>>= )clear all ---S 126 14:397 Axiom cannot compute this integral +--S 126 of 127 14:397 Axiom cannot compute this integral aa:=integrate(1/(cos(a*x))^n,x) --R --R @@ -2285,7 +2285,7 @@ $$ <<*>>= )clear all ---S 127 14:398 Axiom cannot compute this integral +--S 127 of 127 14:398 Axiom cannot compute this integral aa:=integrate(x/cos(a*x)^n,x) --R --R diff --git a/src/input/schaum19.input.pamphlet b/src/input/schaum19.input.pamphlet index eeb4d9d..9d2e474 100644 --- a/src/input/schaum19.input.pamphlet +++ b/src/input/schaum19.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 185 aa:=integrate(sin(a*x)*cos(a*x),x) --R --R @@ -29,7 +29,7 @@ aa:=integrate(sin(a*x)*cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 185 bb:=sin(a*x)^2/(2*a) --R --R 2 @@ -39,7 +39,7 @@ bb:=sin(a*x)^2/(2*a) --R Type: Expression Integer --E ---S 3 +--S 3 of 185 cc:=aa-bb --R --R 2 2 @@ -49,7 +49,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 185 cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2) --R --R 2 2 @@ -57,7 +57,7 @@ cossqrrule:=rule(cos(a)^2 == 1-sin(a)^2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 14:399 Schaums and Axiom differ by a constant +--S 5 of 185 14:399 Schaums and Axiom differ by a constant dd:=cossqrrule cc --R --R 1 @@ -75,7 +75,7 @@ $$ <<*>>= )clear all ---S 6 +--S 6 of 185 aa:=integrate(sin(p*x)*cos(q*x),x) --R --R @@ -86,7 +86,7 @@ aa:=integrate(sin(p*x)*cos(q*x),x) --R Type: Union(Expression Integer,...) --E ---S 7 +--S 7 of 185 bb:=-cos((p-q)*x)/(2*(p-q))-cos((p+q)*x)/(2*(p+q)) --R --R (- q + p)cos((q + p)x) + (q + p)cos((q - p)x) @@ -96,7 +96,7 @@ bb:=-cos((p-q)*x)/(2*(p-q))-cos((p+q)*x)/(2*(p+q)) --R Type: Expression Integer --E ---S 8 +--S 8 of 185 cc:=aa-bb --R --R (3) @@ -109,7 +109,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 9 14:400 Schaums and Axiom agree +--S 9 of 185 14:400 Schaums and Axiom agree complexNormalize cc --R --R (4) 0 @@ -125,7 +125,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 185 aa:=integrate(sin(a*x)^n*cos(a*x),x) --R --R @@ -136,7 +136,7 @@ aa:=integrate(sin(a*x)^n*cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 185 bb:=sin(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -146,7 +146,7 @@ bb:=sin(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 12 +--S 12 of 185 cc:=aa-bb --R --R n log(sin(a x)) n + 1 @@ -156,7 +156,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 13 +--S 13 of 185 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -164,7 +164,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 14 +--S 14 of 185 dd:=explog cc --R --R n + 1 n @@ -174,7 +174,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 15 14:401 Schaums and Axiom agree +--S 15 of 185 14:401 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -190,7 +190,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 185 aa:=integrate(cos(a*x)^n*sin(a*x),x) --R --R @@ -201,7 +201,7 @@ aa:=integrate(cos(a*x)^n*sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 185 bb:=-cos(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -211,7 +211,7 @@ bb:=-cos(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 18 +--S 18 of 185 cc:=aa-bb --R --R n log(cos(a x)) n + 1 @@ -221,7 +221,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 19 +--S 19 of 185 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -229,7 +229,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 20 +--S 20 of 185 dd:=explog cc --R --R n + 1 n @@ -239,7 +239,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 21 14:402 Schaums and Axiom agree +--S 21 of 185 14:402 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -255,7 +255,7 @@ $$ <<*>>= )clear all ---S 22 +--S 22 of 185 aa:=integrate(sin(a*x)^2*cos(a*x)^2,x) --R --R @@ -266,7 +266,7 @@ aa:=integrate(sin(a*x)^2*cos(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 23 +--S 23 of 185 bb:=x/8-sin(4*a*x)/(32*a) --R --R - sin(4a x) + 4a x @@ -275,7 +275,7 @@ bb:=x/8-sin(4*a*x)/(32*a) --R Type: Expression Integer --E ---S 24 +--S 24 of 185 cc:=aa-bb --R --R 3 @@ -285,7 +285,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 25 14:403 Schaums and Axiom agree +--S 25 of 185 14:403 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -301,7 +301,7 @@ $$ <<*>>= )clear all ---S 26 +--S 26 of 185 aa:=integrate(1/(sin(a*x)*cos(a*x)),x) --R --R @@ -313,7 +313,7 @@ aa:=integrate(1/(sin(a*x)*cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 27 +--S 27 of 185 bb:=1/a*log(tan(a*x)) --R --R log(tan(a x)) @@ -322,7 +322,7 @@ bb:=1/a*log(tan(a*x)) --R Type: Expression Integer --E ---S 28 +--S 28 of 185 cc:=aa-bb --R --R sin(a x) 2cos(a x) @@ -333,7 +333,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 29 +--S 29 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -342,7 +342,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 30 +--S 30 of 185 dd:=tanrule cc --R --R sin(a x) sin(a x) 2cos(a x) @@ -353,7 +353,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 31 14:404 Schaums and Axiom differ by a constant +--S 31 of 185 14:404 Schaums and Axiom differ by a constant ee:=expandLog dd --R --R log(- 2) @@ -371,7 +371,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 185 aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x) --R --R @@ -388,7 +388,7 @@ aa:=integrate(1/(sin(a*x)^2*cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 185 bb:=1/a*log(tan(%pi/4+(a*x)/2))-1/(a*sin(a*x)) --R --R 2a x + %pi @@ -399,7 +399,7 @@ bb:=1/a*log(tan(%pi/4+(a*x)/2))-1/(a*sin(a*x)) --R Type: Expression Integer --E ---S 34 +--S 34 of 185 cc:=aa-bb --R --R (3) @@ -415,7 +415,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 35 +--S 35 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -424,7 +424,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 36 +--S 36 of 185 dd:=tanrule cc --R --R (5) @@ -444,7 +444,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 37 +--S 37 of 185 ee:=expandLog dd --R --R (6) @@ -458,7 +458,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 38 14:405 Schaums and Axiom differ by a constant +--S 38 of 185 14:405 Schaums and Axiom differ by a constant ff:=complexNormalize % --R --R log(- 1) @@ -476,7 +476,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 185 aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x) --R --R @@ -488,7 +488,7 @@ aa:=integrate(1/(sin(a*x)*cos(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 185 bb:=1/a*log(tan((a*x)/2))+1/(a*cos(a*x)) --R --R a x @@ -499,7 +499,7 @@ bb:=1/a*log(tan((a*x)/2))+1/(a*cos(a*x)) --R Type: Expression Integer --E ---S 41 +--S 41 of 185 cc:=aa-bb --R --R a x sin(a x) @@ -510,7 +510,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 42 +--S 42 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -519,7 +519,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 43 +--S 43 of 185 dd:=tanrule cc --R --R a x @@ -534,7 +534,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 44 +--S 44 of 185 ee:=expandLog dd --R --R a x a x @@ -545,7 +545,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 45 14:406 Schaums and Axiom differ by a constant +--S 45 of 185 14:406 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R 1 @@ -563,7 +563,7 @@ $$ <<*>>= )clear all ---S 46 +--S 46 of 185 aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x) --R --R @@ -574,7 +574,7 @@ aa:=integrate(1/(sin(a*x)^2*cos(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 47 +--S 47 of 185 bb:=-(2*cot(2*a*x))/a --R --R 2cot(2a x) @@ -583,7 +583,7 @@ bb:=-(2*cot(2*a*x))/a --R Type: Expression Integer --E ---S 48 +--S 48 of 185 cc:=aa-bb --R --R 2 @@ -593,7 +593,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 49 +--S 49 of 185 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -602,7 +602,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 50 +--S 50 of 185 dd:=cotrule cc --R --R 2 @@ -612,7 +612,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 51 14:407 Schaums and Axiom agree +--S 51 of 185 14:407 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -628,7 +628,7 @@ $$ <<*>>= )clear all ---S 52 +--S 52 of 185 aa:=integrate(sin(a*x)^2/cos(a*x),x) --R --R @@ -640,7 +640,7 @@ aa:=integrate(sin(a*x)^2/cos(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 53 +--S 53 of 185 bb:=-sin(a*x)/a+1/a*log(tan((a*x)/2+%pi/4)) --R --R 2a x + %pi @@ -651,7 +651,7 @@ bb:=-sin(a*x)/a+1/a*log(tan((a*x)/2+%pi/4)) --R Type: Expression Integer --E ---S 54 +--S 54 of 185 cc:=aa-bb --R --R (3) @@ -667,7 +667,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 55 +--S 55 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -676,7 +676,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 56 +--S 56 of 185 dd:=tanrule cc --R --R (5) @@ -696,7 +696,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 57 +--S 57 of 185 ee:=expandLog dd --R --R (6) @@ -710,7 +710,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 58 14:408 Schaums and Axiom differ by a constant +--S 58 of 185 14:408 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R log(- 1) @@ -728,7 +728,7 @@ $$ <<*>>= )clear all ---S 59 +--S 59 of 185 aa:=integrate(cos(a*x)^2/sin(a*x),x) --R --R @@ -740,7 +740,7 @@ aa:=integrate(cos(a*x)^2/sin(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 60 +--S 60 of 185 bb:=cos(a*x)/a+1/a*log(tan((a*x)/2)) --R --R a x @@ -751,7 +751,7 @@ bb:=cos(a*x)/a+1/a*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 61 +--S 61 of 185 cc:=aa-bb --R --R a x sin(a x) @@ -762,7 +762,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 62 +--S 62 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -771,7 +771,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 63 +--S 63 of 185 dd:=tanrule cc --R --R a x @@ -786,7 +786,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 64 +--S 64 of 185 ee:=expandLog dd --R --R a x a x @@ -797,7 +797,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 65 14:409 Schaums and Axiom agree +--S 65 of 185 14:409 Schaums and Axiom agree ff:=complexNormalize ee --R --R (7) 0 @@ -814,7 +814,7 @@ $$ <<*>>= )clear all ---S 66 +--S 66 of 185 aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x) --R --R @@ -831,7 +831,7 @@ aa:=integrate(1/(cos(a*x)*(1+sin(a*x))),x) --R Type: Union(Expression Integer,...) --E ---S 67 +--S 67 of 185 bb:=-1/(2*a*(1+sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4)) --R --R 2a x + %pi @@ -842,7 +842,7 @@ bb:=-1/(2*a*(1+sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4)) --R Type: Expression Integer --E ---S 68 +--S 68 of 185 cc:=aa-bb --R --R (3) @@ -858,7 +858,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 69 +--S 69 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -867,7 +867,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 70 +--S 70 of 185 dd:=tanrule cc --R --R (5) @@ -887,7 +887,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 71 +--S 71 of 185 ee:=expandLog dd --R --R (6) @@ -901,7 +901,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 72 +--S 72 of 185 ff:=complexNormalize ee --R --R log(- 1) + 1 @@ -912,7 +912,7 @@ ff:=complexNormalize ee )clear all ---S 73 +--S 73 of 185 aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x) --R --R @@ -929,7 +929,7 @@ aa:=integrate(1/(cos(a*x)*(1-sin(a*x))),x) --R Type: Union(Expression Integer,...) --E ---S 74 +--S 74 of 185 bb:=1/(2*a*(1-sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4)) --R --R 2a x + %pi @@ -940,7 +940,7 @@ bb:=1/(2*a*(1-sin(a*x)))+1/(2*a)*log(tan((a*x)/2+%pi/4)) --R Type: Expression Integer --E ---S 75 +--S 75 of 185 cc:=aa-bb --R --R (3) @@ -956,7 +956,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 76 +--S 76 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -965,7 +965,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 77 +--S 77 of 185 dd:=tanrule cc --R --R (5) @@ -985,7 +985,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 78 +--S 78 of 185 ee:=expandLog dd --R --R (6) @@ -999,7 +999,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 79 14:410 Schaums and Axiom differ by a constant +--S 79 of 185 14:410 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R log(- 1) - 1 @@ -1018,7 +1018,7 @@ $$ <<*>>= )clear all ---S 80 +--S 80 of 185 aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x) --R --R @@ -1030,7 +1030,7 @@ aa:=integrate(1/(sin(a*x)*(1+cos(a*x))),x) --R Type: Union(Expression Integer,...) --E ---S 81 +--S 81 of 185 bb:=1/(2*a*(1+cos(a*x)))+1/(2*a)*log(tan((a*x)/2)) --R --R a x @@ -1041,7 +1041,7 @@ bb:=1/(2*a*(1+cos(a*x)))+1/(2*a)*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 82 +--S 82 of 185 cc:=aa-bb --R --R a x sin(a x) @@ -1052,7 +1052,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 83 +--S 83 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -1061,7 +1061,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 84 +--S 84 of 185 dd:=tanrule cc --R --R a x @@ -1076,7 +1076,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 85 +--S 85 of 185 ee:=expandLog dd --R --R (6) @@ -1088,7 +1088,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 86 +--S 86 of 185 ff:=complexNormalize ee --R --R 1 @@ -1099,7 +1099,7 @@ ff:=complexNormalize ee )clear all ---S 87 +--S 87 of 185 aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x) --R --R @@ -1111,7 +1111,7 @@ aa:=integrate(1/(sin(a*x)*(1-cos(a*x))),x) --R Type: Union(Expression Integer,...) --E ---S 88 +--S 88 of 185 bb:=-1/(2*a*(1-cos(a*x)))+1/(2*a)*log(tan((a*x)/2)) --R --R a x @@ -1122,7 +1122,7 @@ bb:=-1/(2*a*(1-cos(a*x)))+1/(2*a)*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 89 +--S 89 of 185 cc:=aa-bb --R --R a x sin(a x) @@ -1133,7 +1133,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 90 +--S 90 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -1142,7 +1142,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 91 +--S 91 of 185 dd:=tanrule cc --R --R a x @@ -1157,7 +1157,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 92 +--S 92 of 185 ee:=expandLog dd --R --R (6) @@ -1169,7 +1169,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 93 14:411 Schaums and Axiom differ by a constant +--S 93 of 185 14:411 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R 1 @@ -1187,7 +1187,7 @@ $$ <<*>>= )clear all ---S 94 +--S 94 of 185 aa:=integrate(1/(sin(a*x)+cos(a*x)),x) --R --R @@ -1200,7 +1200,7 @@ aa:=integrate(1/(sin(a*x)+cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 95 +--S 95 of 185 bb:=1/(a*sqrt(2))*log(tan((a*x)/2+%pi/8)) --R --R +-+ 4a x + %pi @@ -1211,7 +1211,7 @@ bb:=1/(a*sqrt(2))*log(tan((a*x)/2+%pi/8)) --R Type: Expression Integer --E ---S 96 +--S 96 of 185 cc:=aa-bb --R --R (3) @@ -1228,7 +1228,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 97 +--S 97 of 185 complexNormalize cc --R --R +-+ @@ -1243,7 +1243,7 @@ complexNormalize cc )clear all ---S 98 +--S 98 of 185 aa:=integrate(1/(sin(a*x)-cos(a*x)),x) --R --R @@ -1256,7 +1256,7 @@ aa:=integrate(1/(sin(a*x)-cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 99 +--S 99 of 185 bb:=1/(a*sqrt(2))*log(tan((a*x)/2-%pi/8)) --R --R +-+ 4a x - %pi @@ -1267,7 +1267,7 @@ bb:=1/(a*sqrt(2))*log(tan((a*x)/2-%pi/8)) --R Type: Expression Integer --E ---S 100 +--S 100 of 185 cc:=aa-bb --R --R (3) @@ -1284,7 +1284,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 101 14:412 Schaums and Axiom differ by a constant +--S 101 of 185 14:412 Schaums and Axiom differ by a constant complexNormalize cc --R --R +-+ +-+ @@ -1303,7 +1303,7 @@ $$ <<*>>= )clear all ---S 102 +--S 102 of 185 aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x) --R --R @@ -1315,7 +1315,7 @@ aa:=integrate(sin(a*x)/(sin(a*x)+cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 103 +--S 103 of 185 bb:=x/2-1/(2*a)*log(sin(a*x)+cos(a*x)) --R --R - log(sin(a x) + cos(a x)) + a x @@ -1324,7 +1324,7 @@ bb:=x/2-1/(2*a)*log(sin(a*x)+cos(a*x)) --R Type: Expression Integer --E ---S 104 +--S 104 of 185 cc:=aa-bb --R --R (3) @@ -1336,7 +1336,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 105 +--S 105 of 185 dd:=expandLog cc --R --R log(sin(a x) + cos(a x)) - log(- sin(a x) - cos(a x)) @@ -1345,7 +1345,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 106 +--S 106 of 185 ee:=complexNormalize dd --R --R log(- 1) @@ -1356,7 +1356,7 @@ ee:=complexNormalize dd )clear all ---S 107 +--S 107 of 185 aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x) --R --R @@ -1368,7 +1368,7 @@ aa:=integrate(sin(a*x)/(sin(a*x)-cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 108 +--S 108 of 185 bb:=x/2+1/(2*a)*log(sin(a*x)-cos(a*x)) --R --R log(sin(a x) - cos(a x)) + a x @@ -1377,7 +1377,7 @@ bb:=x/2+1/(2*a)*log(sin(a*x)-cos(a*x)) --R Type: Expression Integer --E ---S 109 +--S 109 of 185 cc:=aa-bb --R --R (3) @@ -1389,7 +1389,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 110 14:413 Schaums and Axiom agree +--S 110 of 185 14:413 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1405,7 +1405,7 @@ $$ <<*>>= )clear all ---S 111 +--S 111 of 185 aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x) --R --R @@ -1417,7 +1417,7 @@ aa:=integrate(cos(a*x)/(sin(a*x)+cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 112 +--S 112 of 185 bb:=x/2+1/(2*a)*log(sin(a*x)+cos(a*x)) --R --R log(sin(a x) + cos(a x)) + a x @@ -1426,7 +1426,7 @@ bb:=x/2+1/(2*a)*log(sin(a*x)+cos(a*x)) --R Type: Expression Integer --E ---S 113 +--S 113 of 185 cc:=aa-bb --R --R (3) @@ -1438,7 +1438,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 114 +--S 114 of 185 dd:=expandLog cc --R --R - log(sin(a x) + cos(a x)) + log(- sin(a x) - cos(a x)) @@ -1447,7 +1447,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 115 +--S 115 of 185 ee:=complexNormalize dd --R --R log(- 1) @@ -1458,7 +1458,7 @@ ee:=complexNormalize dd )clear all ---S 116 +--S 116 of 185 aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x) --R --R @@ -1470,7 +1470,7 @@ aa:=integrate(cos(a*x)/(sin(a*x)-cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 117 +--S 117 of 185 bb:=-x/2+1/(2*a)*log(sin(a*x)-cos(a*x)) --R --R log(sin(a x) - cos(a x)) - a x @@ -1479,7 +1479,7 @@ bb:=-x/2+1/(2*a)*log(sin(a*x)-cos(a*x)) --R Type: Expression Integer --E ---S 118 +--S 118 of 185 cc:=aa-bb --R --R (3) @@ -1491,7 +1491,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 119 14:414 Schaums and Axiom agree +--S 119 of 185 14:414 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1507,7 +1507,7 @@ $$ <<*>>= )clear all ---S 120 +--S 120 of 185 aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x) --R --R @@ -1519,7 +1519,7 @@ aa:=integrate(sin(a*x)/(p+q*cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 121 +--S 121 of 185 bb:=-1/(a*q)*log(p+q*cos(a*x)) --R --R log(q cos(a x) + p) @@ -1528,7 +1528,7 @@ bb:=-1/(a*q)*log(p+q*cos(a*x)) --R Type: Expression Integer --E ---S 122 +--S 122 of 185 cc:=aa-bb --R --R 2 - 2q cos(a x) - 2p @@ -1539,7 +1539,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 123 +--S 123 of 185 dd:=expandLog cc --R --R log(q cos(a x) + p) - log(- q cos(a x) - p) @@ -1548,7 +1548,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 124 14:415 Schaums and Axiom differ by a constant +--S 124 of 185 14:415 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R log(- 1) @@ -1566,7 +1566,7 @@ $$ <<*>>= )clear all ---S 125 +--S 125 of 185 aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x) --R --R @@ -1578,7 +1578,7 @@ aa:=integrate(cos(a*x)/(p+q*sin(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 126 +--S 126 of 185 bb:=1/(a*q)*log(p+q*sin(a*x)) --R --R log(q sin(a x) + p) @@ -1587,7 +1587,7 @@ bb:=1/(a*q)*log(p+q*sin(a*x)) --R Type: Expression Integer --E ---S 127 +--S 127 of 185 cc:=aa-bb --R --R 2q sin(a x) + 2p 2 @@ -1598,7 +1598,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 128 14:416 Schaums and Axiom agree +--S 128 of 185 14:416 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -1614,7 +1614,7 @@ $$ <<*>>= )clear all ---S 129 +--S 129 of 185 aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x) --R --R @@ -1625,7 +1625,7 @@ aa:=integrate(sin(a*x)/(p+q*cos(a*x))^n,x) --R Type: Union(Expression Integer,...) --E ---S 130 +--S 130 of 185 bb:=1/(a*q*(n-1)*(p+q*cos(a*x))^(n-1)) --R --R 1 @@ -1635,7 +1635,7 @@ bb:=1/(a*q*(n-1)*(p+q*cos(a*x))^(n-1)) --R Type: Expression Integer --E ---S 131 +--S 131 of 185 cc:=aa-bb --R --R n log(q cos(a x) + p) n - 1 @@ -1646,7 +1646,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 132 +--S 132 of 185 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1654,7 +1654,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 133 +--S 133 of 185 dd:=explog cc --R --R n n - 1 @@ -1665,7 +1665,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 134 14:417 Schaums and Axiom agree +--S 134 of 185 14:417 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1681,7 +1681,7 @@ $$ <<*>>= )clear all ---S 135 +--S 135 of 185 aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x) --R --R @@ -1692,7 +1692,7 @@ aa:=integrate(cos(a*x)/(p+q*sin(a*x))^n,x) --R Type: Union(Expression Integer,...) --E ---S 136 +--S 136 of 185 bb:=-1/(a*q*(n-1)*(p+q*sin(a*x))^(n-1)) --R --R 1 @@ -1702,7 +1702,7 @@ bb:=-1/(a*q*(n-1)*(p+q*sin(a*x))^(n-1)) --R Type: Expression Integer --E ---S 137 +--S 137 of 185 cc:=aa-bb --R --R n log(q sin(a x) + p) n - 1 @@ -1713,7 +1713,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 138 +--S 138 of 185 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1721,7 +1721,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 139 +--S 139 of 185 dd:=explog cc --R --R n n - 1 @@ -1732,7 +1732,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 140 14:418 Schaums and Axiom agree +--S 140 of 185 14:418 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1748,7 +1748,7 @@ $$ <<*>>= )clear all ---S 141 +--S 141 of 185 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x) --R --R @@ -1769,7 +1769,7 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 142 +--S 142 of 185 bb:=1/(a*sqrt(p^2+q^2))*log(tan((a*x+atan(q/p))/2)) --R --R q @@ -1784,7 +1784,7 @@ bb:=1/(a*sqrt(p^2+q^2))*log(tan((a*x+atan(q/p))/2)) --R Type: Expression Integer --E ---S 143 +--S 143 of 185 cc:=aa-bb --R --R (3) @@ -1810,7 +1810,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 144 +--S 144 of 185 dd:=normalize cc --R --R +-------+ @@ -1827,7 +1827,7 @@ dd:=normalize cc --R Type: Expression Integer --E ---S 145 14:419 Schaums and Axiom differ by a constant +--S 145 of 185 14:419 Schaums and Axiom differ by a constant ee:=ratDenom dd --R --R +-------+ @@ -1862,7 +1862,7 @@ $$ <<*>>= )clear all ---S 146 +--S 146 of 185 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x) --R --R @@ -1904,7 +1904,7 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+r),x) --R Type: Union(List Expression Integer,...) --E ---S 147 +--S 147 of 185 bb1:=2/(a*sqrt(r^2-p^2-q^2))*atan((p+(r-q)*tan((a*x)/2))/sqrt(r^2-p^2-q^2)) --R --R a x @@ -1921,7 +1921,7 @@ bb1:=2/(a*sqrt(r^2-p^2-q^2))*atan((p+(r-q)*tan((a*x)/2))/sqrt(r^2-p^2-q^2)) --R Type: Expression Integer --E ---S 148 +--S 148 of 185 bb2:=1/(a*sqrt(p^2+q^2-r^2))*log((p-sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))/(p+sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))) --R --R +--------------+ @@ -1940,7 +1940,7 @@ bb2:=1/(a*sqrt(p^2+q^2-r^2))*log((p-sqrt(p^2+q^2-r^2)+(r-q)*tan((a*x)/2))/(p+sqr --R Type: Expression Integer --E ---S 149 +--S 149 of 185 cc1:=aa.1-bb1 --R --R (4) @@ -1981,7 +1981,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 150 +--S 150 of 185 cc2:=aa.2-bb1 --R --R (5) @@ -2006,7 +2006,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 151 +--S 151 of 185 cc3:=aa.1-bb2 --R --R (6) @@ -2045,7 +2045,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 152 +--S 152 of 185 cc4:=aa.2-bb2 --R --R (7) @@ -2072,7 +2072,7 @@ cc4:=aa.2-bb2 --R Type: Expression Integer --E ---S 153 14:420 Schaums and Axiom agree +--S 153 of 185 14:420 Schaums and Axiom agree dd2:=normalize cc2 --R --R (8) 0 @@ -2088,7 +2088,7 @@ $$ <<*>>= )clear all ---S 154 +--S 154 of 185 aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x) --R --R @@ -2100,7 +2100,7 @@ aa:=integrate(1/(p*sin(a*x)+q*(1+cos(a*x))),x) --R Type: Union(Expression Integer,...) --E ---S 155 +--S 155 of 185 bb:=1/(a*p)*log(q+p*tan((a*x)/2)) --R --R a x @@ -2111,7 +2111,7 @@ bb:=1/(a*p)*log(q+p*tan((a*x)/2)) --R Type: Expression Integer --E ---S 156 +--S 156 of 185 cc:=aa-bb --R --R a x p sin(a x) + q cos(a x) + q @@ -2122,7 +2122,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 157 +--S 157 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -2131,7 +2131,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 158 +--S 158 of 185 dd:=tanrule cc --R --R a x a x @@ -2146,7 +2146,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 159 +--S 159 of 185 ee:=expandLog dd --R --R (6) @@ -2162,7 +2162,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 160 14:421 Schaums and Axiom agree +--S 160 of 185 14:421 Schaums and Axiom agree ff:=complexNormalize ee --R --R (7) 0 @@ -2179,7 +2179,7 @@ $$ <<*>>= )clear all ---S 161 +--S 161 of 185 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x) --R --R @@ -2212,7 +2212,7 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)+sqrt(p^2+q^2)),x) --R Type: Union(Expression Integer,...) --E ---S 162 +--S 162 of 185 bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4-(a*x+atan(q/p))/2) --R --R q @@ -2227,7 +2227,7 @@ bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4-(a*x+atan(q/p))/2) --R Type: Expression Integer --E ---S 163 +--S 163 of 185 cc:=aa-bb --R --R (3) @@ -2290,7 +2290,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 164 +--S 164 of 185 dd:=normalize cc --R --R (4) @@ -2319,7 +2319,7 @@ dd:=normalize cc --R Type: Expression Integer --E ---S 165 +--S 165 of 185 ee:=ratDenom dd --R --R +-------+ @@ -2333,7 +2333,7 @@ ee:=ratDenom dd )clear all ---S 166 +--S 166 of 185 aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x) --R --R @@ -2366,7 +2366,7 @@ aa:=integrate(1/(p*sin(a*x)+q*cos(a*x)-sqrt(p^2+q^2)),x) --R Type: Union(Expression Integer,...) --E ---S 167 +--S 167 of 185 bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4+(a*x+atan(q/p))/2) --R --R q @@ -2381,7 +2381,7 @@ bb:=-1/(a*sqrt(p^2+q^2))*tan(%pi/4+(a*x+atan(q/p))/2) --R Type: Expression Integer --E ---S 168 +--S 168 of 185 cc:=aa-bb --R --R (3) @@ -2444,7 +2444,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 169 +--S 169 of 185 dd:=normalize cc --R --R (4) @@ -2473,7 +2473,7 @@ dd:=normalize cc --R Type: Expression Integer --E ---S 170 14:422 Schaums and Axiom differ by a constant +--S 170 of 185 14:422 Schaums and Axiom differ by a constant ee:=ratDenom dd --R --R +-------+ @@ -2494,7 +2494,7 @@ $$ <<*>>= )clear all ---S 171 +--S 171 of 185 aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x) --R --R @@ -2508,7 +2508,7 @@ aa:=integrate(1/(p^2*sin(a*x)^2+q^2*cos(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 172 +--S 172 of 185 bb:=1/(a*p*q)*atan((p*tan(a*x))/q) --R --R p tan(a x) @@ -2519,7 +2519,7 @@ bb:=1/(a*p*q)*atan((p*tan(a*x))/q) --R Type: Expression Integer --E ---S 173 +--S 173 of 185 cc:=aa-bb --R --R (3) @@ -2537,7 +2537,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 174 14:423 Schaums and Axiom agree +--S 174 of 185 14:423 Schaums and Axiom agree dd:=normalize cc --R --R (4) 0 @@ -2555,7 +2555,7 @@ $$ <<*>>= )clear all ---S 175 +--S 175 of 185 aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x) --R --R @@ -2567,7 +2567,7 @@ aa:=integrate(1/(p^2*sin(a*x)^2-q^2*cos(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 176 +--S 176 of 185 bb:=1/(2*a*p*q)*log((p*tan(a*x)-q)/(p*tan(a*x)+q)) --R --R p tan(a x) - q @@ -2578,7 +2578,7 @@ bb:=1/(2*a*p*q)*log((p*tan(a*x)-q)/(p*tan(a*x)+q)) --R Type: Expression Integer --E ---S 177 +--S 177 of 185 cc:=aa-bb --R --R (3) @@ -2594,7 +2594,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 178 +--S 178 of 185 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -2603,7 +2603,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 179 +--S 179 of 185 dd:=tanrule cc --R --R (5) @@ -2619,7 +2619,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 180 +--S 180 of 185 ee:=expandLog dd --R --R log(p sin(a x) + q cos(a x)) - log(- p sin(a x) - q cos(a x)) @@ -2628,7 +2628,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 181 14:424 Schaums and Axiom differ by a constant +--S 181 of 185 14:424 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R log(- 1) @@ -2656,7 +2656,7 @@ $$ <<*>>= )clear all ---S 182 14:425 Axiom cannot compute this integral +--S 182 of 185 14:425 Axiom cannot compute this integral aa:=integrate(sin(a*x)^m*cos(a*x)^n,x) --R --R @@ -2690,7 +2690,7 @@ $$ <<*>>= )clear all ---S 183 14:426 Axiom cannot compute this integral +--S 183 of 185 14:426 Axiom cannot compute this integral aa:=integrate(sin(a*x)^m/cos(a*x)^n,x) --R --R @@ -2725,7 +2725,7 @@ $$ <<*>>= )clear all ---S 184 14:427 Axiom cannot compute this integral +--S 184 of 185 14:427 Axiom cannot compute this integral aa:=integrate(cos(a*x)^m/sin(a*x)^n,x) --R --R @@ -2756,7 +2756,7 @@ $$ <<*>>= )clear all ---S 185 14:428 Axiom cannot compute this integral +--S 185 of 185 14:428 Axiom cannot compute this integral aa:=integrate(1/(sin(a*x)^m*cos(a*x)^n),x) --R --R diff --git a/src/input/schaum2.input.pamphlet b/src/input/schaum2.input.pamphlet index 7a4ef98..aab2406 100644 --- a/src/input/schaum2.input.pamphlet +++ b/src/input/schaum2.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 98 aa:=integrate(1/sqrt(a*x+b),x) --R --R @@ -29,7 +29,7 @@ aa:=integrate(1/sqrt(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 98 bb:=(2*sqrt(a*x+b))/a --R --R @@ -40,7 +40,7 @@ bb:=(2*sqrt(a*x+b))/a --R Type: Expression Integer --E ---S 3 14:84 Schaums and Axiom agree +--S 3 of 98 14:84 Schaums and Axiom agree cc:=aa-bb --R --R @@ -57,7 +57,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 98 aa:=integrate(x/sqrt(a*x+b),x) --R --R @@ -69,7 +69,7 @@ aa:=integrate(x/sqrt(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 98 bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b) --R --R @@ -81,7 +81,7 @@ bb:=(2*(a*x-2*b))/(3*a^2)*sqrt(a*x+b) --R Type: Expression Integer --E ---S 6 14:85 Schaums and Axiom agree +--S 6 of 98 14:85 Schaums and Axiom agree cc:=aa-bb --R --R @@ -98,7 +98,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 98 aa:=integrate(x^2/sqrt(a*x+b),x) --R --R @@ -110,7 +110,7 @@ aa:=integrate(x^2/sqrt(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 98 bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b) --R --R @@ -122,7 +122,7 @@ bb:=(2*(3*a^2*x^2-4*a*b*x+8*b^2))/(15*a^3)*sqrt(a*x+b) --R Type: Expression Integer --E ---S 9 14:86 Schaums and Axiom agree +--S 9 of 98 14:86 Schaums and Axiom agree cc:=aa-bb --R --R @@ -149,7 +149,7 @@ Note: the first answer assumes $b > 0$ and the second assumes $b < 0$. <<*>>= )clear all ---S 10 +--S 10 of 98 aa:=integrate(1/(x*sqrt(a*x+b)),x) --R --R @@ -165,7 +165,7 @@ aa:=integrate(1/(x*sqrt(a*x+b)),x) @ Cleary Spiegel's first answer assumes $b > 0$: <<*>>= ---S 11 +--S 11 of 98 bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b))) --R --R @@ -182,7 +182,7 @@ bb1:=1/sqrt(b)*log((sqrt(a*x+b)-sqrt(b))/(sqrt(a*x+b)+sqrt(b))) @ So we try the difference of the two results <<*>>= ---S 12 +--S 12 of 98 cc11:=aa.1-bb1 --R --R +-------+ +-+ +-------+ +-+ @@ -201,7 +201,7 @@ But the results don't simplify to 0. So we try some other tricks. Since both functions are of the form log(f(x))/sqrt(b) we extract the f(x) from each. First we get the function from Axiom's first answer: <<*>>= ---S 13 +--S 13 of 98 ff:=exp(aa.1*sqrt(b)) --R --R +-------+ +-+ @@ -213,7 +213,7 @@ ff:=exp(aa.1*sqrt(b)) @ and we get the same form from Spiegel's answer <<*>>= ---S 14 +--S 14 of 98 gg:=exp(bb1*sqrt(b)) --R --R +-------+ +-+ @@ -230,7 +230,7 @@ denominator by $1 == (sqrt(a*x+b) - sqrt(b))/(sqrt(a*x+b) - sqrt(b))$. First we multiply the numerator by $(sqrt(a*x+b) - sqrt(b))$ <<*>>= ---S 15 +--S 15 of 98 gg1:=gg*(sqrt(a*x+b) - sqrt(b)) --R --R +-+ +-------+ @@ -243,7 +243,7 @@ gg1:=gg*(sqrt(a*x+b) - sqrt(b)) @ Now we multiply the denominator by $(sqrt(a*x+b) - sqrt(b))$ <<*>>= ---S 16 +--S 16 of 98 gg2:=gg1/(sqrt(a*x+b) - sqrt(b)) --R --R +-+ +-------+ @@ -255,7 +255,7 @@ gg2:=gg1/(sqrt(a*x+b) - sqrt(b)) @ and now we multiply by the integration constant $a*sqrt(b)$ <<*>>= ---S 17 +--S 17 of 98 gg3:=gg2*(a*sqrt(b)) --R --R +-------+ +-+ @@ -267,7 +267,7 @@ gg3:=gg2*(a*sqrt(b)) @ and when we difference this with ff, the Axiom answer we get: <<*>>= ---S 18 14:87a Schaums and Axiom differ by a constant +--S 18 of 98 14:87a Schaums and Axiom differ by a constant ff-gg3 --R --R (9) 0 @@ -279,7 +279,7 @@ So the constant of integration difference is $a*sqrt(b)$ Now we look at the second equations. We difference Axiom's second answer from Spiegel's answer: <<*>>= ---S 19 +--S 19 of 98 t1:=aa.2-bb1 --R --R +-------+ +-+ +---+ +-------+ @@ -296,7 +296,7 @@ t1:=aa.2-bb1 and again they do not simplify to zero. But we can show that both answers differ by a constant because the derivative is zero: <<*>>= ---S 20 +--S 20 of 98 D(t1,x) --R --R (11) 0 @@ -307,7 +307,7 @@ D(t1,x) Rather than find the constant this time we will differentiate both answers and compare them with the original equation. <<*>>= ---S 21 +--S 21 of 98 target:=1/(x*sqrt(a*x+b)) --R --R 1 @@ -319,7 +319,7 @@ target:=1/(x*sqrt(a*x+b)) @ and we select the second Axiom solution <<*>>= ---S 22 +--S 22 of 98 aa2:=aa.2 --R --R +---+ +-------+ @@ -334,7 +334,7 @@ aa2:=aa.2 @ take its derivative <<*>>= ---S 23 +--S 23 of 98 ad2:=D(aa2,x) --R --R 1 @@ -347,7 +347,7 @@ ad2:=D(aa2,x) When we take the difference of Axiom's input and the derivative of the output we see: <<*>>= ---S 24 +--S 24 of 98 ad2-target --R --R (15) 0 @@ -359,7 +359,7 @@ Thus the original equation and Axiom's derivative of the integral are equal. Now we do the same with Spiegel's answer. We take the derivative of his answer. <<*>>= ---S 25 +--S 25 of 98 ab1:=D(bb1,x) --R --R +-------+ +-+ @@ -372,7 +372,7 @@ ab1:=D(bb1,x) @ and we difference it from the original equation <<*>>= ---S 26 14:87b Schaums and Axiom differ by a constant +--S 26 of 98 14:87b Schaums and Axiom differ by a constant ab1-target --R --R (17) 0 @@ -392,7 +392,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 98 aa:=integrate(1/(x^2*sqrt(a*x+b)),x) --R --R @@ -418,7 +418,7 @@ aa:=integrate(1/(x^2*sqrt(a*x+b)),x) In order to write down the book answer we need to first take the integral which has two results <<*>>= ---S 28 +--S 28 of 98 dd:=integrate(1/(x*sqrt(a*x+b)),x) --R --R @@ -435,7 +435,7 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x) and derive two results for the book answer. The first result assumes $b > 0$ <<*>>= ---S 29 +--S 29 of 98 bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1 --R --R @@ -451,7 +451,7 @@ bb1:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.1 @ and the second result assumes $b < 0$. <<*>>= ---S 30 +--S 30 of 98 bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2 --R --R @@ -469,7 +469,7 @@ bb2:=-sqrt(a*x+b)/(b*x)-a/(2*b)*dd.2 So we compute the difference of Axiom's first result with Spiegel's first result <<*>>= ---S 31 +--S 31 of 98 cc11:=bb1-aa.1 --R --R (5) @@ -490,7 +490,7 @@ cc11:=bb1-aa.1 @ we compute its derivative <<*>>= ---S 32 +--S 32 of 98 D(cc11,x) --R --R (6) 0 @@ -501,7 +501,7 @@ and we can see that the answers differ by a constant, the constant of integration. So Axiom's first answer should differentiate back to the target equation. <<*>>= ---S 33 +--S 33 of 98 target:=1/(x^2*sqrt(a*x+b)) --R --R 1 @@ -513,7 +513,7 @@ target:=1/(x^2*sqrt(a*x+b)) @ We differentiate Axiom's first answer <<*>>= ---S 34 +--S 34 of 98 ad1:=D(aa.1,x) --R --R +-+ +-------+ 2 @@ -526,7 +526,7 @@ ad1:=D(aa.1,x) @ and subtract it from the target equation <<*>>= ---S 35 +--S 35 of 98 ad1-target --R --R (9) 0 @@ -535,7 +535,7 @@ ad1-target @ and now we do the same with first Spiegel's answer: <<*>>= ---S 36 +--S 36 of 98 bd1:=D(bb1,x) --R --R +-+ +-------+ 2 @@ -548,7 +548,7 @@ bd1:=D(bb1,x) @ and we subtract it from the target <<*>>= ---S 37 +--S 37 of 98 bd1-target --R --R (11) 0 @@ -561,7 +561,7 @@ integrals differ by a constant. Now we look at the second answers. We difference the answers and can see immediately that they are equal. <<*>>= ---S 38 14:88 Schaums and Axiom differ by a constant +--S 38 of 98 14:88 Schaums and Axiom differ by a constant cc22:=bb2-aa.2 --R --R @@ -578,7 +578,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 98 aa:=integrate(sqrt(a*x+b),x) --R --R @@ -590,7 +590,7 @@ aa:=integrate(sqrt(a*x+b),x) --E @ <<*>>= ---S 40 +--S 40 of 98 bb:=(2*sqrt((a*x+b)^3))/(3*a) --R --R @@ -603,7 +603,7 @@ bb:=(2*sqrt((a*x+b)^3))/(3*a) --E @ <<*>>= ---S 41 +--S 41 of 98 cc:=aa-bb --R --R +----------------------------+ @@ -616,7 +616,7 @@ cc:=aa-bb @ Since this didn't simplify we could check each answer using the derivative <<*>>= ---S 42 +--S 42 of 98 target:=sqrt(a*x+b) --R --R +-------+ @@ -626,7 +626,7 @@ target:=sqrt(a*x+b) @ We take the derivative of Axiom's answer <<*>>= ---S 43 +--S 43 of 98 t1:=D(aa,x) --R --R a x + b @@ -638,7 +638,7 @@ t1:=D(aa,x) @ And we subtract the target from the derivative of Axiom's answer <<*>>= ---S 44 +--S 44 of 98 t1-target --R --R (6) 0 @@ -647,7 +647,7 @@ t1-target @ So they are equal. Now we do the same with Spiegel's answer <<*>>= ---S 45 +--S 45 of 98 t2:=D(bb,x) --R --R 2 2 2 @@ -661,7 +661,7 @@ t2:=D(bb,x) @ The numerator is <<*>>= ---S 46 +--S 46 of 98 nn:=(a*x+b)^2 --R --R 2 2 2 @@ -670,7 +670,7 @@ nn:=(a*x+b)^2 --E @ <<*>>= ---S 47 +--S 47 of 98 mm:=(a*x+b)^3 --R --R 3 3 2 2 2 3 @@ -680,7 +680,7 @@ mm:=(a*x+b)^3 @ which expands to Spiegel's version. <<*>>= ---S 48 14:89 Schaums and Axiom differ by a constant +--S 48 of 98 14:89 Schaums and Axiom differ by a constant result=nn/sqrt(mm) --R --R 2 2 2 @@ -702,7 +702,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 98 aa:=integrate(x*sqrt(a*x+b),x) --R --R @@ -714,7 +714,7 @@ aa:=integrate(x*sqrt(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 50 +--S 50 of 98 bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3) --R --R @@ -727,7 +727,7 @@ bb:=(2*(3*a*x-2*b))/(15*a^2)*sqrt((a*x+b)^3) --R Type: Expression Integer --E ---S 51 +--S 51 of 98 cc:=aa-bb --R --R (3) @@ -743,7 +743,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 52 14:90 Schaums and Axiom agree +--S 52 of 98 14:90 Schaums and Axiom agree dd:=rootSimp cc --R --R (4) 0 @@ -760,7 +760,7 @@ Note: the sqrt term is almost certainly $\sqrt{(ax+b)}$ <<*>>= )clear all ---S 53 +--S 53 of 98 aa:=integrate(x^2*sqrt(a*x+b),x) --R --R @@ -772,7 +772,7 @@ aa:=integrate(x^2*sqrt(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 54 +--S 54 of 98 bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^3)*sqrt((a+b*x)^3) --R --R @@ -785,7 +785,7 @@ bb:=(2*(15*a^2*x^2-12*a*b*x+8*b^2))/(105*a^3)*sqrt((a+b*x)^3) --R Type: Expression Integer --E ---S 55 14:91 Axiom cannot simplify this expression. Schaums typo? +--S 55 of 98 14:91 Axiom cannot simplify this expression. Schaums typo? cc:=aa-bb --R --R (3) @@ -807,7 +807,7 @@ differs from schaums on by the order of the variables in the square root. (We can square the term (a*x+b) and drag it under the square root to get the cubic term). It appears that Schaums has a typo. <<*>>= ---S 56 +--S 56 of 98 factor numer aa --R --R 2 2 2 +-------+ @@ -824,7 +824,7 @@ $$ <<*>>= )clear all ---S 57 +--S 57 of 98 aa:=integrate(sqrt(a*x+b)/x,x) --R --R @@ -841,7 +841,7 @@ aa:=integrate(sqrt(a*x+b)/x,x) --R Type: Union(List Expression Integer,...) --E ---S 58 +--S 58 of 98 dd:=integrate(1/(x*sqrt(a*x+b)),x) --R --R @@ -855,7 +855,7 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x) --R Type: Union(List Expression Integer,...) --E ---S 59 +--S 59 of 98 bb1:=2*sqrt(a*x+b)+b*dd.1 --R --R @@ -869,7 +869,7 @@ bb1:=2*sqrt(a*x+b)+b*dd.1 --R Type: Expression Integer --E ---S 60 +--S 60 of 98 bb2:=2*sqrt(a*x+b)+b*dd.2 --R --R @@ -883,7 +883,7 @@ bb2:=2*sqrt(a*x+b)+b*dd.2 --R Type: Expression Integer --E ---S 61 +--S 61 of 98 cc11:=bb1-aa.1 --R --R @@ -898,7 +898,7 @@ cc11:=bb1-aa.1 --R Type: Expression Integer --E ---S 62 +--S 62 of 98 cc12:=bb1-aa.2 --R --R @@ -913,7 +913,7 @@ cc12:=bb1-aa.2 --R Type: Expression Integer --E ---S 63 +--S 63 of 98 cc21:=bb2-aa.1 --R --R @@ -928,7 +928,7 @@ cc21:=bb2-aa.1 --R Type: Expression Integer --E ---S 64 +--S 64 of 98 cc22:=bb2-aa.2 --R --R @@ -943,7 +943,7 @@ cc22:=bb2-aa.2 --R Type: Expression Integer --E ---S 65 14:92 Schaums and Axiom agree +--S 65 of 98 14:92 Schaums and Axiom agree dd22:=ratDenom cc22 --R --R (9) 0 @@ -959,7 +959,7 @@ $$ <<*>>= )clear all ---S 65 +--S 65 of 98 aa:=integrate(sqrt(a*x+b)/x^2,x) --R --R @@ -981,7 +981,7 @@ aa:=integrate(sqrt(a*x+b)/x^2,x) --R Type: Union(List Expression Integer,...) --E ---S 66 +--S 66 of 98 dd:=integrate(1/(x*sqrt(a*x+b)),x) --R --R @@ -995,7 +995,7 @@ dd:=integrate(1/(x*sqrt(a*x+b)),x) --R Type: Union(List Expression Integer,...) --E ---S 67 +--S 67 of 98 bb1:=-sqrt(a*x+b)/x+a/2*dd.1 --R --R @@ -1009,7 +1009,7 @@ bb1:=-sqrt(a*x+b)/x+a/2*dd.1 --R Type: Expression Integer --E ---S 68 +--S 68 of 98 bb2:=-sqrt(a*x+b)/x+a/2*dd.2 --R --R @@ -1023,7 +1023,7 @@ bb2:=-sqrt(a*x+b)/x+a/2*dd.2 --R Type: Expression Integer --E ---S 69 +--S 69 of 98 cc11:=bb1-aa.1 --R --R @@ -1031,7 +1031,7 @@ cc11:=bb1-aa.1 --R Type: Expression Integer --E ---S 70 +--S 70 of 98 cc21:=bb-aa.1 --R --R @@ -1046,7 +1046,7 @@ cc21:=bb-aa.1 --R Type: Expression Integer --E ---S 71 +--S 71 of 98 cc12:=bb1-aa.2 --R --R @@ -1061,7 +1061,7 @@ cc12:=bb1-aa.2 --R Type: Expression Integer --E ---S 72 14:93 Schaums and Axiom agree +--S 72 of 98 14:93 Schaums and Axiom agree cc22:=bb2-aa.2 --R --R @@ -1079,7 +1079,7 @@ $$ <<*>>= )clear all ---S 73 14:94 Axiom cannot do this integral +--S 73 of 98 14:94 Axiom cannot do this integral aa:=integrate(x^m/sqrt(a*x+b),x) --R --R @@ -1101,7 +1101,7 @@ $$ <<*>>= )clear all ---S 74 14:95 Axiom cannot do this integral +--S 74 of 98 14:95 Axiom cannot do this integral aa:=integrate(1/(x^m*sqrt(a*x+b)),x) --R --R @@ -1123,7 +1123,7 @@ $$ <<*>>= )clear all ---S 75 14:96 Axiom cannot do this integral +--S 75 of 98 14:96 Axiom cannot do this integral aa:=integrate(x^m*sqrt(a*x+b),x) --R --R @@ -1144,7 +1144,7 @@ $$ <<*>>= )clear all ---S 76 14:97 Axiom cannot do this integral +--S 76 of 98 14:97 Axiom cannot do this integral aa:=integrate(sqrt(a*x+b)/x^m,x) --R --R @@ -1167,7 +1167,7 @@ Note: 14.98 is the same as 14.97 <<*>>= )clear all ---S 77 14:98 Axiom cannot do this integral +--S 77 of 98 14:98 Axiom cannot do this integral aa:=integrate(sqrt(a*x+b)/x^m,x) --R --R @@ -1188,7 +1188,7 @@ $$ <<*>>= )clear all ---S 78 +--S 78 of 98 aa:=integrate((a*x+b)^(m/2),x) --R --R @@ -1201,7 +1201,7 @@ aa:=integrate((a*x+b)^(m/2),x) --R Type: Union(Expression Integer,...) --E ---S 79 +--S 79 of 98 bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2)) --R --R @@ -1214,7 +1214,7 @@ bb:=(2*(a*x+b)^((m+2)/2))/(a*(m+2)) --R Type: Expression Integer --E ---S 80 +--S 80 of 98 cc:=aa-bb --R --R @@ -1227,7 +1227,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 81 +--S 81 of 98 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1235,7 +1235,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 82 +--S 82 of 98 dd:=explog cc --R --R m + 2 m @@ -1247,7 +1247,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 83 14:99 Schaums and Axiom agree +--S 83 of 98 14:99 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1264,7 +1264,7 @@ $$ <<*>>= )clear all ---S 84 +--S 84 of 98 aa:=integrate(x*(a*x+b)^(m/2),x) --R --R @@ -1278,7 +1278,7 @@ aa:=integrate(x*(a*x+b)^(m/2),x) --R Type: Union(Expression Integer,...) --E ---S 85 +--S 85 of 98 bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2)) --R --R @@ -1292,7 +1292,7 @@ bb:=(2*(a*x+b)^((m+4)/2))/(a^2*(m+4))-(2*b*(a*x+b)^((m+2)/2))/(a^2*(m+2)) --R Type: Expression Integer --E ---S 86 +--S 86 of 98 cc:=aa-bb --R --R @@ -1312,7 +1312,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 87 +--S 87 of 98 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1320,7 +1320,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 88 +--S 88 of 98 dd:=explog cc --R --R (5) @@ -1339,7 +1339,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 89 14:100 Schaums and Axiom agree +--S 89 of 98 14:100 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1357,7 +1357,7 @@ $$ <<*>>= )clear all ---S 90 +--S 90 of 98 aa:=integrate(x^2*(a*x+b)^(m/2),x) --R --R @@ -1375,7 +1375,7 @@ aa:=integrate(x^2*(a*x+b)^(m/2),x) --R Type: Union(Expression Integer,...) --E ---S 91 +--S 91 of 98 bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_ (4*b*(a*x+b)^((m+4)/2))/(a^3*(m+4))+_ (2*b^2*(a*x+b)^((m+2)/2))/(a^3*(m+2)) @@ -1397,7 +1397,7 @@ bb:=(2*(a*x+b)^((m+6)/2))/(a^3*(m+6))-_ --R Type: Expression Integer --E ---S 92 +--S 92 of 98 cc:=aa-bb --R --R @@ -1425,7 +1425,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 93 +--S 93 of 98 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1433,7 +1433,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 94 +--S 94 of 98 dd:=explog cc --R --R (5) @@ -1460,7 +1460,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 95 14:101 Schaums and Axiom agree +--S 95 of 98 14:101 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1477,7 +1477,7 @@ $$ <<*>>= )clear all ---S 96 14:102 Axiom cannot do this integral +--S 96 of 98 14:102 Axiom cannot do this integral aa:=integrate((a*x+b)^(m/2)/x,x) --R --R @@ -1499,7 +1499,7 @@ $$ <<*>>= )clear all ---S 97 14:103 Axiom cannot do this integral +--S 97 of 98 14:103 Axiom cannot do this integral aa:=integrate((a*x+b)^(m/2)/x^2,x) --R --R @@ -1522,7 +1522,7 @@ $$ <<*>>= )clear all ---S 98 14:104 Axiom cannot do this integral +--S 98 of 98 14:104 Axiom cannot do this integral aa:=integrate(1/(x*(a*x+b)^(m/2)),x) --R --R diff --git a/src/input/schaum20.input.pamphlet b/src/input/schaum20.input.pamphlet index e6981a6..272f151 100644 --- a/src/input/schaum20.input.pamphlet +++ b/src/input/schaum20.input.pamphlet @@ -19,7 +19,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 56 aa:=integrate(tan(a*x),x) --R --R @@ -30,7 +30,7 @@ aa:=integrate(tan(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 56 bb1:=-1/a*log(cos(a*x)) --R --R log(cos(a x)) @@ -39,7 +39,7 @@ bb1:=-1/a*log(cos(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 56 bb2:=1/a*log(sec(a*x)) --R --R log(sec(a x)) @@ -48,7 +48,7 @@ bb2:=1/a*log(sec(a*x)) --R Type: Expression Integer --E ---S 4 +--S 4 of 56 cc1:=aa-bb1 --R --R 2 @@ -58,7 +58,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 5 +--S 5 of 56 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -67,7 +67,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 6 +--S 6 of 56 dd1:=tanrule cc1 --R --R 2 2 @@ -80,7 +80,7 @@ dd1:=tanrule cc1 --R Type: Expression Integer --E ---S 7 +--S 7 of 56 ee1:=expandLog dd1 --R --R 2 2 @@ -90,7 +90,7 @@ ee1:=expandLog dd1 --R Type: Expression Integer --E ---S 8 +--S 8 of 56 sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R --R 2 2 @@ -98,7 +98,7 @@ sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 9 14:429 Schaums and Axiom agree +--S 9 of 56 14:429 Schaums and Axiom agree ff1:=sincossqrrule ee1 --R --R (9) 0 @@ -114,7 +114,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 56 aa:=integrate(tan(a*x)^2,x) --R --R @@ -124,7 +124,7 @@ aa:=integrate(tan(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 56 bb:=tan(a*x)/a-x --R --R tan(a x) - a x @@ -133,7 +133,7 @@ bb:=tan(a*x)/a-x --R Type: Expression Integer --E ---S 12 14:430 Schaums and Axiom agree +--S 12 of 56 14:430 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -149,7 +149,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 56 aa:=integrate(tan(a*x)^3,x) --R --R @@ -160,7 +160,7 @@ aa:=integrate(tan(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 56 bb:=tan(a*x)^2/(2*a)+1/a*log(cos(a*x)) --R --R 2 @@ -170,7 +170,7 @@ bb:=tan(a*x)^2/(2*a)+1/a*log(cos(a*x)) --R Type: Expression Integer --E ---S 15 +--S 15 of 56 cc:=aa-bb --R --R 2 @@ -180,7 +180,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 16 +--S 16 of 56 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -189,7 +189,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 17 +--S 17 of 56 dd:=tanrule cc --R --R 2 2 @@ -202,7 +202,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 18 +--S 18 of 56 ee:=expandLog dd --R --R 2 2 @@ -212,7 +212,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 19 +--S 19 of 56 sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R --R 2 2 @@ -220,7 +220,7 @@ sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 20 14:431 Schaums and Axiom agree +--S 20 of 56 14:431 Schaums and Axiom agree ff:=sincossqrrule ee --R --R (8) 0 @@ -236,7 +236,7 @@ $$ <<*>>= )clear all ---S 21 +--S 21 of 56 aa:=integrate(tan(a*x)^n*sec(a*x)^2,x) --R --R @@ -249,7 +249,7 @@ aa:=integrate(tan(a*x)^n*sec(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 22 +--S 22 of 56 bb:=tan(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -259,7 +259,7 @@ bb:=tan(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 23 +--S 23 of 56 cc:=aa-bb --R --R sin(a x) @@ -271,7 +271,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 24 +--S 24 of 56 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -279,7 +279,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 25 +--S 25 of 56 dd:=explog cc --R --R n + 1 sin(a x) n @@ -290,7 +290,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 26 +--S 26 of 56 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -299,7 +299,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 27 +--S 27 of 56 ee:=tanrule dd --R --R sin(a x) n + 1 sin(a x) n @@ -310,7 +310,7 @@ ee:=tanrule dd --R Type: Expression Integer --E ---S 28 14:432 Schaums and Axiom agree +--S 28 of 56 14:432 Schaums and Axiom agree ff:=complexNormalize ee --R --R (8) 0 @@ -326,7 +326,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 56 aa:=integrate(sec(a*x)^2/tan(a*x),x) --R --R @@ -338,7 +338,7 @@ aa:=integrate(sec(a*x)^2/tan(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 56 bb:=1/a*log(tan(a*x)) --R --R log(tan(a x)) @@ -347,7 +347,7 @@ bb:=1/a*log(tan(a*x)) --R Type: Expression Integer --E ---S 31 +--S 31 of 56 cc:=aa-bb --R --R sin(a x) 2cos(a x) @@ -358,7 +358,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 +--S 32 of 56 dd:=expandLog cc --R --R - log(tan(a x)) + log(sin(a x)) - log(cos(a x)) - log(- 2) @@ -367,7 +367,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 33 14:433 Schaums and Axiom differ by a constant +--S 33 of 56 14:433 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R log(- 2) @@ -385,7 +385,7 @@ $$ <<*>>= )clear all ---S 34 +--S 34 of 56 aa:=integrate(1/tan(a*x),x) --R --R @@ -396,7 +396,7 @@ aa:=integrate(1/tan(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 35 +--S 35 of 56 bb:=1/a*log(sin(a*x)) --R --R log(sin(a x)) @@ -405,7 +405,7 @@ bb:=1/a*log(sin(a*x)) --R Type: Expression Integer --E ---S 36 +--S 36 of 56 cc:=aa-bb --R --R 2 @@ -415,7 +415,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 37 +--S 37 of 56 complexNormalize cc --R --R (4) 0 @@ -432,7 +432,7 @@ $$ <<*>>= )clear all ---S 38 14:435 Axiom cannot compute this integral +--S 38 of 56 14:435 Axiom cannot compute this integral aa:=integrate(x*tan(a*x),x) --R --R @@ -453,7 +453,7 @@ $$ <<*>>= )clear all ---S 39 14:436 Axiom cannot compute this integral +--S 39 of 56 14:436 Axiom cannot compute this integral aa:=integrate(tan(a*x)/x,x) --R --R @@ -473,7 +473,7 @@ $$ <<*>>= )clear all ---S 40 +--S 40 of 56 aa:=integrate(x*tan(a*x)^2,x) --R --R @@ -485,7 +485,7 @@ aa:=integrate(x*tan(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 41 +--S 41 of 56 bb:=(x*tan(a*x))/a+1/a^2*log(cos(a*x))-x^2/2 --R --R 2 2 @@ -496,7 +496,7 @@ bb:=(x*tan(a*x))/a+1/a^2*log(cos(a*x))-x^2/2 --R Type: Expression Integer --E ---S 42 +--S 42 of 56 cc:=aa-bb --R --R 2 @@ -507,7 +507,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 43 +--S 43 of 56 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -516,7 +516,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 44 +--S 44 of 56 dd:=tanrule cc --R --R 2 2 @@ -530,7 +530,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 45 +--S 45 of 56 ee:=expandLog dd --R --R 2 2 @@ -541,7 +541,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 46 +--S 46 of 56 sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R --R 2 2 @@ -549,7 +549,7 @@ sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 47 14:437 Schaums and Axiom agree +--S 47 of 56 14:437 Schaums and Axiom agree ff:=sincossqrrule ee --R --R (8) 0 @@ -565,7 +565,7 @@ $$ <<*>>= )clear all ---S 48 +--S 48 of 56 aa:=integrate(1/(p+q*tan(a*x)),x) --R --R @@ -577,7 +577,7 @@ aa:=integrate(1/(p+q*tan(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 49 +--S 49 of 56 bb:=(p*x)/(p^2+q^2)+q/(a*(p^2+q^2))*log(q*sin(a*x)+p*cos(a*x)) --R --R q log(q sin(a x) + p cos(a x)) + a p x @@ -587,7 +587,7 @@ bb:=(p*x)/(p^2+q^2)+q/(a*(p^2+q^2))*log(q*sin(a*x)+p*cos(a*x)) --R Type: Expression Integer --E ---S 50 +--S 50 of 56 cc:=aa-bb --R --R (3) @@ -601,7 +601,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 51 +--S 51 of 56 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -610,7 +610,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 52 +--S 52 of 56 dd:=tanrule cc --R --R (5) @@ -629,7 +629,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 53 +--S 53 of 56 ee:=expandLog dd --R --R 2 2 @@ -640,7 +640,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 54 +--S 54 of 56 sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R --R 2 2 @@ -648,7 +648,7 @@ sincossqrrule:=rule(sin(a)^2+cos(a)^2 == 1) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 55 14:438 Schaums and Axiom agree +--S 55 of 56 14:438 Schaums and Axiom agree ff:=sincossqrrule ee --R --R (8) 0 @@ -664,7 +664,7 @@ $$ <<*>>= )clear all ---S 56 14:439 Axiom cannot compute this integral +--S 56 of 56 14:439 Axiom cannot compute this integral aa:=integrate(tan(a*x)^n,x) --R --R diff --git a/src/input/schaum21.input.pamphlet b/src/input/schaum21.input.pamphlet index 2c24de5..cc64923 100644 --- a/src/input/schaum21.input.pamphlet +++ b/src/input/schaum21.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 53 aa:=integrate(cot(a*x),x) --R --R @@ -30,7 +30,7 @@ aa:=integrate(cot(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 53 bb:=1/a*log(sin(a*x)) --R --R log(sin(a x)) @@ -39,7 +39,7 @@ bb:=1/a*log(sin(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 53 cc:=aa-bb --R --R sin(2a x) 2 @@ -50,7 +50,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 53 dd:=expandLog cc --R --R 2log(sin(2a x)) - 2log(sin(a x)) - log(cos(2a x) + 1) - log(2) @@ -59,7 +59,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 5 14:440 Schaums and Axiom agree +--S 5 of 53 14:440 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -75,7 +75,7 @@ $$ <<*>>= )clear all ---S 6 +--S 6 of 53 aa:=integrate(cot(a*x)^2,x) --R --R @@ -85,7 +85,7 @@ aa:=integrate(cot(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 7 +--S 7 of 53 bb:=-cot(a*x)/a-x --R --R - cot(a x) - a x @@ -94,7 +94,7 @@ bb:=-cot(a*x)/a-x --R Type: Expression Integer --E ---S 8 +--S 8 of 53 cc:=aa-bb --R --R cot(a x)sin(2a x) - cos(2a x) - 1 @@ -103,7 +103,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 9 +--S 9 of 53 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -112,7 +112,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 10 +--S 10 of 53 dd:=cotrule cc --R --R cos(a x)sin(2a x) + (- cos(2a x) - 1)sin(a x) @@ -121,7 +121,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 11 14:441 Schaums and Axiom agree +--S 11 of 53 14:441 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -137,7 +137,7 @@ $$ <<*>>= )clear all ---S 12 +--S 12 of 53 aa:=integrate(cot(a*x)^3,x) --R --R @@ -152,7 +152,7 @@ aa:=integrate(cot(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 13 +--S 13 of 53 bb:=-cot(a*x)^2/(2*a)-1/a*log(sin(a*x)) --R --R 2 @@ -162,7 +162,7 @@ bb:=-cot(a*x)^2/(2*a)-1/a*log(sin(a*x)) --R Type: Expression Integer --E ---S 14 +--S 14 of 53 cc:=aa-bb --R --R (3) @@ -180,7 +180,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 15 +--S 15 of 53 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -189,7 +189,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 16 +--S 16 of 53 dd:=cotrule cc --R --R (5) @@ -212,7 +212,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 17 +--S 17 of 53 ee:=expandLog dd --R --R (6) @@ -236,7 +236,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 18 14:442 Schaums and Axiom agree +--S 18 of 53 14:442 Schaums and Axiom agree ff:=complexNormalize ee --R --R (7) 0 @@ -252,7 +252,7 @@ $$ <<*>>= )clear all ---S 19 +--S 19 of 53 aa:=integrate(cot(a*x)^n*csc(a*x)^2,x) --R --R @@ -265,7 +265,7 @@ aa:=integrate(cot(a*x)^n*csc(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 20 +--S 20 of 53 bb:=-cot(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -275,7 +275,7 @@ bb:=-cot(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 21 +--S 21 of 53 cc:=aa-bb --R --R cos(a x) @@ -287,7 +287,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 22 +--S 22 of 53 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -295,7 +295,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 23 +--S 23 of 53 dd:=explog cc --R --R n + 1 cos(a x) n @@ -306,7 +306,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 24 +--S 24 of 53 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -315,7 +315,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 25 +--S 25 of 53 ee:=cotrule dd --R --R cos(a x) n + 1 cos(a x) n @@ -326,7 +326,7 @@ ee:=cotrule dd --R Type: Expression Integer --E ---S 26 14:443 Schaums and Axiom agree +--S 26 of 53 14:443 Schaums and Axiom agree ff:=complexNormalize ee --R --R (8) 0 @@ -342,7 +342,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 53 aa:=integrate(csc(a*x)^2/cot(a*x),x) --R --R @@ -354,7 +354,7 @@ aa:=integrate(csc(a*x)^2/cot(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 28 +--S 28 of 53 bb:=-1/a*log(cot(a*x)) --R --R log(cot(a x)) @@ -363,7 +363,7 @@ bb:=-1/a*log(cot(a*x)) --R Type: Expression Integer --E ---S 29 +--S 29 of 53 cc:=aa-bb --R --R sin(a x) 2cos(a x) @@ -374,7 +374,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 30 +--S 30 of 53 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -383,7 +383,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 31 +--S 31 of 53 dd:=cotrule cc --R --R sin(a x) cos(a x) 2cos(a x) @@ -394,7 +394,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 32 14:444 Schaums and Axiom differ by a constant +--S 32 of 53 14:444 Schaums and Axiom differ by a constant ee:=expandLog dd --R --R log(- 2) @@ -412,7 +412,7 @@ $$ <<*>>= )clear all ---S 33 +--S 33 of 53 aa:=integrate(1/cot(a*x),x) --R --R @@ -424,7 +424,7 @@ aa:=integrate(1/cot(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 34 +--S 34 of 53 bb:=-1/a*log(cos(a*x)) --R --R log(cos(a x)) @@ -433,7 +433,7 @@ bb:=-1/a*log(cos(a*x)) --R Type: Expression Integer --E ---S 35 +--S 35 of 53 cc:=aa-bb --R --R 2 @@ -444,7 +444,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 36 +--S 36 of 53 dd:=expandLog cc --R --R - log(cos(2a x) + 1) + 2log(cos(a x)) + log(2) @@ -453,7 +453,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 37 14:445 Schaums and Axiom agree +--S 37 of 53 14:445 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -471,7 +471,7 @@ $$ <<*>>= )clear all ---S 38 14:446 Axiom cannot compute this integral +--S 38 of 53 14:446 Axiom cannot compute this integral aa:=integrate(x*cot(a*x),x) --R --R @@ -492,7 +492,7 @@ $$ <<*>>= )clear all ---S 39 14:447 Axiom cannot compute this integral +--S 39 of 53 14:447 Axiom cannot compute this integral aa:=integrate(cot(a*x)/x,x) --R --R @@ -512,7 +512,7 @@ $$ <<*>>= )clear all ---S 40 +--S 40 of 53 aa:=integrate(x*cot(a*x)^2,x) --R --R @@ -529,7 +529,7 @@ aa:=integrate(x*cot(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 41 +--S 41 of 53 bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))-x^2/2 --R --R 2 2 @@ -540,7 +540,7 @@ bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x))-x^2/2 --R Type: Expression Integer --E ---S 42 +--S 42 of 53 cc:=aa-bb --R --R (3) @@ -559,7 +559,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 43 +--S 43 of 53 dd:=expandLog cc --R --R (4) @@ -574,7 +574,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 44 14:448 Schaums and Axiom agree +--S 44 of 53 14:448 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -590,7 +590,7 @@ $$ <<*>>= )clear all ---S 45 +--S 45 of 53 aa:=integrate(1/(p+q*cot(a*x)),x) --R --R @@ -604,7 +604,7 @@ aa:=integrate(1/(p+q*cot(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 46 +--S 46 of 53 bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x)) --R --R - q log(p sin(a x) + q cos(a x)) + a p x @@ -614,7 +614,7 @@ bb:=(p*x)/(p^2+q^2)-q/(a*(p^2+q^2))*log(p*sin(a*x)+q*cos(a*x)) --R Type: Expression Integer --E ---S 47 +--S 47 of 53 cc:=aa-bb --R --R (3) @@ -631,14 +631,14 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 48 +--S 48 of 53 sindblrule:=rule(sin(2*a) == 2*sin(a)*cos(a)) --R --R (4) sin(2a) == 2cos(a)sin(a) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 49 +--S 49 of 53 dd:=sindblrule cc --R --R (5) @@ -653,7 +653,7 @@ dd:=sindblrule cc --R Type: Expression Integer --E ---S 50 +--S 50 of 53 cosdblrule:=rule(cos(2*a) == 2*cos(a)^2-1) --R --R 2 @@ -661,7 +661,7 @@ cosdblrule:=rule(cos(2*a) == 2*cos(a)^2-1) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 51 +--S 51 of 53 ee:=cosdblrule dd --R --R (7) @@ -679,7 +679,7 @@ ee:=cosdblrule dd --R Type: Expression Integer --E ---S 52 14:449 Schaums and Axiom agree +--S 52 of 53 14:449 Schaums and Axiom agree ff:=expandLog % --R --R (8) 0 @@ -696,7 +696,7 @@ $$ <<*>>= )clear all ---S 53 14:450 Axiom cannot compute this integral +--S 53 of 53 14:450 Axiom cannot compute this integral aa:=integrate(cot(a*x)^n,x) --R --R diff --git a/src/input/schaum22.input.pamphlet b/src/input/schaum22.input.pamphlet index 42fad96..bd4a575 100644 --- a/src/input/schaum22.input.pamphlet +++ b/src/input/schaum22.input.pamphlet @@ -19,7 +19,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 52 aa:=integrate(sec(a*x),x) --R --R @@ -31,7 +31,7 @@ aa:=integrate(sec(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 52 bb1:=1/a*log(sec(a*x)+tan(a*x)) --R --R log(tan(a x) + sec(a x)) @@ -40,7 +40,7 @@ bb1:=1/a*log(sec(a*x)+tan(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 52 bb2:=1/a*log(tan((a*x)/2+%pi/4)) --R --R 2a x + %pi @@ -51,7 +51,7 @@ bb2:=1/a*log(tan((a*x)/2+%pi/4)) --R Type: Expression Integer --E ---S 4 +--S 4 of 52 cc1:=aa-bb1 --R --R (4) @@ -67,7 +67,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 5 +--S 5 of 52 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -76,7 +76,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 6 +--S 6 of 52 dd1:=tanrule cc1 --R --R (6) @@ -92,7 +92,7 @@ dd1:=tanrule cc1 --R Type: Expression Integer --E ---S 7 +--S 7 of 52 secrule:=rule(sec(a) == 1/cos(a)) --R --R 1 @@ -101,7 +101,7 @@ secrule:=rule(sec(a) == 1/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 8 +--S 8 of 52 ee1:=secrule dd1 --R --R (8) @@ -117,7 +117,7 @@ ee1:=secrule dd1 --R Type: Expression Integer --E ---S 9 +--S 9 of 52 ff1:=expandLog ee1 --R --R (9) @@ -129,7 +129,7 @@ ff1:=expandLog ee1 --R Type: Expression Integer --E ---S 10 +--S 10 of 52 gg1:=complexNormalize ff1 --R --R log(- 1) @@ -138,7 +138,7 @@ gg1:=complexNormalize ff1 --R Type: Expression Integer --E ---S 11 +--S 11 of 52 cc2:=aa-bb2 --R --R (11) @@ -154,7 +154,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 12 +--S 12 of 52 dd2:=tanrule cc2 --R --R (12) @@ -174,7 +174,7 @@ dd2:=tanrule cc2 --R Type: Expression Integer --E ---S 13 +--S 13 of 52 ee2:=expandLog dd2 --R --R (13) @@ -188,7 +188,7 @@ ee2:=expandLog dd2 --R Type: Expression Integer --E ---S 14 14:451 Schaums and Axiom differ by a constant +--S 14 of 52 14:451 Schaums and Axiom differ by a constant ff2:=complexNormalize ee2 --R --R log(- 1) @@ -206,7 +206,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 52 aa:=integrate(sec(a*x)^2,x) --R --R @@ -216,7 +216,7 @@ aa:=integrate(sec(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 16 +--S 16 of 52 bb:=tan(a*x)/a --R --R tan(a x) @@ -225,7 +225,7 @@ bb:=tan(a*x)/a --R Type: Expression Integer --E ---S 17 +--S 17 of 52 cc:=aa-bb --R --R - cos(a x)tan(a x) + sin(a x) @@ -234,7 +234,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 18 +--S 18 of 52 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -243,7 +243,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 19 14:452 Schaums and Axiom agree +--S 19 of 52 14:452 Schaums and Axiom agree dd:=tanrule cc --R --R (5) 0 @@ -259,7 +259,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 52 aa:=integrate(sec(a*x)^3,x) --R --R @@ -277,7 +277,7 @@ aa:=integrate(sec(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 52 bb:=(sec(a*x)*tan(a*x))/(2*a)+1/(2*a)*log(sec(a*x)+tan(a*x)) --R --R log(tan(a x) + sec(a x)) + sec(a x)tan(a x) @@ -286,7 +286,7 @@ bb:=(sec(a*x)*tan(a*x))/(2*a)+1/(2*a)*log(sec(a*x)+tan(a*x)) --R Type: Expression Integer --E ---S 22 +--S 22 of 52 cc:=aa-bb --R --R (3) @@ -308,7 +308,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 23 +--S 23 of 52 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -317,7 +317,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 24 +--S 24 of 52 dd:=tanrule cc --R --R (5) @@ -338,7 +338,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 25 +--S 25 of 52 secrule:=rule(sec(a) == 1/cos(a)) --R --R 1 @@ -347,7 +347,7 @@ secrule:=rule(sec(a) == 1/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 26 +--S 26 of 52 ee:=secrule dd --R --R (7) @@ -363,7 +363,7 @@ ee:=secrule dd --R Type: Expression Integer --E ---S 27 +--S 27 of 52 ff:=expandLog ee --R --R (8) @@ -375,7 +375,7 @@ ff:=expandLog ee --R Type: Expression Integer --E ---S 28 14:453 Schaums and Axiom differ by a constant +--S 28 of 52 14:453 Schaums and Axiom differ by a constant gg:=complexNormalize ff --R --R log(- 1) @@ -393,7 +393,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 52 aa:=integrate(sec(a*x)^n*tan(a*x),x) --R --R 1 @@ -408,7 +408,7 @@ aa:=integrate(sec(a*x)^n*tan(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 52 bb:=sec(a*x)^n/(n*a) --R --R n @@ -418,7 +418,7 @@ bb:=sec(a*x)^n/(n*a) --R Type: Expression Integer --E ---S 31 +--S 31 of 52 cc:=aa-bb --R --R 1 @@ -433,7 +433,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 14:454 Schaums and Axiom agree +--S 32 of 52 14:454 Schaums and Axiom agree normalize cc --R --R (4) 0 @@ -449,7 +449,7 @@ $$ <<*>>= )clear all ---S 33 +--S 33 of 52 aa:=integrate(1/sec(a*x),x) --R --R @@ -459,7 +459,7 @@ aa:=integrate(1/sec(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 34 +--S 34 of 52 bb:=sin(a*x)/a --R --R sin(a x) @@ -468,7 +468,7 @@ bb:=sin(a*x)/a --R Type: Expression Integer --E ---S 35 14:455 Schaums and Axiom agree +--S 35 of 52 14:455 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -485,7 +485,7 @@ $$ <<*>>= )clear all ---S 36 14:456 Axiom cannot compute this integral +--S 36 of 52 14:456 Axiom cannot compute this integral aa:=integrate(x*sec(a*x),x) --R --R @@ -506,7 +506,7 @@ $$ <<*>>= )clear all ---S 37 14:457 Axiom cannot compute this integral +--S 37 of 52 14:457 Axiom cannot compute this integral aa:=integrate(sec(a*x)/x,x) --R --R @@ -526,7 +526,7 @@ $$ <<*>>= )clear all ---S 38 +--S 38 of 52 aa:=integrate(x*sec(a*x)^2,x) --R --R @@ -540,7 +540,7 @@ aa:=integrate(x*sec(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 39 +--S 39 of 52 bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x)) --R --R log(cos(a x)) + a x tan(a x) @@ -550,7 +550,7 @@ bb:=x/a*tan(a*x)+1/a^2*log(cos(a*x)) --R Type: Expression Integer --E ---S 40 +--S 40 of 52 cc:=aa-bb --R --R (3) @@ -567,7 +567,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 41 +--S 41 of 52 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -576,7 +576,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 42 +--S 42 of 52 dd:=tanrule cc --R --R 2 2cos(a x) @@ -588,7 +588,7 @@ dd:=tanrule cc --R Type: Expression Integer --E ---S 43 14:458 Schaums and Axiom differ by a constant +--S 43 of 52 14:458 Schaums and Axiom differ by a constant ee:=expandLog dd --R --R - log(2) + log(- 2) @@ -607,7 +607,7 @@ $$ <<*>>= )clear all ---S 44 +--S 44 of 52 aa:=integrate(1/(q+p*sec(a*x)),x) --R --R @@ -633,7 +633,7 @@ aa:=integrate(1/(q+p*sec(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 45 +--S 45 of 52 t1:=integrate(1/(p+q*cos(a*x)),x) --R --R (2) @@ -658,7 +658,7 @@ t1:=integrate(1/(p+q*cos(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 46 +--S 46 of 52 bb1:=x/q-p/q*t1.1 --R --R (3) @@ -674,7 +674,7 @@ bb1:=x/q-p/q*t1.1 --R Type: Expression Integer --E ---S 47 +--S 47 of 52 bb2:=x/q-p/q*t1.2 --R --R +---------+ @@ -689,7 +689,7 @@ bb2:=x/q-p/q*t1.2 --R Type: Expression Integer --E ---S 48 +--S 48 of 52 cc1:=aa.1-bb1 --R --R (5) @@ -711,7 +711,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 49 +--S 49 of 52 cc2:=aa.1-bb2 --R --R (6) @@ -733,7 +733,7 @@ cc2:=aa.1-bb2 --R Type: Expression Integer --E ---S 50 +--S 50 of 52 cc3:=aa.2-bb1 --R --R (7) @@ -755,7 +755,7 @@ cc3:=aa.2-bb1 --R Type: Expression Integer --E ---S 51 14:459 Schaums and Axiom agree +--S 51 of 52 14:459 Schaums and Axiom agree cc4:=aa.2-bb2 --R --R (8) 0 @@ -772,7 +772,7 @@ $$ <<*>>= )clear all ---S 52 14:460 Axiom cannot compute this integral +--S 52 of 52 14:460 Axiom cannot compute this integral aa:=integrate(sec(a*x)^n,x) --R --R diff --git a/src/input/schaum23.input.pamphlet b/src/input/schaum23.input.pamphlet index 96485e2..fdf5b12 100644 --- a/src/input/schaum23.input.pamphlet +++ b/src/input/schaum23.input.pamphlet @@ -19,7 +19,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 55 aa:=integrate(csc(a*x),x) --R --R @@ -31,7 +31,7 @@ aa:=integrate(csc(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 55 bb1:=1/a*log(csc(a*x)-cot(a*x)) --R --R log(csc(a x) - cot(a x)) @@ -40,7 +40,7 @@ bb1:=1/a*log(csc(a*x)-cot(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 55 bb2:=1/a*log(tan((a*x)/2)) --R --R a x @@ -51,7 +51,7 @@ bb2:=1/a*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 4 +--S 4 of 55 cc1:=aa-bb1 --R --R sin(a x) @@ -62,7 +62,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 5 +--S 5 of 55 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -71,7 +71,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 6 +--S 6 of 55 dd1:=cotrule cc1 --R --R sin(a x) csc(a x)sin(a x) - cos(a x) @@ -82,7 +82,7 @@ dd1:=cotrule cc1 --R Type: Expression Integer --E ---S 7 +--S 7 of 55 cscrule:=rule(csc(a) == 1/sin(a)) --R --R 1 @@ -91,7 +91,7 @@ cscrule:=rule(csc(a) == 1/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 8 +--S 8 of 55 ee1:=cscrule dd1 --R --R sin(a x) - cos(a x) + 1 @@ -102,7 +102,7 @@ ee1:=cscrule dd1 --R Type: Expression Integer --E ---S 9 +--S 9 of 55 ff1:=expandLog ee1 --R --R 2log(sin(a x)) - log(cos(a x) + 1) - log(cos(a x) - 1) - log(- 1) @@ -111,7 +111,7 @@ ff1:=expandLog ee1 --R Type: Expression Integer --E ---S 10 +--S 10 of 55 gg1:=complexNormalize ff1 --R --R 2log(- 1) @@ -120,7 +120,7 @@ gg1:=complexNormalize ff1 --R Type: Expression Integer --E ---S 11 +--S 11 of 55 cc2:=aa-bb2 --R --R a x sin(a x) @@ -131,7 +131,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 12 +--S 12 of 55 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -140,7 +140,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 13 +--S 13 of 55 dd2:=tanrule cc2 --R --R a x @@ -155,7 +155,7 @@ dd2:=tanrule cc2 --R Type: Expression Integer --E ---S 14 +--S 14 of 55 ee2:=expandLog dd2 --R --R a x a x @@ -166,7 +166,7 @@ ee2:=expandLog dd2 --R Type: Expression Integer --E ---S 15 14:461 Schaums and Axiom agree +--S 15 of 55 14:461 Schaums and Axiom agree ff2:=complexNormalize ee2 --R --R (15) 0 @@ -182,7 +182,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 55 aa:=integrate(csc(a*x)^2,x) --R --R @@ -192,7 +192,7 @@ aa:=integrate(csc(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 55 bb:=-cot(a*x)/a --R --R cot(a x) @@ -201,7 +201,7 @@ bb:=-cot(a*x)/a --R Type: Expression Integer --E ---S 18 +--S 18 of 55 cc:=aa-bb --R --R cot(a x)sin(a x) - cos(a x) @@ -210,7 +210,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 19 +--S 19 of 55 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -219,7 +219,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 20 14:462 Schaums and Axiom agree +--S 20 of 55 14:462 Schaums and Axiom agree dd:=cotrule cc --R --R (5) 0 @@ -235,7 +235,7 @@ $$ <<*>>= )clear all ---S 21 +--S 21 of 55 aa:=integrate(csc(a*x)^3,x) --R --R @@ -248,7 +248,7 @@ aa:=integrate(csc(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 22 +--S 22 of 55 bb:=-(csc(a*x)*cot(a*x))/(2*a)+1/(2*a)*log(tan((a*x)/2)) --R --R a x @@ -259,7 +259,7 @@ bb:=-(csc(a*x)*cot(a*x))/(2*a)+1/(2*a)*log(tan((a*x)/2)) --R Type: Expression Integer --E ---S 23 +--S 23 of 55 cc:=aa-bb --R --R (3) @@ -275,7 +275,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 24 +--S 24 of 55 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -284,7 +284,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 25 +--S 25 of 55 dd:=cotrule cc --R --R (5) @@ -304,7 +304,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 26 +--S 26 of 55 tanrule:=rule(tan(a) == sin(a)/cos(a)) --R --R sin(a) @@ -313,7 +313,7 @@ tanrule:=rule(tan(a) == sin(a)/cos(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 27 +--S 27 of 55 ee:=tanrule dd --R --R (7) @@ -337,7 +337,7 @@ ee:=tanrule dd --R Type: Expression Integer --E ---S 28 +--S 28 of 55 cscrule:=rule(csc(a) == 1/sin(a)) --R --R 1 @@ -346,7 +346,7 @@ cscrule:=rule(csc(a) == 1/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 29 +--S 29 of 55 ff:=cscrule ee --R --R (9) @@ -369,7 +369,7 @@ ff:=cscrule ee --R Type: Expression Integer --E ---S 30 +--S 30 of 55 gg:=expandLog ff --R --R (10) @@ -394,7 +394,7 @@ gg:=expandLog ff --R Type: Expression Integer --E ---S 31 14:463 Schaums and Axiom agree +--S 31 of 55 14:463 Schaums and Axiom agree hh:=complexNormalize gg --R --R (11) 0 @@ -410,7 +410,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 55 aa:=integrate(csc(a*x)^n*cot(a*x),x) --R --R @@ -426,7 +426,7 @@ aa:=integrate(csc(a*x)^n*cot(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 55 bb:=-csc(a*x)^n/(n*a) --R --R n @@ -436,7 +436,7 @@ bb:=-csc(a*x)^n/(n*a) --R Type: Expression Integer --E ---S 34 +--S 34 of 55 cc:=aa-bb --R --R 1 @@ -451,7 +451,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 35 14:464 Schaums and Axiom agree +--S 35 of 55 14:464 Schaums and Axiom agree normalize cc --R --R (4) 0 @@ -467,7 +467,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 55 aa:=integrate(1/csc(a*x),x) --R --R @@ -477,7 +477,7 @@ aa:=integrate(1/csc(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 55 bb:=-cos(a*x)/a --R --R cos(a x) @@ -486,7 +486,7 @@ bb:=-cos(a*x)/a --R Type: Expression Integer --E ---S 38 14:465 Schaums and Axiom agree +--S 38 of 55 14:465 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -503,7 +503,7 @@ $$ <<*>>= )clear all ---S 39 14:466 Axiom cannot compute this integral +--S 39 of 55 14:466 Axiom cannot compute this integral aa:=integrate(x*csc(a*x),x) --R --R @@ -524,7 +524,7 @@ $$ <<*>>= )clear all ---S 40 14:467 Axiom cannot compute this integral +--S 40 of 55 14:467 Axiom cannot compute this integral aa:=integrate(csc(a*x)/x,x) --R --R @@ -544,7 +544,7 @@ $$ <<*>>= )clear all ---S 41 +--S 41 of 55 aa:=integrate(x*csc(a*x)^2,x) --R --R @@ -557,7 +557,7 @@ aa:=integrate(x*csc(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 55 bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x)) --R --R log(sin(a x)) - a x cot(a x) @@ -567,7 +567,7 @@ bb:=-(x*cot(a*x))/a+1/a^2*log(sin(a*x)) --R Type: Expression Integer --E ---S 43 +--S 43 of 55 cc:=aa-bb --R --R (3) @@ -584,7 +584,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 44 +--S 44 of 55 cotrule:=rule(cot(a) == cos(a)/sin(a)) --R --R cos(a) @@ -593,7 +593,7 @@ cotrule:=rule(cot(a) == cos(a)/sin(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 45 +--S 45 of 55 dd:=cotrule cc --R --R sin(a x) 2 @@ -605,7 +605,7 @@ dd:=cotrule cc --R Type: Expression Integer --E ---S 46 14:468 Schaums and Axiom differ by a constant +--S 46 of 55 14:468 Schaums and Axiom differ by a constant ee:=expandLog dd --R --R log(2) @@ -624,7 +624,7 @@ $$ <<*>>= )clear all ---S 47 +--S 47 of 55 aa:=integrate(1/(q+p*csc(a*x)),x) --R --R @@ -663,7 +663,7 @@ aa:=integrate(1/(q+p*csc(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 48 +--S 48 of 55 t1:=integrate(1/(p+q*sin(a*x)),x) --R --R (2) @@ -695,7 +695,7 @@ t1:=integrate(1/(p+q*sin(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 49 +--S 49 of 55 bb1:=x/q-p/q*t1.1 --R --R (3) @@ -722,7 +722,7 @@ bb1:=x/q-p/q*t1.1 --R Type: Expression Integer --E ---S 50 +--S 50 of 55 bb2:=x/q-p/q*t1.2 --R --R +---------+ @@ -738,7 +738,7 @@ bb2:=x/q-p/q*t1.2 --R Type: Expression Integer --E ---S 51 +--S 51 of 55 cc1:=aa.1-bb1 --R --R (5) @@ -772,7 +772,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 52 +--S 52 of 55 cc2:=aa.2-bb1 --R --R (6) @@ -803,7 +803,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 53 +--S 53 of 55 cc3:=aa.1-bb2 --R --R (7) @@ -834,7 +834,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 54 14:469 Schaums and Axiom agree +--S 54 of 55 14:469 Schaums and Axiom agree cc4:=aa.2-bb2 --R --R (8) 0 @@ -851,7 +851,7 @@ $$ <<*>>= )clear all ---S 55 14:470 Axiom cannot compute this integral +--S 55 of 55 14:470 Axiom cannot compute this integral aa:=integrate(csc(a*x)^n,x) --R --R diff --git a/src/input/schaum24.input.pamphlet b/src/input/schaum24.input.pamphlet index 71f28d5..7042d3a 100644 --- a/src/input/schaum24.input.pamphlet +++ b/src/input/schaum24.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 146 aa:=integrate(asin(x/a),x) --R --R @@ -33,7 +33,7 @@ aa:=integrate(asin(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 146 bb:=s+asin(x/a)+sqrt(a^2-x^2) --R --R +---------+ @@ -43,7 +43,7 @@ bb:=s+asin(x/a)+sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 3 14:471 Axiom cannot simplify this expression +--S 3 of 146 14:471 Axiom cannot simplify this expression cc:=aa-bb --R --R +---------+ @@ -68,7 +68,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 146 aa:=integrate(x*asin(x/a),x) --R --R @@ -83,7 +83,7 @@ aa:=integrate(x*asin(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 146 bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4 --R --R +---------+ @@ -95,7 +95,7 @@ bb:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4 --R Type: Expression Integer --E ---S 6 +--S 6 of 146 cc:=aa-bb --R --R +---------+ @@ -119,7 +119,7 @@ point values and expect the same numeric results. So we try that here. @ This is the initial integrand. <<*>>= ---S 7 +--S 7 of 146 t1:=x*asin(x/a) --R --R x @@ -130,7 +130,7 @@ t1:=x*asin(x/a) @ This is the integral result provided by Axiom. <<*>>= ---S 8 +--S 8 of 146 t2:=integrate(t1,x) --R --R +---------+ @@ -146,7 +146,7 @@ t2:=integrate(t1,x) @ This is the derivative of the integral computed by Axiom <<*>>= ---S 9 +--S 9 of 146 t3:=D(t2,x) --R --R +---------+ @@ -162,7 +162,7 @@ t3:=D(t2,x) @ This is the integral result provided by Schaums <<*>>= ---S 10 +--S 10 of 146 t4:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4 --R --R +---------+ @@ -177,7 +177,7 @@ t4:=(x^2/2-a^2/4)*asin(x/a)+(x*sqrt(a^2-x^2))/4 This is the derivative of the integral of the original function according to Schaums. <<*>>= ---S 11 +--S 11 of 146 t5:=D(t4,x) --R --R (5) @@ -199,7 +199,7 @@ t5:=D(t4,x) @ Now we create a function for computing the integrand's values. <<*>>= ---S 12 +--S 12 of 146 f:=makeFloatFunction(t1,x,a) --I Compiling function %BF with type (DoubleFloat,DoubleFloat) -> --R DoubleFloat @@ -210,7 +210,7 @@ f:=makeFloatFunction(t1,x,a) @ Now we create a function for computing Axiom's values for its integrand. <<*>>= ---S 13 +--S 13 of 146 axiom:=makeFloatFunction(t3,x,a) --I Compiling function %BJ with type (DoubleFloat,DoubleFloat) -> --R DoubleFloat @@ -221,7 +221,7 @@ axiom:=makeFloatFunction(t3,x,a) @ Now we create a function for computing Schams values for its integrand. <<*>>= ---S 14 +--S 14 of 146 schaums:=makeFloatFunction(t5,x,a) --I Compiling function %BK with type (DoubleFloat,DoubleFloat) -> --R DoubleFloat @@ -237,7 +237,7 @@ functions are only equal within the branch cut range. This is a generic problem with all of the inverse functions that are multi-valued. <<*>>= ---S 15 14:472 Schaums and Axiom agree (modulo branch cuts) +--S 15 of 146 14:472 Schaums and Axiom agree (modulo branch cuts) [ [f(i::Float,i::Float+1.0::Float)::Float,axiom(i::Float,i::Float+1.0::Float)::Float,schaums(i::Float,i::Float+1.0::Float)::Float] for i in 1..4] --R --R (9) @@ -257,7 +257,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 146 aa:=integrate(x^2*asin(x/a),x) --R --R @@ -272,7 +272,7 @@ aa:=integrate(x^2*asin(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 146 bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9 --R --R +---------+ @@ -284,7 +284,7 @@ bb:=x^3/3*asin(x/a)+((x^2+2*a^2)*sqrt(a^2-x^2))/9 --R Type: Expression Integer --E ---S 18 14:473 Axiom cannot simplify this expression +--S 18 of 146 14:473 Axiom cannot simplify this expression cc:=aa-bb --R --R +---------+ @@ -309,7 +309,7 @@ $$ <<*>>= )clear all ---S 19 14:474 Axiom cannot compute this integral +--S 19 of 146 14:474 Axiom cannot compute this integral aa:=integrate(asin(x/a)/x,x) --R --R @@ -331,7 +331,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 146 aa:=integrate(asin(x/a)/x^2,x) --R --R @@ -347,7 +347,7 @@ aa:=integrate(asin(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 146 bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -360,7 +360,7 @@ bb:=-asin(x/a)/x-1/a*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 22 14:475 Axiom cannot simplify this expression +--S 22 of 146 14:475 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -388,7 +388,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 146 aa:=integrate(asin(x/a)^2,x) --R --R @@ -403,7 +403,7 @@ aa:=integrate(asin(x/a)^2,x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 146 bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a) --R --R +---------+ @@ -413,7 +413,7 @@ bb:=x*asin(x/a)^2-2*x+2*sqrt(a^2-x^2)*asin(x/a) --R Type: Expression Integer --E ---S 25 14:476 Axiom cannot simplify this expression +--S 25 of 146 14:476 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -442,7 +442,7 @@ $$ <<*>>= )clear all ---S 26 +--S 26 of 146 aa:=integrate(acos(x/a),x) --R --R @@ -457,7 +457,7 @@ aa:=integrate(acos(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 27 +--S 27 of 146 bb:=x*acos(x/a)-sqrt(a^2-x^2) --R --R +---------+ @@ -467,7 +467,7 @@ bb:=x*acos(x/a)-sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 28 14:477 Axiom cannot simplify this expression +--S 28 of 146 14:477 Axiom cannot simplify this expression cc:=aa-bb --R --R +---------+ @@ -491,7 +491,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 146 aa:=integrate(x*acos(x/a),x) --R --R @@ -506,7 +506,7 @@ aa:=integrate(x*acos(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 146 bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4 --R --R +---------+ @@ -518,7 +518,7 @@ bb:=(x^2/2-a^2/4)*acos(x/a)-(x*sqrt(a^2-x^2))/4 --R Type: Expression Integer --E ---S 31 14:478 Axiom cannot simplify this expression +--S 31 of 146 14:478 Axiom cannot simplify this expression cc:=aa-bb --R --R +---------+ @@ -541,7 +541,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 146 aa:=integrate(x^2*acos(x/a),x) --R --R @@ -556,7 +556,7 @@ aa:=integrate(x^2*acos(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 146 bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9 --R --R +---------+ @@ -568,7 +568,7 @@ bb:=x^3/3*acos(x/a)-((x^2+2*a^2)*sqrt(a^2-x^2))/9 --R Type: Expression Integer --E ---S 34 14:479 Axiom cannot simplify this expression +--S 34 of 146 14:479 Axiom cannot simplify this expression cc:=aa-bb --R --R +---------+ @@ -591,7 +591,7 @@ $$ <<*>>= )clear all ---S 35 14:480 Axiom cannot compute this integral +--S 35 of 146 14:480 Axiom cannot compute this integral aa:=integrate(acos(x/a)/x,x) --R --R @@ -612,7 +612,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 146 aa:=integrate(acos(x/a)/x^2,x) --R --R @@ -628,7 +628,7 @@ aa:=integrate(acos(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 146 bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x) --R --R +---------+ @@ -641,7 +641,7 @@ bb:=-acos(x/a)/x+1/a*log((a+sqrt(a^2-x^2))/x) --R Type: Expression Integer --E ---S 38 14:481 Axiom cannot simplify this expression +--S 38 of 146 14:481 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -669,7 +669,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 146 aa:=integrate(acos(x/a)^2,x) --R --R @@ -684,7 +684,7 @@ aa:=integrate(acos(x/a)^2,x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 146 bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a) --R --R +---------+ @@ -694,7 +694,7 @@ bb:=x*acos(x/a)^2-2*x-2*sqrt(a^2-x^2)*acos(x/a) --R Type: Expression Integer --E ---S 41 14:482 Axiom cannot simplify this expression +--S 41 of 146 14:482 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -723,7 +723,7 @@ $$ <<*>>= )clear all ---S 42 +--S 42 of 146 aa:=integrate(atan(x/a),x) --R --R @@ -736,7 +736,7 @@ aa:=integrate(atan(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 43 +--S 43 of 146 bb:=x*atan(x/a)-a/2*log(x^2+a^2) --R --R 2 2 x @@ -747,7 +747,7 @@ bb:=x*atan(x/a)-a/2*log(x^2+a^2) --R Type: Expression Integer --E ---S 44 +--S 44 of 146 cc:=aa-bb --R --R x 2a x @@ -759,7 +759,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 45 +--S 45 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -770,7 +770,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 46 +--S 46 of 146 dd:=atanrule cc --R --R 2 2 @@ -783,7 +783,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 47 14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?) +--S 47 of 146 14:483 SCHAUMS AND AXIOM DIFFER? (BRANCH CUTS?) ee:=expandLog dd --R --R %i x log(- 1) @@ -801,7 +801,7 @@ $$ <<*>>= )clear all ---S 48 14:484 Axiom cannot compute this integral +--S 48 of 146 14:484 Axiom cannot compute this integral aa:=integrate(x*tan(x/a),x) --R --R @@ -821,7 +821,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 146 aa:=integrate(x^2*atan(x/a),x) --R --R @@ -834,7 +834,7 @@ aa:=integrate(x^2*atan(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 50 +--S 50 of 146 bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2) --R --R 3 2 2 3 x 2 @@ -845,7 +845,7 @@ bb:=x^3/2*atan(x/a)-(a*x^2)/6+a^3/6*log(x^2+a^2) --R Type: Expression Integer --E ---S 51 14:485 Axiom cannot simplify this expression +--S 51 of 146 14:485 Axiom cannot simplify this expression cc:=aa-bb --R --R 3 x 3 2a x @@ -866,7 +866,7 @@ $$ <<*>>= )clear all ---S 52 14:486 Axiom cannot compute this integral +--S 52 of 146 14:486 Axiom cannot compute this integral aa:=integrate(atan(x/a)/x,x) --R --R @@ -888,7 +888,7 @@ $$ <<*>>= )clear all ---S 53 +--S 53 of 146 aa:=integrate(atan(x/a)/x^2,x) --R --R @@ -901,7 +901,7 @@ aa:=integrate(atan(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 54 +--S 54 of 146 bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2) --R --R 2 2 @@ -914,7 +914,7 @@ bb:=-1/x*atan(x/a)-1/(2*a)*log((x^2+a^2)/x^2) --R Type: Expression Integer --E ---S 55 +--S 55 of 146 cc:=aa-bb --R --R (3) @@ -928,7 +928,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 56 +--S 56 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -939,7 +939,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 57 +--S 57 of 146 dd:=atanrule cc --R --R (5) @@ -959,7 +959,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 58 14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?) +--S 58 of 146 14:487 SCHAUMS AND AXIOM DIFFER? (branch cuts?) ee:=expandLog dd --R --R %i log(- 1) @@ -977,7 +977,7 @@ $$ <<*>>= )clear all ---S 59 +--S 59 of 146 aa:=integrate(acot(x/a),x) --R --R @@ -990,7 +990,7 @@ aa:=integrate(acot(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 60 +--S 60 of 146 bb:=x*acot(x/a)+a/2*log(x^2+a^2) --R --R 2 2 x @@ -1001,7 +1001,7 @@ bb:=x*acot(x/a)+a/2*log(x^2+a^2) --R Type: Expression Integer --E ---S 61 +--S 61 of 146 cc:=aa-bb --R --R 2a x x @@ -1013,7 +1013,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 62 +--S 62 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1024,7 +1024,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 63 +--S 63 of 146 dd:=atanrule cc --R --R 2 2 @@ -1037,7 +1037,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 64 +--S 64 of 146 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R --R x + %i @@ -1048,7 +1048,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 65 +--S 65 of 146 ee:=acotrule dd --R --R 2 2 @@ -1061,7 +1061,7 @@ ee:=acotrule dd --R Type: Expression Complex Integer --E ---S 66 14:488 Axiom and Schaums agree +--S 66 of 146 14:488 Axiom and Schaums agree ff:=expandLog % --R --R (8) 0 @@ -1077,7 +1077,7 @@ $$ <<*>>= )clear all ---S 67 +--S 67 of 146 aa:=integrate(x*acot(x/a),x) --R --R @@ -1090,7 +1090,7 @@ aa:=integrate(x*acot(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 68 +--S 68 of 146 bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2 --R --R 2 2 x @@ -1101,7 +1101,7 @@ bb:=1/2*(x^2+a^2)*acot(x/a)+(a*x)/2 --R Type: Expression Integer --E ---S 69 +--S 69 of 146 cc:=aa-bb --R --R 2 2 2a x 2 2 x @@ -1113,7 +1113,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 70 +--S 70 of 146 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R --R x + %i @@ -1124,7 +1124,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 71 +--S 71 of 146 dd:=acotrule cc --R --R 2 2 x + %i a 2 2 2a x @@ -1136,7 +1136,7 @@ dd:=acotrule cc --R Type: Expression Complex Integer --E ---S 72 +--S 72 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1147,7 +1147,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 73 +--S 73 of 146 ee:=atanrule dd --R --R (7) @@ -1161,7 +1161,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 74 14:489 Axiom and Schaums agree +--S 74 of 146 14:489 Axiom and Schaums agree ff:=expandLog ee --R --R (8) 0 @@ -1177,7 +1177,7 @@ $$ <<*>>= )clear all ---S 75 +--S 75 of 146 aa:=integrate(x^2*acot(x/a),x) --R --R @@ -1190,7 +1190,7 @@ aa:=integrate(x^2*acot(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 76 +--S 76 of 146 bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2) --R --R 3 2 2 3 x 2 @@ -1201,7 +1201,7 @@ bb:=x^3/3*acot(x/a)+(a*x^2)/6-a^3/6*log(x^2+a^2) --R Type: Expression Integer --E ---S 77 +--S 77 of 146 cc:=aa-bb --R --R 3 2a x 3 x @@ -1213,7 +1213,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 78 +--S 78 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1224,7 +1224,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 79 +--S 79 of 146 dd:=atanrule cc --R --R 2 2 @@ -1237,7 +1237,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 80 +--S 80 of 146 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R --R x + %i @@ -1248,7 +1248,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 81 +--S 81 of 146 ee:=acotrule dd --R --R 2 2 @@ -1261,7 +1261,7 @@ ee:=acotrule dd --R Type: Expression Complex Integer --E ---S 82 14:490 Axiom and Schaums agree +--S 82 of 146 14:490 Axiom and Schaums agree ff:=expandLog ee --R --R (8) 0 @@ -1277,7 +1277,7 @@ $$ <<*>>= )clear all ---S 83 14:491 Axiom cannot compute this integral +--S 83 of 146 14:491 Axiom cannot compute this integral aa:=integrate(acot(x/a)/x,x) --R --R @@ -1298,7 +1298,7 @@ $$ <<*>>= )clear all ---S 84 +--S 84 of 146 aa:=integrate(acot(x/a)/x^2,x) --R --R @@ -1311,7 +1311,7 @@ aa:=integrate(acot(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 85 +--S 85 of 146 bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2) --R --R 2 2 @@ -1324,7 +1324,7 @@ bb:=-acot(x/a)/x+1/(2*a)*log((x^2+a^2)/x^2) --R Type: Expression Integer --E ---S 86 +--S 86 of 146 cc:=aa-bb --R --R (3) @@ -1338,7 +1338,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 87 +--S 87 of 146 acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R --R x + %i @@ -1349,7 +1349,7 @@ acotrule:=rule(acot(x) == -%i/2*log((%i*x-1)/(%i*x+1))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 88 +--S 88 of 146 dd:=acotrule cc --R --R (5) @@ -1368,7 +1368,7 @@ dd:=acotrule cc --R Type: Expression Complex Integer --E ---S 89 +--S 89 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1379,7 +1379,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 90 +--S 90 of 146 ee:=atanrule dd --R --R (7) @@ -1399,7 +1399,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 91 14:492 Schaums and Axiom agree +--S 91 of 146 14:492 Schaums and Axiom agree ff:=expandLog ee --R --R (8) 0 @@ -1425,7 +1425,7 @@ $$ <<*>>= )clear all ---S 92 +--S 92 of 146 aa:=integrate(asec(x/a),x) --R --R @@ -1447,7 +1447,7 @@ aa:=integrate(asec(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 93 +--S 93 of 146 bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2)) --R --R +-------+ @@ -1457,7 +1457,7 @@ bb1:=x*asec(x/a)-a*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 94 +--S 94 of 146 bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2)) --R --R +-------+ @@ -1467,7 +1467,7 @@ bb2:=x*asec(x/a)+a*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 95 +--S 95 of 146 cc1:=aa-bb1 --R --R (4) @@ -1490,7 +1490,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 96 14:493 Axiom cannot simplify these expressions +--S 96 of 146 14:493 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -1532,7 +1532,7 @@ $$ <<*>>= )clear all ---S 97 +--S 97 of 146 aa:=integrate(x*asec(x/a),x) --R --R @@ -1547,7 +1547,7 @@ aa:=integrate(x*asec(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 98 +--S 98 of 146 bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2 --R --R +-------+ @@ -1559,7 +1559,7 @@ bb1:=x^2/2*asec(x/a)-(a*sqrt(x^2-a^2))/2 --R Type: Expression Integer --E ---S 99 +--S 99 of 146 bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2 --R --R +-------+ @@ -1571,7 +1571,7 @@ bb2:=x^2/2*asec(x/a)+(a*sqrt(x^2-a^2))/2 --R Type: Expression Integer --E ---S 100 +--S 100 of 146 cc1:=aa-bb1 --R --R (4) @@ -1586,7 +1586,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 101 14:494 Axiom cannot simplify these expressions +--S 101 of 146 14:494 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -1627,7 +1627,7 @@ $$ <<*>>= )clear all ---S 102 +--S 102 of 146 aa:=integrate(x^2*asec(x/a),x) --R --R @@ -1650,7 +1650,7 @@ aa:=integrate(x^2*asec(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 103 +--S 103 of 146 bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -1662,7 +1662,7 @@ bb1:=x^3/3*asec(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 104 +--S 104 of 146 bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -1674,7 +1674,7 @@ bb2:=x^3/3*asec(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 105 +--S 105 of 146 cc1:=aa-bb1 --R --R (4) @@ -1702,7 +1702,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 106 14:495 Axiom cannot simplify these expressions +--S 106 of 146 14:495 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -1742,7 +1742,7 @@ $$ <<*>>= )clear all ---S 107 14:496 Axiom cannot compute this integral +--S 107 of 146 14:496 Axiom cannot compute this integral aa:=integrate(asec(x/a)/x,x) --R --R @@ -1773,7 +1773,7 @@ $$ <<*>>= )clear all ---S 108 +--S 108 of 146 aa:=integrate(asec(x/a)/x^2,x) --R --R @@ -1789,7 +1789,7 @@ aa:=integrate(asec(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 109 +--S 109 of 146 bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x) --R --R +-------+ @@ -1801,7 +1801,7 @@ bb1:=-asec(x/a)/x+sqrt(x^2-a^2)/(a*x) --R Type: Expression Integer --E ---S 110 +--S 110 of 146 bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x) --R --R +-------+ @@ -1813,7 +1813,7 @@ bb2:=-asec(x/a)/x-sqrt(x^2-a^2)/(a*x) --R Type: Expression Integer --E ---S 111 +--S 111 of 146 cc1:=aa-bb1 --R --R (4) @@ -1833,7 +1833,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 112 14:497 Axiom cannot simplify these expressions +--S 112 of 146 14:497 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -1872,7 +1872,7 @@ $$ <<*>>= )clear all ---S 113 +--S 113 of 146 aa:=integrate(acsc(x/a),x) --R --R @@ -1894,7 +1894,7 @@ aa:=integrate(acsc(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 114 +--S 114 of 146 bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2)) --R --R +-------+ @@ -1904,7 +1904,7 @@ bb1:=x*acsc(x/a)+a*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 115 +--S 115 of 146 bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2)) --R --R +-------+ @@ -1914,7 +1914,7 @@ bb2:=x*acsc(x/a)-a*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 116 +--S 116 of 146 cc1:=aa-bb1 --R --R (4) @@ -1937,7 +1937,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 117 14:498 Axiom cannot simplify these expressions +--S 117 of 146 14:498 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -1980,7 +1980,7 @@ $$ <<*>>= )clear all ---S 118 +--S 118 of 146 aa:=integrate(x*acsc(x/a),x) --R --R @@ -1995,7 +1995,7 @@ aa:=integrate(x*acsc(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 119 +--S 119 of 146 bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2 --R --R +-------+ @@ -2007,7 +2007,7 @@ bb1:=x^2/2*acsc(x/a)+(a*sqrt(x^2-a^2))/2 --R Type: Expression Integer --E ---S 120 +--S 120 of 146 bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2 --R --R +-------+ @@ -2019,7 +2019,7 @@ bb2:=x^2/2*acsc(x/a)-(a*sqrt(x^2-a^2))/2 --R Type: Expression Integer --E ---S 121 +--S 121 of 146 cc1:=aa-bb1 --R --R (4) @@ -2034,7 +2034,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 122 14:499 Axiom cannot simplify these expressions +--S 122 of 146 14:499 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -2075,7 +2075,7 @@ $$ <<*>>= )clear all ---S 123 +--S 123 of 146 aa:=integrate(x^2*acsc(x/a),x) --R --R @@ -2098,7 +2098,7 @@ aa:=integrate(x^2*acsc(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 124 +--S 124 of 146 bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -2110,7 +2110,7 @@ bb1:=x^3/3*acsc(x/a)+(a*x*sqrt(x^2-a^2))/6+a^3/6*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 125 +--S 125 of 146 bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2)) --R --R +-------+ +-------+ @@ -2122,7 +2122,7 @@ bb2:=x^3/3*acsc(x/a)-(a*x*sqrt(x^2-a^2))/6-a^3/6*log(x+sqrt(x^2-a^2)) --R Type: Expression Integer --E ---S 126 +--S 126 of 146 cc1:=aa-bb1 --R --R (4) @@ -2150,7 +2150,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 127 14:500 Axiom cannot simplify this expression +--S 127 of 146 14:500 Axiom cannot simplify this expression cc2:=aa-bb2 --R --R (5) @@ -2189,7 +2189,7 @@ $$ <<*>>= )clear all ---S 128 14:501 Axiom cannot compute this integral +--S 128 of 146 14:501 Axiom cannot compute this integral aa:=integrate(acsc(x/a)/x,x) --R --R @@ -2220,7 +2220,7 @@ $$ <<*>>= )clear all ---S 129 +--S 129 of 146 aa:=integrate(acsc(x/a)/x^2,x) --R --R @@ -2236,7 +2236,7 @@ aa:=integrate(acsc(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 130 +--S 130 of 146 bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x) --R --R +-------+ @@ -2248,7 +2248,7 @@ bb1:=-acsc(x/a)/x-sqrt(x^2-a^2)/(a*x) --R Type: Expression Integer --E ---S 131 +--S 131 of 146 bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x) --R --R +-------+ @@ -2260,7 +2260,7 @@ bb2:=-acsc(x/a)/x+sqrt(x^2-a^2)/(a*x) --R Type: Expression Integer --E ---S 132 +--S 132 of 146 cc1:=aa-bb1 --R --R (4) @@ -2281,7 +2281,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 133 14:502 Axiom cannot simplify this expression +--S 133 of 146 14:502 Axiom cannot simplify this expression cc2:=aa-bb2 --R --R (5) @@ -2311,7 +2311,7 @@ $$ <<*>>= )clear all ---S 134 14:503 Axiom cannot compute this integral +--S 134 of 146 14:503 Axiom cannot compute this integral aa:=integrate(x^m*asin(x/a),x) --R --R @@ -2331,7 +2331,7 @@ $$ <<*>>= )clear all ---S 135 14:504 Axiom cannot compute this integral +--S 135 of 146 14:504 Axiom cannot compute this integral aa:=integrate(x^m*acos(x/a),x) --R --R @@ -2357,7 +2357,7 @@ have the same form but are expressed in terms of asin, acos, and acot. <<*>>= )clear all ---S 136 +--S 136 of 146 aa:=integrate(x*m*atan(x/a),x) --R --R @@ -2370,7 +2370,7 @@ aa:=integrate(x*m*atan(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 137 +--S 137 of 146 t1:=integrate(x^(m+1)/(x^2+a^2),x) --E @ @@ -2382,7 +2382,7 @@ difference from the original formula. So first we generate the derivative: <<*>>= ---S 138 +--S 138 of 146 bb:=D(aa,x) --R --R 2a x @@ -2396,7 +2396,7 @@ bb:=D(aa,x) @ Then we input the original expression <<*>>= ---S 139 +--S 139 of 146 aa1:=x*m*atan(x/a) --R --R x @@ -2407,7 +2407,7 @@ aa1:=x*m*atan(x/a) @ Now we take their difference <<*>>= ---S 140 +--S 140 of 146 dd:=aa1-bb --R --R x 2a x @@ -2421,7 +2421,7 @@ dd:=aa1-bb @ Now we input the atan transformation <<*>>= ---S 141 +--S 141 of 146 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -2434,7 +2434,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) @ And apply the transformation to the difference <<*>>= ---S 142 +--S 142 of 146 ee:=atanrule dd --R --R 2 2 @@ -2449,7 +2449,7 @@ ee:=atanrule dd @ And now we simplify <<*>>= ---S 143 14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?) +--S 143 of 146 14:505 SCHAUMS AND AXIOM DISAGREE? (branch cuts?) ff:=expandLog ee --R --R %i m x log(- 1) @@ -2471,7 +2471,7 @@ $$ <<*>>= )clear all ---S 144 14:506 Axiom cannot compute this integral +--S 144 of 146 14:506 Axiom cannot compute this integral aa:=integrate(x^m*acot(x/a),x) --R --R @@ -2501,7 +2501,7 @@ $$ <<*>>= )clear all ---S 145 14:507 Axiom cannot compute this integral +--S 145 of 146 14:507 Axiom cannot compute this integral aa:=integrate(x^m*asec(x/a),x) --R --R @@ -2531,7 +2531,7 @@ $$ <<*>>= )clear all ---S 146 14:508 Axiom cannot compute this integral +--S 146 of 146 14:508 Axiom cannot compute this integral aa:=integrate(x^m*acsc(x/a),x) --R --R diff --git a/src/input/schaum25.input.pamphlet b/src/input/schaum25.input.pamphlet index 0a55f34..75694f8 100644 --- a/src/input/schaum25.input.pamphlet +++ b/src/input/schaum25.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 40 aa:=integrate(%e^(a*x),x) --R --R a x @@ -28,7 +28,7 @@ aa:=integrate(%e^(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 40 bb:=%e^(a*x)/a --R --R a x @@ -38,7 +38,7 @@ bb:=%e^(a*x)/a --R Type: Expression Integer --E ---S 3 14:509 Schaums and Axiom agree +--S 3 of 40 14:509 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -54,7 +54,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 40 aa:=integrate(x*%e^(a*x),x) --R --R a x @@ -65,7 +65,7 @@ aa:=integrate(x*%e^(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 40 bb:=%e^(a*x)/a*(x-1/a) --R --R a x @@ -76,7 +76,7 @@ bb:=%e^(a*x)/a*(x-1/a) --R Type: Expression Integer --E ---S 6 14:510 Schaums and Axiom agree +--S 6 of 40 14:510 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -92,7 +92,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 40 aa:=integrate(x^2*%e^(a*x),x) --R --R 2 2 a x @@ -103,7 +103,7 @@ aa:=integrate(x^2*%e^(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 40 bb:=%e^(a*x)/a*(x^2-(2*x)/a+2/a^2) --R --R 2 2 a x @@ -114,7 +114,7 @@ bb:=%e^(a*x)/a*(x^2-(2*x)/a+2/a^2) --R Type: Expression Integer --E ---S 9 14:511 Schaums and Axiom agree +--S 9 of 40 14:511 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -139,7 +139,7 @@ $$ <<*>>= )clear all ---S 10 14:512 Axiom cannot compute this integral +--S 10 of 40 14:512 Axiom cannot compute this integral aa:=integrate(x^n*%e^(a*x),x) --R --R x @@ -160,7 +160,7 @@ $$ <<*>>= )clear all ---S 11 14:513 Schaums and Axiom agree by definition +--S 11 of 40 14:513 Schaums and Axiom agree by definition aa:=integrate(%e^(a*x)/x,x) --R --R (1) Ei(a x) @@ -176,7 +176,7 @@ $$ <<*>>= )clear all ---S 12 14:514 Axiom cannot compute this integral +--S 12 of 40 14:514 Axiom cannot compute this integral aa:=integrate(%e^(a*x)/x^n,x) --R --I x %I a @@ -196,7 +196,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 40 aa:=integrate(1/(p+q*%e^(a*x)),x) --R --R a x @@ -206,7 +206,7 @@ aa:=integrate(1/(p+q*%e^(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 40 bb:=x/p-1/(a*p)*log(p+q*%e^(a*x)) --R --R a x @@ -216,7 +216,7 @@ bb:=x/p-1/(a*p)*log(p+q*%e^(a*x)) --R Type: Expression Integer --E ---S 15 14:515 Schaums and Axiom agree +--S 15 of 40 14:515 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -232,7 +232,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 40 aa:=integrate(1/(p+q*%e^(a*x))^2,x) --R --R a x a x a x @@ -243,7 +243,7 @@ aa:=integrate(1/(p+q*%e^(a*x))^2,x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 40 bb:=x/p^2+1/(a*p*(p+q*%e^(a*x)))-1/(a*p^2)*log(p+q*%e^(a*x)) --R --R a x a x a x @@ -254,7 +254,7 @@ bb:=x/p^2+1/(a*p*(p+q*%e^(a*x)))-1/(a*p^2)*log(p+q*%e^(a*x)) --R Type: Expression Integer --E ---S 18 14:516 Schaums and Axiom agree +--S 18 of 40 14:516 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -279,7 +279,7 @@ $$ <<*>>= )clear all ---S 19 +--S 19 of 40 aa:=integrate(1/(p*%e^(a*x)+q*%e^-(a*x)),x) --R --R a x 2 +-----+ a x @@ -293,7 +293,7 @@ aa:=integrate(1/(p*%e^(a*x)+q*%e^-(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 20 +--S 20 of 40 bb1:=1/(a*sqrt(p*q))*atan(sqrt(p/q)*%e^(a*x)) --R --R +-+ @@ -306,7 +306,7 @@ bb1:=1/(a*sqrt(p*q))*atan(sqrt(p/q)*%e^(a*x)) --R Type: Expression Integer --E ---S 21 +--S 21 of 40 bb2:=1/(2*a*sqrt(-p*q))*log((%e^(a*x)-sqrt(-q/p))/(%e^(a*x)+sqrt(-q/p))) --R --R +---+ @@ -324,7 +324,7 @@ bb2:=1/(2*a*sqrt(-p*q))*log((%e^(a*x)-sqrt(-q/p))/(%e^(a*x)+sqrt(-q/p))) --R Type: Expression Integer --E ---S 22 +--S 22 of 40 cc1:=aa.1-bb1 --R --R (4) @@ -339,7 +339,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 23 +--S 23 of 40 cc2:=aa.2-bb1 --R --R a x +---+ +-+ @@ -352,7 +352,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 24 +--S 24 of 40 cc3:=aa.1-bb2 --R --R +---+ @@ -370,7 +370,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 25 14:517 Axiom cannot simplify these expressions +--S 25 of 40 14:517 Axiom cannot simplify these expressions cc4:=aa.2-bb2 --R --R +---+ @@ -397,7 +397,7 @@ $$ <<*>>= )clear all ---S 26 +--S 26 of 40 aa:=integrate(%e^(a*x)*sin(b*x),x) --R --R a x a x @@ -408,7 +408,7 @@ aa:=integrate(%e^(a*x)*sin(b*x),x) --R Type: Union(Expression Integer,...) --E ---S 27 +--S 27 of 40 bb:=((%e^(a*x))*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2) --R --R a x a x @@ -419,7 +419,7 @@ bb:=((%e^(a*x))*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2) --R Type: Expression Integer --E ---S 28 14:518 Schaums and Axiom agree +--S 28 of 40 14:518 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -435,7 +435,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 40 aa:=integrate(%e^(a*x)*cos(b*x),x) --R --R a x a x @@ -446,7 +446,7 @@ aa:=integrate(%e^(a*x)*cos(b*x),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 40 bb:=((%e^(a*x))*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2) --R --R a x a x @@ -457,7 +457,7 @@ bb:=((%e^(a*x))*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2) --R Type: Expression Integer --E ---S 31 14:519 Schaums and Axiom agree +--S 31 of 40 14:519 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -474,7 +474,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 40 aa:=integrate(x*%e^(a*x)*sin(b*x),x) --R --R (1) @@ -486,7 +486,7 @@ aa:=integrate(x*%e^(a*x)*sin(b*x),x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 40 bb:=(x*%e^(a*x)*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*sin(b*x)-2*a*b*cos(b*x)))/(a^2+b^2)^2 --R --R (2) @@ -498,7 +498,7 @@ bb:=(x*%e^(a*x)*(a*sin(b*x)-b*cos(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*sin(b*x) --R Type: Expression Integer --E ---S 34 14:520 Schaums and Axiom agree +--S 34 of 40 14:520 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -515,7 +515,7 @@ $$ <<*>>= )clear all ---S 35 +--S 35 of 40 aa:=integrate(x*%e^(a*x)*cos(b*x),x) --R --R (1) @@ -527,7 +527,7 @@ aa:=integrate(x*%e^(a*x)*cos(b*x),x) --R Type: Union(Expression Integer,...) --E ---S 36 +--S 36 of 40 bb:=(x*%e^(a*x)*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*cos(b*x)+2*a*b*sin(b*x)))/(a^2+b^2)^2 --R --R (2) @@ -539,7 +539,7 @@ bb:=(x*%e^(a*x)*(a*cos(b*x)+b*sin(b*x)))/(a^2+b^2)-(%e^(a*x)*((a^2-b^2)*cos(b*x) --R Type: Expression Integer --E ---S 37 14:521 Schaums and Axiom agree +--S 37 of 40 14:521 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -555,7 +555,7 @@ $$ <<*>>= )clear all ---S 38 14:522 Schaums and Axiom agree by definition +--S 38 of 40 14:522 Schaums and Axiom agree by definition aa:=integrate(%e^(a*x)*log(x),x) --R --R a x @@ -575,7 +575,7 @@ $$ <<*>>= )clear all ---S 39 14:523 Axiom cannot compute this integral +--S 39 of 40 14:523 Axiom cannot compute this integral aa:=integrate(%e^(a*x)*sin(b*x)^n,x) --R --R x @@ -595,7 +595,7 @@ $$ <<*>>= )clear all ---S 40 14:524 Axiom cannot compute this integral +--S 40 of 40 14:524 Axiom cannot compute this integral aa:=integrate(%e^(a*x)*cos(b*x)^n,x) --R --R x diff --git a/src/input/schaum26.input.pamphlet b/src/input/schaum26.input.pamphlet index 9bdeec5..a75d995 100644 --- a/src/input/schaum26.input.pamphlet +++ b/src/input/schaum26.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 43 aa:=integrate(log(x),x) --R --R @@ -26,14 +26,14 @@ aa:=integrate(log(x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 43 bb:=x*log(x)-x --R --R (2) x log(x) - x --R Type: Expression Integer --E ---S 3 14:525 Schaums and Axiom agree +--S 3 of 43 14:525 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -49,7 +49,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 43 aa:=integrate(x*log(x),x) --R --R @@ -60,7 +60,7 @@ aa:=integrate(x*log(x),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 43 bb:=x^2/2*(log(x)-1/2) --R --R 2 2 @@ -70,7 +70,7 @@ bb:=x^2/2*(log(x)-1/2) --R Type: Expression Integer --E ---S 6 14:526 Schaums and Axiom agree +--S 6 of 43 14:526 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -86,7 +86,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 43 aa:=integrate(x^m*log(x),x) --R --R @@ -98,7 +98,7 @@ aa:=integrate(x^m*log(x),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 43 bb:=x^(m+1)/(m+1)*(log(x)-1/(m+1)) --R --R m + 1 @@ -109,7 +109,7 @@ bb:=x^(m+1)/(m+1)*(log(x)-1/(m+1)) --R Type: Expression Integer --E ---S 9 +--S 9 of 43 cc:=aa-bb --R --R m log(x) m + 1 @@ -120,7 +120,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 10 +--S 10 of 43 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -128,7 +128,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 11 +--S 11 of 43 dd:=explog cc --R --R m + 1 m @@ -139,7 +139,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 12 14:527 Schaums and Axiom agree +--S 12 of 43 14:527 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -155,7 +155,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 43 aa:=integrate(log(x)/x,x) --R --R @@ -166,7 +166,7 @@ aa:=integrate(log(x)/x,x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 43 bb:=1/2*log(x)^2 --R --R 2 @@ -176,7 +176,7 @@ bb:=1/2*log(x)^2 --R Type: Expression Integer --E ---S 15 14:528 Schaums and Axiom agree +--S 15 of 43 14:528 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -192,7 +192,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 43 aa:=integrate(log(x)/x^2,x) --R --R @@ -202,7 +202,7 @@ aa:=integrate(log(x)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 43 bb:=-log(x)/x-1/x --R --R - log(x) - 1 @@ -211,7 +211,7 @@ bb:=-log(x)/x-1/x --R Type: Expression Integer --E ---S 18 14:529 Schaums and Axiom agree +--S 18 of 43 14:529 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -227,7 +227,7 @@ $$ <<*>>= )clear all ---S 19 +--S 19 of 43 aa:=integrate(log(x)^2,x) --R --R @@ -236,7 +236,7 @@ aa:=integrate(log(x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 20 +--S 20 of 43 bb:=x*log(x)^2-2*x*log(x)+2*x --R --R 2 @@ -244,7 +244,7 @@ bb:=x*log(x)^2-2*x*log(x)+2*x --R Type: Expression Integer --E ---S 21 14:530 Schaums and Axiom agree +--S 21 of 43 14:530 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -260,7 +260,7 @@ $$ <<*>>= )clear all ---S 22 +--S 22 of 43 aa:=integrate(log(x)^n/x,x) --R --R @@ -271,7 +271,7 @@ aa:=integrate(log(x)^n/x,x) --R Type: Union(Expression Integer,...) --E ---S 23 +--S 23 of 43 bb:=log(x)^(n+1)/(n+1) --R --R n + 1 @@ -281,7 +281,7 @@ bb:=log(x)^(n+1)/(n+1) --R Type: Expression Integer --E ---S 24 +--S 24 of 43 cc:=aa-bb --R --R n log(log(x)) n + 1 @@ -291,7 +291,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 25 +--S 25 of 43 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -299,7 +299,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 26 +--S 26 of 43 dd:=explog cc --R --R n + 1 n @@ -309,7 +309,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 27 14:531 Schaums and Axiom agree +--S 27 of 43 14:531 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -325,7 +325,7 @@ $$ <<*>>= )clear all ---S 28 +--S 28 of 43 aa:=integrate(1/(x*log(x)),x) --R --R @@ -333,14 +333,14 @@ aa:=integrate(1/(x*log(x)),x) --R Type: Union(Expression Integer,...) --E ---S 29 +--S 29 of 43 bb:=log(log(x)) --R --R (2) log(log(x)) --R Type: Expression Integer --E ---S 30 14:532 Schaums and Axiom agree +--S 30 of 43 14:532 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -358,7 +358,7 @@ $$ <<*>>= )clear all ---S 31 14:533 Schaums and Axiom agree by definition +--S 31 of 43 14:533 Schaums and Axiom agree by definition aa:=integrate(1/log(x),x) --R --R @@ -376,7 +376,7 @@ $$ <<*>>= )clear all ---S 32 14:534 Axiom cannot compute this integral +--S 32 of 43 14:534 Axiom cannot compute this integral aa:=integrate(x^m/log(x),x) --R --R @@ -396,7 +396,7 @@ $$ <<*>>= )clear all ---S 33 14:535 Axiom cannot compute this integral +--S 33 of 43 14:535 Axiom cannot compute this integral aa:=integrate(log(x)^n,x) --R --R @@ -416,7 +416,7 @@ $$ <<*>>= )clear all ---S 34 14:536 Axiom cannot compute this integral +--S 34 of 43 14:536 Axiom cannot compute this integral aa:=integrate(x^m*log(x)^n,x) --R --R @@ -436,7 +436,7 @@ $$ <<*>>= )clear all ---S 35 +--S 35 of 43 aa:=integrate(log(x^2+a^2),x) --R --R @@ -446,7 +446,7 @@ aa:=integrate(log(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 36 +--S 36 of 43 bb:=x*log(x^2+a^2)-2*x+2*a*atan(x/a) --R --R 2 2 x @@ -455,7 +455,7 @@ bb:=x*log(x^2+a^2)-2*x+2*a*atan(x/a) --R Type: Expression Integer --E ---S 37 14:537 Schaums and Axiom agree +--S 37 of 43 14:537 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -471,7 +471,7 @@ $$ <<*>>= )clear all ---S 38 +--S 38 of 43 aa:=integrate(log(x^2-a^2),x) --R --R @@ -480,7 +480,7 @@ aa:=integrate(log(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 39 +--S 39 of 43 bb:=x*log(x^2-a^2)-2*x+a*log((x+a)/(x-a)) --R --R 2 2 x + a @@ -489,7 +489,7 @@ bb:=x*log(x^2-a^2)-2*x+a*log((x+a)/(x-a)) --R Type: Expression Integer --E ---S 40 +--S 40 of 43 cc:=aa-bb --R --R x + a @@ -498,7 +498,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 41 14:538 Schaums and Axiom agree +--S 41 of 43 14:538 Schaums and Axiom agree dd:=expandLog cc --R --R (4) 0 @@ -515,7 +515,7 @@ $$ <<*>>= )clear all ---S 42 +--S 42 of 43 aa:=integrate(x^m*log(x^2+a^2),x) --R --R @@ -528,7 +528,7 @@ aa:=integrate(x^m*log(x^2+a^2),x) )clear all ---S 43 14:539 Axiom cannot compute this integral +--S 43 of 43 14:539 Axiom cannot compute this integral aa:=integrate(x^m*log(x^2-a^2),x) --R --R diff --git a/src/input/schaum27.input.pamphlet b/src/input/schaum27.input.pamphlet index 68d33a3..3563060 100644 --- a/src/input/schaum27.input.pamphlet +++ b/src/input/schaum27.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 84 aa:=integrate(sinh(a*x),x) --R --R cosh(a x) @@ -27,7 +27,7 @@ aa:=integrate(sinh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 84 bb:=cosh(a*x)/a --R --R cosh(a x) @@ -36,7 +36,7 @@ bb:=cosh(a*x)/a --R Type: Expression Integer --E ---S 3 14:540 Schaums and Axiom agree +--S 3 of 84 14:540 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -52,7 +52,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 84 aa:=integrate(x*sinh(a*x),x) --R --R @@ -63,7 +63,7 @@ aa:=integrate(x*sinh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 84 bb:=(x*cosh(a*x))/a-sinh(a*x)/a^2 --R --R - sinh(a x) + a x cosh(a x) @@ -73,7 +73,7 @@ bb:=(x*cosh(a*x))/a-sinh(a*x)/a^2 --R Type: Expression Integer --E ---S 6 14:541 Schaums and Axiom agree +--S 6 of 84 14:541 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -89,7 +89,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 84 aa:=integrate(x^2*sinh(a*x),x) --R --R @@ -101,7 +101,7 @@ aa:=integrate(x^2*sinh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 84 bb:=(x^2/a+2/a^3)*cosh(a*x)-(2*x)/a^2*sinh(a*x) --R --R 2 2 @@ -112,7 +112,7 @@ bb:=(x^2/a+2/a^3)*cosh(a*x)-(2*x)/a^2*sinh(a*x) --R Type: Expression Integer --E ---S 9 14:542 Schaums and Axiom agree +--S 9 of 84 14:542 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -128,7 +128,7 @@ $$ <<*>>= )clear all ---S 10 14:543 Axiom cannot compute this integral +--S 10 of 84 14:543 Axiom cannot compute this integral aa:=integrate(sinh(a*x)/x,x) --R --R @@ -148,7 +148,7 @@ $$ <<*>>= )clear all ---S 11 14:544 Axiom cannot compute this integral +--S 11 of 84 14:544 Axiom cannot compute this integral aa:=integrate(sinh(a*x)/x^2,x) --R --R @@ -169,7 +169,7 @@ $$ <<*>>= )clear all ---S 12 +--S 12 of 84 aa:=integrate(1/sinh(a*x),x) --R --R @@ -179,7 +179,7 @@ aa:=integrate(1/sinh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 13 +--S 13 of 84 bb:=1/a*log(tanh(a*x)/2) --R --R tanh(a x) @@ -190,7 +190,7 @@ bb:=1/a*log(tanh(a*x)/2) --R Type: Expression Integer --E ---S 14 14:545 Axiom cannot simplify this expression +--S 14 of 84 14:545 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -214,7 +214,7 @@ $$ <<*>>= )clear all ---S 15 14:546 Axiom cannot compute this integral +--S 15 of 84 14:546 Axiom cannot compute this integral aa:=integrate(x/sinh(a*x),x) --R --R @@ -234,7 +234,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 84 aa:=integrate(sinh(a*x)^2,x) --R --R @@ -244,7 +244,7 @@ aa:=integrate(sinh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 84 bb:=(sinh(a*x)*cosh(a*x))/(2*a)-x/2 --R --R cosh(a x)sinh(a x) - a x @@ -253,7 +253,7 @@ bb:=(sinh(a*x)*cosh(a*x))/(2*a)-x/2 --R Type: Expression Integer --E ---S 18 14:547 Schaums and Axiom agree +--S 18 of 84 14:547 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -269,7 +269,7 @@ $$ <<*>>= )clear all ---S 19 +--S 19 of 84 aa:=integrate(x*sinh(a*x)^2,x) --R --R @@ -281,7 +281,7 @@ aa:=integrate(x*sinh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 20 +--S 20 of 84 bb:=(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)-x^2/4 --R --R 2 2 @@ -292,7 +292,7 @@ bb:=(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2)-x^2/4 --R Type: Expression Integer --E ---S 21 +--S 21 of 84 cc:=aa-bb --R --R (3) @@ -307,7 +307,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 22 +--S 22 of 84 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -316,7 +316,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 23 +--S 23 of 84 dd:=sinhsqrrule cc --R --R (5) @@ -328,7 +328,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 24 +--S 24 of 84 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -337,7 +337,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 25 +--S 25 of 84 ee:=coshsqrrule dd --R --R - x sinh(2a x) + 2x cosh(a x)sinh(a x) @@ -346,7 +346,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 26 +--S 26 of 84 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %K sinh(y + x) - %K sinh(y - x) @@ -355,7 +355,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 27 14:548 Schaums and Axiom agree +--S 27 of 84 14:548 Schaums and Axiom agree ff:=sinhcoshrule ee --R --R (9) 0 @@ -371,7 +371,7 @@ $$ <<*>>= )clear all ---S 28 +--S 28 of 84 aa:=integrate(1/sinh(a*x)^2,x) --R --R @@ -382,7 +382,7 @@ aa:=integrate(1/sinh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 29 +--S 29 of 84 bb:=-coth(a*x)/a --R --R coth(a x) @@ -391,7 +391,7 @@ bb:=-coth(a*x)/a --R Type: Expression Integer --E ---S 30 +--S 30 of 84 cc:=aa-bb --R --R (3) @@ -406,7 +406,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 31 +--S 31 of 84 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -415,7 +415,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 32 +--S 32 of 84 dd:=sinhsqrrule cc --R --R (5) @@ -427,7 +427,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 33 +--S 33 of 84 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -436,7 +436,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 34 +--S 34 of 84 ee:=coshsqrrule dd --R --R 2cosh(a x)coth(a x)sinh(a x) + (cosh(2a x) - 1)coth(a x) - 2 @@ -445,7 +445,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 35 +--S 35 of 84 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --I %B sinh(y + x) - %B sinh(y - x) --I (8) %B cosh(y)sinh(x) == ------------------------------- @@ -453,7 +453,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 36 +--S 36 of 84 ff:=sinhcoshrule ee --R --R coth(a x)sinh(2a x) + (cosh(2a x) - 1)coth(a x) - 2 @@ -462,7 +462,7 @@ ff:=sinhcoshrule ee --R Type: Expression Integer --E ---S 37 +--S 37 of 84 cothrule:=rule(coth(x) == cosh(x)/sinh(x)) --R --R cosh(x) @@ -471,7 +471,7 @@ cothrule:=rule(coth(x) == cosh(x)/sinh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 38 +--S 38 of 84 gg:=cothrule ff --R --R cosh(a x)sinh(2a x) - 2sinh(a x) + cosh(a x)cosh(2a x) - cosh(a x) @@ -480,7 +480,7 @@ gg:=cothrule ff --R Type: Expression Integer --E ---S 39 +--S 39 of 84 hh:=sinhcoshrule gg --R --R sinh(3a x) - 3sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x) @@ -489,7 +489,7 @@ hh:=sinhcoshrule gg --R Type: Expression Integer --E ---S 40 +--S 40 of 84 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R --I %M cosh(y + x) - %M cosh(y - x) @@ -498,7 +498,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 41 +--S 41 of 84 ii:=sinhsinhrule gg --R --R 2cosh(a x)sinh(2a x) - 4sinh(a x) + 2cosh(a x)cosh(2a x) - 2cosh(a x) @@ -507,7 +507,7 @@ ii:=sinhsinhrule gg --R Type: Expression Integer --E ---S 42 +--S 42 of 84 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R --I %N cosh(y + x) + %N cosh(y - x) @@ -516,7 +516,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 43 +--S 43 of 84 jj:=coshcoshrule ii --R --R 2cosh(a x)sinh(2a x) - 4sinh(a x) + cosh(3a x) - cosh(a x) @@ -525,7 +525,7 @@ jj:=coshcoshrule ii --R Type: Expression Integer --E ---S 44 14:549 Schaums and Axiom differ by a constant +--S 44 of 84 14:549 Schaums and Axiom differ by a constant kk:=sinhcoshrule jj --R --R 1 @@ -543,7 +543,7 @@ $$ <<*>>= )clear all ---S 45 +--S 45 of 84 aa:=integrate(sinh(a*x)*sinh(p*x),x) --R --R @@ -554,7 +554,7 @@ aa:=integrate(sinh(a*x)*sinh(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 46 +--S 46 of 84 bb:=(sinh(a+p)*x)/(2*(a+p))-(sinh(a-p)*x)/(2*(a-p)) --R --R (p - a)x sinh(p + a) + (- p - a)x sinh(p - a) @@ -564,7 +564,7 @@ bb:=(sinh(a+p)*x)/(2*(a+p))-(sinh(a-p)*x)/(2*(a-p)) --R Type: Expression Integer --E ---S 47 14:550 Axiom cannot simplify this expression +--S 47 of 84 14:550 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -593,7 +593,7 @@ $$ <<*>>= )clear all ---S 48 +--S 48 of 84 aa:=integrate(sinh(a*x)*sin(p*x),x) --R --R @@ -611,7 +611,7 @@ aa:=integrate(sinh(a*x)*sin(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 49 +--S 49 of 84 bb:=(a*cosh(a*x)*sin(p*x)-p*sinh(a*x)*cos(p*x))/(a^2+p^2) --R --R - p cos(p x)sinh(a x) + a cosh(a x)sin(p x) @@ -621,7 +621,7 @@ bb:=(a*cosh(a*x)*sin(p*x)-p*sinh(a*x)*cos(p*x))/(a^2+p^2) --R Type: Expression Integer --E ---S 50 +--S 50 of 84 cc:=aa-bb --R --R (3) @@ -636,7 +636,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 51 +--S 51 of 84 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -645,7 +645,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 52 +--S 52 of 84 dd:=sinhsqrrule cc --R --R (5) @@ -660,7 +660,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 53 +--S 53 of 84 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -669,7 +669,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 54 14:551 Schaums and Axiom agree +--S 54 of 84 14:551 Schaums and Axiom agree ee:=coshsqrrule dd --R --R (7) 0 @@ -685,7 +685,7 @@ $$ <<*>>= )clear all ---S 55 +--S 55 of 84 aa:=integrate(sinh(a*x)*cos(p*x),x) --R --R @@ -703,7 +703,7 @@ aa:=integrate(sinh(a*x)*cos(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 56 +--S 56 of 84 bb:=(a*cosh(a*x)*cos(p*x)+p*sinh(a*x)*sin(p*x))/(a^2+p^2) --R --R p sin(p x)sinh(a x) + a cos(p x)cosh(a x) @@ -713,7 +713,7 @@ bb:=(a*cosh(a*x)*cos(p*x)+p*sinh(a*x)*sin(p*x))/(a^2+p^2) --R Type: Expression Integer --E ---S 57 +--S 57 of 84 cc:=aa-bb --R --R (3) @@ -728,7 +728,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 58 +--S 58 of 84 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -737,7 +737,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 59 +--S 59 of 84 dd:=sinhsqrrule cc --R --R (5) @@ -752,7 +752,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 60 +--S 60 of 84 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -761,7 +761,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 61 14:552 Schaums and Axiom agree +--S 61 of 84 14:552 Schaums and Axiom agree ee:=coshsqrrule dd --R --R (7) 0 @@ -778,7 +778,7 @@ $$ <<*>>= )clear all ---S 62 +--S 62 of 84 aa:=integrate(1/(p+q*sinh(a*x)),x) --R --R @@ -808,7 +808,7 @@ aa:=integrate(1/(p+q*sinh(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 63 +--S 63 of 84 bb:=1/(a*sqrt(p^2+q^2))*log((q*%e^(a*x)+p-sqrt(p^2+q^2))/(q*%e^(a*x)+p+sqrt(p^2+q^2))) --R --R +-------+ @@ -825,7 +825,7 @@ bb:=1/(a*sqrt(p^2+q^2))*log((q*%e^(a*x)+p-sqrt(p^2+q^2))/(q*%e^(a*x)+p+sqrt(p^2+ --R Type: Expression Integer --E ---S 64 14:553 Axiom cannot simplify this expression +--S 64 of 84 14:553 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -872,7 +872,7 @@ $$ <<*>>= )clear all ---S 65 +--S 65 of 84 aa:=integrate(1/(p*q*sinh(a*x))^2,x) --R --R @@ -884,7 +884,7 @@ aa:=integrate(1/(p*q*sinh(a*x))^2,x) --R Type: Union(Expression Integer,...) --E ---S 66 +--S 66 of 84 t1:=integrate(1/(p+q*sinh(a*x)),x) --R --R (2) @@ -913,7 +913,7 @@ t1:=integrate(1/(p+q*sinh(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 67 +--S 67 of 84 bb:=(-q*cosh(a*x))/(a*(p^2+q^2)*(p+q*sinh(a*x)))+p/(p^2+q^2)*t1 --R --R (3) @@ -949,7 +949,7 @@ bb:=(-q*cosh(a*x))/(a*(p^2+q^2)*(p+q*sinh(a*x)))+p/(p^2+q^2)*t1 --R Type: Expression Integer --E ---S 68 14:554 Axiom cannot simplify this expression +--S 68 of 84 14:554 Axiom cannot simplify this expression cc:=aa-bb --R --R (4) @@ -1033,7 +1033,7 @@ $$ <<*>>= )clear all ---S 69 +--S 69 of 84 aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x) --R --R @@ -1097,7 +1097,7 @@ aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 70 +--S 70 of 84 bb1:=1/(a*p*sqrt(q^2-p^2))*atan((sqrt(q^2-p^2)*tanh(a*x))/p) --R --R +-------+ @@ -1112,7 +1112,7 @@ bb1:=1/(a*p*sqrt(q^2-p^2))*atan((sqrt(q^2-p^2)*tanh(a*x))/p) --R Type: Expression Integer --E ---S 71 +--S 71 of 84 bb2:=1/(2*a*p*sqrt(p^2-q^2))*log((p+sqrt(p^2-q^2)*tanh(a*x))/(p-sqrt(p^2-q^2)*tanh(a*x))) --R --R +---------+ @@ -1129,7 +1129,7 @@ bb2:=1/(2*a*p*sqrt(p^2-q^2))*log((p+sqrt(p^2-q^2)*tanh(a*x))/(p-sqrt(p^2-q^2)*ta --R Type: Expression Integer --E ---S 72 +--S 72 of 84 cc1:=aa.1-bb1 --R --R (4) @@ -1184,7 +1184,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 73 +--S 73 of 84 cc2:=aa.2-bb1 --R --R (5) @@ -1211,7 +1211,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 74 +--S 74 of 84 cc3:=aa.2-bb1 --R --R (6) @@ -1238,7 +1238,7 @@ cc3:=aa.2-bb1 --R Type: Expression Integer --E ---S 75 14:555 Axiom cannot simplify this expression +--S 75 of 84 14:555 Axiom cannot simplify this expression cc4:=aa.2-bb2 --R --R (7) @@ -1281,7 +1281,7 @@ $$ <<*>>= )clear all ---S 76 +--S 76 of 84 aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x) --R --R @@ -1345,7 +1345,7 @@ aa:=integrate(1/(p^2+q^2*sinh(a*x)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 77 +--S 77 of 84 bb:=1/(2*a*p*sqrt(p^2+q^2))*log((p+sqrt(p^2+q^2)*tanh(a*x))/(p-sqrt(p^2+q^2)*tanh(a*x))) --R --R +-------+ @@ -1362,7 +1362,7 @@ bb:=1/(2*a*p*sqrt(p^2+q^2))*log((p+sqrt(p^2+q^2)*tanh(a*x))/(p-sqrt(p^2+q^2)*tan --R Type: Expression Integer --E ---S 78 +--S 78 of 84 cc1:=aa.1-bb --R --R (3) @@ -1419,7 +1419,7 @@ cc1:=aa.1-bb --R Type: Expression Integer --E ---S 79 14:556 Axiom cannot simplify this expression +--S 79 of 84 14:556 Axiom cannot simplify this expression cc2:=aa.2-bb --R --R (4) @@ -1461,7 +1461,7 @@ $$ <<*>>= )clear all ---S 80 14:557 Axiom cannot compute this integral +--S 80 of 84 14:557 Axiom cannot compute this integral aa:=integrate(x^m*sinh(a*x),x) --R --R @@ -1481,7 +1481,7 @@ $$ <<*>>= )clear all ---S 81 14:558 Axiom cannot compute this integral +--S 81 of 84 14:558 Axiom cannot compute this integral aa:=integrate(sinh(a*x)^n,x) --R --R @@ -1501,7 +1501,7 @@ $$ <<*>>= )clear all ---S 82 14:559 Axiom cannot compute this integral +--S 82 of 84 14:559 Axiom cannot compute this integral aa:=integrate(sinh(a*x)/x^n,x) --R --R x @@ -1523,7 +1523,7 @@ $$ <<*>>= )clear all ---S 83 14:560 Axiom cannot compute this integral +--S 83 of 84 14:560 Axiom cannot compute this integral aa:=integrate(1/sinh(a*x)^n,x) --R --R @@ -1546,7 +1546,7 @@ $$ <<*>>= )clear all ---S 84 14:561 Axiom cannot compute this integral +--S 84 of 84 14:561 Axiom cannot compute this integral aa:=integrate(x/sinh(a*x)^n,x) --R --R diff --git a/src/input/schaum28.input.pamphlet b/src/input/schaum28.input.pamphlet index 49efb0e..0015905 100644 --- a/src/input/schaum28.input.pamphlet +++ b/src/input/schaum28.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 139 aa:=integrate(cosh(a*x),x) --R --R @@ -28,7 +28,7 @@ aa:=integrate(cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 139 bb:=sinh(a*x)/a --R --R sinh(a x) @@ -37,7 +37,7 @@ bb:=sinh(a*x)/a --R Type: Expression Integer --E ---S 3 14:562 Schaums and Axiom agree +--S 3 of 139 14:562 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -53,7 +53,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 139 aa:=integrate(x*cosh(a*x),x) --R --R @@ -64,7 +64,7 @@ aa:=integrate(x*cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 139 bb:=(x*sinh(a*x))/a-cosh(a*x)/a^2 --R --R a x sinh(a x) - cosh(a x) @@ -74,7 +74,7 @@ bb:=(x*sinh(a*x))/a-cosh(a*x)/a^2 --R Type: Expression Integer --E ---S 6 14:563 Schaums and Axiom agree +--S 6 of 139 14:563 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -90,7 +90,7 @@ $$ <<*>>= )clear all ---S 7 +--S 7 of 139 aa:=integrate(x^2*cosh(a*x),x) --R --R @@ -102,7 +102,7 @@ aa:=integrate(x^2*cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 139 bb:=-(2*x*cosh(a*x))/a^2+(x^2/a+2/a^3)*sinh(a*x) --R --R 2 2 @@ -113,7 +113,7 @@ bb:=-(2*x*cosh(a*x))/a^2+(x^2/a+2/a^3)*sinh(a*x) --R Type: Expression Integer --E ---S 9 14:564 Schaums and Axiom agree +--S 9 of 139 14:564 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -131,7 +131,7 @@ $$ <<*>>= )clear all ---S 10 14:565 Axiom cannot compute this integral +--S 10 of 139 14:565 Axiom cannot compute this integral aa:=integrate(cosh(a*x)/x,x) --R --R @@ -151,7 +151,7 @@ $$ <<*>>= )clear all ---S 11 14:566 Axiom cannot compute this integral +--S 11 of 139 14:566 Axiom cannot compute this integral aa:=integrate(cosh(a*x)/x^2,x) --R --R @@ -172,7 +172,7 @@ $$ <<*>>= )clear all ---S 12 +--S 12 of 139 aa:=integrate(1/cosh(a*x),x) --R --R @@ -182,7 +182,7 @@ aa:=integrate(1/cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 13 +--S 13 of 139 bb:=2/a*atan(%e^(a*x)) --R --R a x @@ -192,7 +192,7 @@ bb:=2/a*atan(%e^(a*x)) --R Type: Expression Integer --E ---S 14 +--S 14 of 139 cc:=aa-bb --R --R a x @@ -202,7 +202,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 15 14:567 Schaums and Axiom agree +--S 15 of 139 14:567 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -219,7 +219,7 @@ $$ <<*>>= )clear all ---S 16 14:568 Axiom cannot compute this integral +--S 16 of 139 14:568 Axiom cannot compute this integral aa:=integrate(x/cosh(a*x),x) --R --R @@ -243,7 +243,7 @@ $$ <<*>>= )clear all ---S 17 +--S 17 of 139 aa:=integrate(cosh(a*x)^2,x) --R --R @@ -253,7 +253,7 @@ aa:=integrate(cosh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 18 +--S 18 of 139 bb:=x/2+(sinh(a*x)*cosh(a*x))/(2*a) --R --R cosh(a x)sinh(a x) + a x @@ -262,7 +262,7 @@ bb:=x/2+(sinh(a*x)*cosh(a*x))/(2*a) --R Type: Expression Integer --E ---S 19 14:569 Schaums and Axiom agree +--S 19 of 139 14:569 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -279,7 +279,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 139 aa:=integrate(x*cosh(a*x)^2,x) --R --R @@ -291,7 +291,7 @@ aa:=integrate(x*cosh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 139 bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2) --R --R 2 2 @@ -302,7 +302,7 @@ bb:=x^2/4+(x*sinh(2*a*x))/(4*a)-cosh(2*a*x)/(8*a^2) --R Type: Expression Integer --E ---S 22 +--S 22 of 139 cc:=aa-bb --R --R (3) @@ -317,7 +317,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 23 +--S 23 of 139 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -326,7 +326,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 24 +--S 24 of 139 dd:=sinhsqrrule cc --R --R (5) @@ -338,7 +338,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 25 +--S 25 of 139 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -347,7 +347,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 26 +--S 26 of 139 ee:=coshsqrrule dd --R --R - x sinh(2a x) + 2x cosh(a x)sinh(a x) @@ -356,7 +356,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 27 +--S 27 of 139 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %S sinh(y + x) - %S sinh(y - x) @@ -365,7 +365,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 28 14:570 Schaums and Axiom agree +--S 28 of 139 14:570 Schaums and Axiom agree ff:=sinhcoshrule ee --R --R (9) 0 @@ -381,7 +381,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 139 aa:=integrate(1/cosh(a*x)^2,x) --R --R @@ -392,7 +392,7 @@ aa:=integrate(1/cosh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 139 bb:=tanh(a*x)/a --R --R tanh(a x) @@ -401,7 +401,7 @@ bb:=tanh(a*x)/a --R Type: Expression Integer --E ---S 31 +--S 31 of 139 cc:=aa-bb --R --R 2 2 @@ -412,7 +412,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 14:571 Schaums and Axiom differ by a constant +--S 32 of 139 14:571 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 1 @@ -430,7 +430,7 @@ $$ <<*>>= )clear all ---S 33 +--S 33 of 139 aa:=integrate(cosh(a*x)*cosh(p*x),x) --R --R @@ -441,7 +441,7 @@ aa:=integrate(cosh(a*x)*cosh(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 34 +--S 34 of 139 bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p)) --R --R (p - a)x sinh(p + a) + (p + a)x sinh(p - a) @@ -451,7 +451,7 @@ bb:=(sinh(a-p)*x)/(2*(a-p))+(sinh(a+p)*x)/(2*(a+p)) --R Type: Expression Integer --E ---S 35 +--S 35 of 139 cc:=aa-bb --R --R (3) @@ -471,7 +471,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 36 +--S 36 of 139 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -480,7 +480,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 37 +--S 37 of 139 dd:=sinhsqrrule cc --R --R (5) @@ -497,7 +497,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 38 +--S 38 of 139 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -506,7 +506,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 39 +--S 39 of 139 ee:=coshsqrrule dd --R --R (7) @@ -519,7 +519,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 40 +--S 40 of 139 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %V sinh(y + x) - %V sinh(y - x) @@ -528,7 +528,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 41 14:572 Axiom cannot simplify this expression +--S 41 of 139 14:572 Axiom cannot simplify this expression ff:=sinhcoshrule ee --R --R (9) @@ -550,7 +550,7 @@ $$ <<*>>= )clear all ---S 42 +--S 42 of 139 aa:=integrate(cosh(a*x)*sin(p*x),x) --R --R @@ -568,7 +568,7 @@ aa:=integrate(cosh(a*x)*sin(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 43 +--S 43 of 139 bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2) --R --R a sin(p x)sinh(a x) - p cos(p x)cosh(a x) @@ -578,7 +578,7 @@ bb:=(a*sinh(a*x)*sin(p*x)-p*cosh(a*x)*cos(p*x))/(a^2+p^2) --R Type: Expression Integer --E ---S 44 +--S 44 of 139 cc:=aa-bb --R --R (3) @@ -593,7 +593,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 45 +--S 45 of 139 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -602,7 +602,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 46 +--S 46 of 139 dd:=coshsqrrule cc --R --R (5) @@ -616,7 +616,7 @@ dd:=coshsqrrule cc --R Type: Expression Integer --E ---S 47 +--S 47 of 139 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -625,7 +625,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 48 14:573 Schaums and Axiom agree +--S 48 of 139 14:573 Schaums and Axiom agree ee:=sinhsqrrule dd --R --R (7) 0 @@ -641,7 +641,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 139 aa:=integrate(cosh(a*x)*cos(p*x),x) --R --R @@ -659,7 +659,7 @@ aa:=integrate(cosh(a*x)*cos(p*x),x) --R Type: Union(Expression Integer,...) --E ---S 50 +--S 50 of 139 bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2) --R --R a cos(p x)sinh(a x) + p cosh(a x)sin(p x) @@ -669,7 +669,7 @@ bb:=(a*sinh(a*x)*cos(p*x)+p*cosh(a*x)*sin(p*x))/(a^2+p^2) --R Type: Expression Integer --E ---S 51 +--S 51 of 139 cc:=aa-bb --R --R (3) @@ -684,7 +684,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 52 +--S 52 of 139 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -693,7 +693,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 53 +--S 53 of 139 dd:=coshsqrrule cc --R --R (5) @@ -707,7 +707,7 @@ dd:=coshsqrrule cc --R Type: Expression Integer --E ---S 54 +--S 54 of 139 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -716,7 +716,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 55 14:574 Schaums and Axiom agree +--S 55 of 139 14:574 Schaums and Axiom agree ee:=sinhsqrrule dd --R --R (7) 0 @@ -732,7 +732,7 @@ $$ <<*>>= )clear all ---S 56 +--S 56 of 139 aa:=integrate(1/(cosh(a*x)+1),x) --R --R @@ -742,7 +742,7 @@ aa:=integrate(1/(cosh(a*x)+1),x) --R Type: Union(Expression Integer,...) --E ---S 57 +--S 57 of 139 bb:=1/a*tanh((a*x)/2) --R --R a x @@ -753,7 +753,7 @@ bb:=1/a*tanh((a*x)/2) --R Type: Expression Integer --E ---S 58 +--S 58 of 139 cc:=aa-bb --R --R a x @@ -764,7 +764,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 59 +--S 59 of 139 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R --R sinh(x) @@ -773,7 +773,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 60 +--S 60 of 139 dd:=tanhrule cc --R --R a x a x a x @@ -786,7 +786,7 @@ dd:=tanhrule cc --R Type: Expression Integer --E ---S 61 +--S 61 of 139 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %BC sinh(y + x) - %BC sinh(y - x) @@ -795,7 +795,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 62 +--S 62 of 139 ee:=sinhcoshrule dd --R --R 3a x a x a x a x @@ -808,7 +808,7 @@ ee:=sinhcoshrule dd --R Type: Expression Integer --E ---S 63 +--S 63 of 139 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R --I %BD sinh(y + x) - %BD sinh(y - x) @@ -817,7 +817,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 64 +--S 64 of 139 ff:=sinhsinhrule ee --R --R 3a x a x 3a x a x @@ -830,7 +830,7 @@ ff:=sinhsinhrule ee --R Type: Expression Integer --E ---S 65 +--S 65 of 139 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R --I %BC cosh(y + x) + %BC cosh(y - x) @@ -839,7 +839,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 66 14:575 Schaums and Axiom differ by a constant +--S 66 of 139 14:575 Schaums and Axiom differ by a constant gg:=coshcoshrule ff --R --R 1 @@ -857,7 +857,7 @@ $$ <<*>>= )clear all ---S 67 +--S 67 of 139 aa:=integrate(1/(cosh(a*x)-1),x) --R --R @@ -867,7 +867,7 @@ aa:=integrate(1/(cosh(a*x)-1),x) --R Type: Union(Expression Integer,...) --E ---S 68 +--S 68 of 139 bb:=-1/a*coth((a*x)/2) --R --R a x @@ -878,7 +878,7 @@ bb:=-1/a*coth((a*x)/2) --R Type: Expression Integer --E ---S 69 +--S 69 of 139 cc:=aa-bb --R --R a x a x @@ -889,7 +889,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 70 +--S 70 of 139 cothrule:=rule(coth(x) == cosh(x)/sinh(x)) --R --R cosh(x) @@ -898,7 +898,7 @@ cothrule:=rule(coth(x) == cosh(x)/sinh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 71 +--S 71 of 139 dd:=cothrule cc --R --R a x a x a x a x @@ -911,7 +911,7 @@ dd:=cothrule cc --R Type: Expression Integer --E ---S 72 +--S 72 of 139 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %BD sinh(y + x) - %BD sinh(y - x) @@ -920,7 +920,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 73 +--S 73 of 139 ee:=sinhcoshrule dd --R --R 3a x a x a x a x @@ -933,7 +933,7 @@ ee:=sinhcoshrule dd --R Type: Expression Integer --E ---S 74 +--S 74 of 139 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R --I %BE cosh(y + x) - %BE cosh(y - x) @@ -942,7 +942,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 75 +--S 75 of 139 ff:=sinhsinhrule ee --R --R 3a x a x a x a x @@ -955,7 +955,7 @@ ff:=sinhsinhrule ee --R Type: Expression Integer --E ---S 76 +--S 76 of 139 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R --I %BF cosh(y + x) + %BF cosh(y - x) @@ -964,7 +964,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 77 14:576 Schaums and Axiom differ by a constant +--S 77 of 139 14:576 Schaums and Axiom differ by a constant gg:=coshcoshrule ff --R --R 1 @@ -982,7 +982,7 @@ $$ <<*>>= )clear all ---S 78 +--S 78 of 139 aa:=integrate(x/(cosh(a*x)+1),x) --R --R @@ -996,7 +996,7 @@ aa:=integrate(x/(cosh(a*x)+1),x) --R Type: Union(Expression Integer,...) --E ---S 79 +--S 79 of 139 bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2)) --R --R a x a x @@ -1008,7 +1008,7 @@ bb:=x/a*tanh((a*x)/2)-2/a^2*log(cosh((a*x)/2)) --R Type: Expression Integer --E ---S 80 +--S 80 of 139 cc:=aa-bb --R --R (3) @@ -1029,7 +1029,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 81 +--S 81 of 139 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R --R sinh(x) @@ -1038,7 +1038,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 82 +--S 82 of 139 dd:=tanhrule cc --R --R (5) @@ -1066,7 +1066,7 @@ dd:=tanhrule cc --R Type: Expression Integer --E ---S 83 +--S 83 of 139 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R --I %BG cosh(y + x) + %BG cosh(y - x) @@ -1075,7 +1075,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 84 +--S 84 of 139 ee:=coshcoshrule dd --R --R (7) @@ -1103,7 +1103,7 @@ ee:=coshcoshrule dd --R Type: Expression Integer --E ---S 85 +--S 85 of 139 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %BH sinh(y + x) - %BH sinh(y - x) @@ -1112,7 +1112,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 86 +--S 86 of 139 ff:=sinhcoshrule ee --R --R (9) @@ -1140,7 +1140,7 @@ ff:=sinhcoshrule ee --R Type: Expression Integer --E ---S 87 +--S 87 of 139 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R --I %BI cosh(y + x) - %BI cosh(y - x) @@ -1149,7 +1149,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 88 +--S 88 of 139 gg:=sinhsinhrule ff --R --R a x @@ -1161,7 +1161,7 @@ gg:=sinhsinhrule ff --R Type: Expression Integer --E ---S 89 14:577 Schaums and Axiom differ by a constant +--S 89 of 139 14:577 Schaums and Axiom differ by a constant complexNormalize gg --R --R 2log(2) @@ -1180,7 +1180,7 @@ $$ <<*>>= )clear all ---S 90 +--S 90 of 139 aa:=integrate(x/(cosh(a*x)-1),x) --R --R @@ -1194,7 +1194,7 @@ aa:=integrate(x/(cosh(a*x)-1),x) --R Type: Union(Expression Integer,...) --E ---S 91 +--S 91 of 139 bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2)) --R --R a x a x @@ -1206,7 +1206,7 @@ bb:=-x/a*coth((a*x)/2)+2/a^2*log(sinh((a*x)/2)) --R Type: Expression Integer --E ---S 92 +--S 92 of 139 cc:=aa-bb --R --R (3) @@ -1227,7 +1227,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 93 +--S 93 of 139 cothrule:=rule(coth(x) == cosh(x)/sinh(x)) --R --R cosh(x) @@ -1236,7 +1236,7 @@ cothrule:=rule(coth(x) == cosh(x)/sinh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 94 +--S 94 of 139 dd:=cothrule cc --R --R (5) @@ -1264,7 +1264,7 @@ dd:=cothrule cc --R Type: Expression Integer --E ---S 95 +--S 95 of 139 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %BJ sinh(y + x) - %BJ sinh(y - x) @@ -1273,7 +1273,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 96 +--S 96 of 139 ee:=sinhcoshrule dd --R --R (7) @@ -1301,7 +1301,7 @@ ee:=sinhcoshrule dd --R Type: Expression Integer --E ---S 97 +--S 97 of 139 sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R --I %BK cosh(y + x) - %BK cosh(y - x) @@ -1310,7 +1310,7 @@ sinhsinhrule:=rule(sinh(x)*sinh(y)==1/2*(cosh(x+y)-cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 98 +--S 98 of 139 ff:=sinhsinhrule ee --R --R (9) @@ -1338,7 +1338,7 @@ ff:=sinhsinhrule ee --R Type: Expression Integer --E ---S 99 +--S 99 of 139 coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R --I %BL cosh(y + x) + %BL cosh(y - x) @@ -1347,7 +1347,7 @@ coshcoshrule:=rule(cosh(x)*cosh(y)==1/2*(cosh(x+y)+cosh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 100 +--S 100 of 139 gg:=coshcoshrule ff --R --R a x @@ -1359,7 +1359,7 @@ gg:=coshcoshrule ff --R Type: Expression Integer --E ---S 101 14:578 Schaums and Axiom differ by a constant +--S 101 of 139 14:578 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R 2log(2) @@ -1378,7 +1378,7 @@ $$ <<*>>= )clear all ---S 102 +--S 102 of 139 aa:=integrate(1/(cosh(a*x)+1)^2,x) --R --R @@ -1396,7 +1396,7 @@ aa:=integrate(1/(cosh(a*x)+1)^2,x) --R Type: Union(Expression Integer,...) --E ---S 103 +--S 103 of 139 bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3 --R --R a x 3 a x @@ -1407,7 +1407,7 @@ bb:=1/(2*a)*tanh((a*x)/2)-1/(6*a)*tanh((a*x)/2)^3 --R Type: Expression Integer --E ---S 104 14:579 Axiom cannot compute this integral +--S 104 of 139 14:579 Axiom cannot compute this integral cc:=aa-bb --R --R (3) @@ -1458,7 +1458,7 @@ $$ <<*>>= )clear all ---S 105 +--S 105 of 139 aa:=integrate(1/(cosh(a*x)-1)^2,x) --R --R @@ -1476,7 +1476,7 @@ aa:=integrate(1/(cosh(a*x)-1)^2,x) --R Type: Union(Expression Integer,...) --E ---S 106 +--S 106 of 139 bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3 --R --R a x 3 a x @@ -1487,7 +1487,7 @@ bb:=1/(2*a)*coth((a*x)/2)-1/(6*a)*coth((a*x)/2)^3 --R Type: Expression Integer --E ---S 107 14:580 Axiom cannot simplify this expression +--S 107 of 139 14:580 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -1546,7 +1546,7 @@ $$ <<*>>= )clear all ---S 108 +--S 108 of 139 aa:=integrate(1/(p+q*cosh(a*x)),x) --R --R @@ -1588,7 +1588,7 @@ aa:=integrate(1/(p+q*cosh(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 109 +--S 109 of 139 bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2)) --R --R a x @@ -1604,7 +1604,7 @@ bb1:=2/(a*sqrt(q^2-p^2))*atan((q*%e^(a*x)+p)/sqrt(q^2-p^2)) --R Type: Expression Integer --E ---S 110 +--S 110 of 139 bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2-q^2))) --R --R +---------+ @@ -1621,7 +1621,7 @@ bb2:=1/(a*sqrt(p^2-q^2))*log((q*%e^(a*x)+p-sqrt(p^2-q^2))/(q*%e^(a*x)+p+sqrt(p^2 --R Type: Expression Integer --E ---S 111 +--S 111 of 139 cc1:=aa.1-bb1 --R --R (4) @@ -1661,7 +1661,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 112 +--S 112 of 139 cc2:=aa.2-bb1 --R --R +-------+ @@ -1678,7 +1678,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 113 +--S 113 of 139 cc3:=aa.1-bb2 --R --R (6) @@ -1715,7 +1715,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 114 14:581 Axiom cannot simplify this expression +--S 114 of 139 14:581 Axiom cannot simplify this expression cc4:=aa.2-bb2 --R --R (7) @@ -1751,7 +1751,7 @@ $$ <<*>>= )clear all ---S 115 +--S 115 of 139 aa:=integrate(1/(p+q*cosh(a*x))^2,x) --R --R @@ -1833,7 +1833,7 @@ aa:=integrate(1/(p+q*cosh(a*x))^2,x) --R Type: Union(List Expression Integer,...) --E ---S 116 +--S 116 of 139 t1:=integrate(1/(p+q*cosh(a*x)),x) --R --R (2) @@ -1874,7 +1874,7 @@ t1:=integrate(1/(p+q*cosh(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 117 +--S 117 of 139 bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1 --R --R (3) @@ -1910,7 +1910,7 @@ bb1:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.1 --R Type: Expression Integer --E ---S 118 +--S 118 of 139 bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2 --R --R (4) @@ -1931,7 +1931,7 @@ bb2:=(q*sinh(a*x))/(a*(q^2-p^2)*(p+q*cosh(a*x)))-p/(q^2-p^2)*t1.2 --R Type: Expression Integer --E ---S 119 +--S 119 of 139 cc1:=aa.1-bb1 --R --R (5) @@ -2027,7 +2027,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 120 +--S 120 of 139 cc2:=aa.2-bb1 --R --R (6) @@ -2115,7 +2115,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 121 +--S 121 of 139 cc3:=aa.1-bb2 --R --R (7) @@ -2203,7 +2203,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 122 14:582 Axiom cannot simplify this expression +--S 122 of 139 14:582 Axiom cannot simplify this expression cc4:=aa.2-bb2 --R --R (8) @@ -2253,7 +2253,7 @@ $$ <<*>>= )clear all ---S 123 +--S 123 of 139 aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x) --R --R @@ -2321,7 +2321,7 @@ aa:=integrate(1/(p^2-q^2*cosh(a*x)^2),x) --R Type: Union(List Expression Integer,...) --E ---S 124 +--S 124 of 139 bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p^2-q^2))) --R --R +---------+ @@ -2338,7 +2338,7 @@ bb1:=1/(2*a*p*sqrt(p^2-q^2))*log((p*tanh(a*x)+sqrt(p^2-q^2))/(p*tanh(a*x)-sqrt(p --R Type: Expression Integer --E ---S 125 +--S 125 of 139 bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2)) --R --R p tanh(a x) @@ -2353,7 +2353,7 @@ bb2:=-1/(a*p*sqrt(q^2-p^2))*atan((p*tanh(a*x))/sqrt(q^2-p^2)) --R Type: Expression Integer --E ---S 126 +--S 126 of 139 cc1:=aa.1-bb1 --R --R (4) @@ -2406,7 +2406,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 127 +--S 127 of 139 cc2:=aa.2-bb1 --R --R (5) @@ -2443,7 +2443,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 128 +--S 128 of 139 cc3:=aa.1-bb2 --R --R (6) @@ -2502,7 +2502,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 129 14:583 Axiom cannot simplify this expression +--S 129 of 139 14:583 Axiom cannot simplify this expression cc4:=aa.2-bb2 --R --R (7) @@ -2552,7 +2552,7 @@ $$ <<*>>= )clear all ---S 130 +--S 130 of 139 aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x) --R --R @@ -2598,7 +2598,7 @@ aa:=integrate(1/(p^2+q^2*cosh(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 131 +--S 131 of 139 bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p^2+q^2))) --R --R +-------+ @@ -2615,7 +2615,7 @@ bb1:=1/(2*a*p*sqrt(p^2+q^2))*log((p*tanh(a*x)+sqrt(p^2+q^2))/(p*tanh(a*x)-sqrt(p --R Type: Expression Integer --E ---S 132 +--S 132 of 139 bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2)) --R --R p tanh(a x) @@ -2630,7 +2630,7 @@ bb2:=1/(a*p*sqrt(p^2+q^2))*atan((p*tanh(a*x))/sqrt(p^2+q^2)) --R Type: Expression Integer --E ---S 133 +--S 133 of 139 cc1:=aa-bb1 --R --R (4) @@ -2683,7 +2683,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 134 14:584 Axiom cannot simplify this expression +--S 134 of 139 14:584 Axiom cannot simplify this expression cc2:=aa-bb2 --R --R (5) @@ -2743,7 +2743,7 @@ $$ <<*>>= )clear all ---S 135 14:585 Axiom cannot compute this integral +--S 135 of 139 14:585 Axiom cannot compute this integral aa:=integrate(x^m*cosh(a*x),x) --R --R @@ -2763,7 +2763,7 @@ $$ <<*>>= )clear all ---S 136 14:586 Axiom cannot compute this integral +--S 136 of 139 14:586 Axiom cannot compute this integral aa:=integrate(cosh(a*x)^n,x) --R --R @@ -2784,7 +2784,7 @@ $$ <<*>>= )clear all ---S 137 14:587 Axiom cannot compute this integral +--S 137 of 139 14:587 Axiom cannot compute this integral aa:=integrate(cosh(a*x)/x^n,x) --R --R @@ -2806,7 +2806,7 @@ $$ <<*>>= )clear all ---S 138 14:588 Axiom cannot compute this integral +--S 138 of 139 14:588 Axiom cannot compute this integral aa:=integrate(1/cosh(a*x)^n,x) --R --R @@ -2829,7 +2829,7 @@ $$ <<*>>= )clear all ---S 139 14:589 Axiom cannot compute this integral +--S 139 of 139 14:589 Axiom cannot compute this integral aa:=integrate(1/cosh(a*x)^n,x) --R --R diff --git a/src/input/schaum29.input.pamphlet b/src/input/schaum29.input.pamphlet index 9c79630..559e612 100644 --- a/src/input/schaum29.input.pamphlet +++ b/src/input/schaum29.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 81 aa:=integrate(sinh(a*x)*cosh(a*x),x) --R --R @@ -29,7 +29,7 @@ aa:=integrate(sinh(a*x)*cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 81 bb:=sinh(a*x)^2/(2*a) --R --R 2 @@ -39,7 +39,7 @@ bb:=sinh(a*x)^2/(2*a) --R Type: Expression Integer --E ---S 3 +--S 3 of 81 cc:=aa-bb --R --R 2 2 @@ -49,7 +49,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 81 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -58,7 +58,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 +--S 5 of 81 dd:=sinhsqrrule cc --R --R 2 @@ -68,7 +68,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 6 +--S 6 of 81 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -77,7 +77,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 7 14:590 Schaums and Axiom differ by a constant +--S 7 of 81 14:590 Schaums and Axiom differ by a constant ee:=coshsqrrule dd --R --R 1 @@ -95,7 +95,7 @@ $$ <<*>>= )clear all ---S 8 +--S 8 of 81 aa:=integrate(sinh(p*x)*cosh(q*x),x) --R --R @@ -106,7 +106,7 @@ aa:=integrate(sinh(p*x)*cosh(q*x),x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 81 bb:=(cosh(p+q)*x)/(2*(p+q))+(cosh(p-q)*x)/(2*(p-q)) --R --R (q - p)x cosh(q + p) + (- q - p)x cosh(q - p) @@ -116,7 +116,7 @@ bb:=(cosh(p+q)*x)/(2*(p+q))+(cosh(p-q)*x)/(2*(p-q)) --R Type: Expression Integer --E ---S 10 14:591 Axiom cannot simplify this expression +--S 10 of 81 14:591 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -144,7 +144,7 @@ $$ <<*>>= )clear all ---S 11 +--S 11 of 81 aa:=integrate(sinh(a*x)^n*cosh(a*x),x) --R --R @@ -155,7 +155,7 @@ aa:=integrate(sinh(a*x)^n*cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 12 +--S 12 of 81 bb:=sinh(a*x)/((n+1)*a) --R --R sinh(a x) @@ -164,7 +164,7 @@ bb:=sinh(a*x)/((n+1)*a) --R Type: Expression Integer --E ---S 13 14:592 Axiom cannot simplify this expression +--S 13 of 81 14:592 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -187,7 +187,7 @@ $$ <<*>>= )clear all ---S 14 +--S 14 of 81 aa:=integrate(cosh(a*x)^n*sinh(a*x),x) --R --R @@ -198,7 +198,7 @@ aa:=integrate(cosh(a*x)^n*sinh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 15 +--S 15 of 81 bb:=cosh(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -208,7 +208,7 @@ bb:=cosh(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 16 14:593 Axiom cannot simplify this expression +--S 16 of 81 14:593 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -231,7 +231,7 @@ $$ <<*>>= )clear all ---S 17 +--S 17 of 81 aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x) --R --R @@ -242,7 +242,7 @@ aa:=integrate(sinh(a*x)^2*cosh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 18 +--S 18 of 81 bb:=sinh(4*a*x)/(32*a)-x/8 --R --R sinh(4a x) - 4a x @@ -251,7 +251,7 @@ bb:=sinh(4*a*x)/(32*a)-x/8 --R Type: Expression Integer --E ---S 19 14:594 Schaums and Axiom agree +--S 19 of 81 14:594 Schaums and Axiom agree cc:=complexNormalize(aa-bb) --R --R (3) 0 @@ -267,7 +267,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 81 aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x) --R --R @@ -279,7 +279,7 @@ aa:=integrate(1/(sinh(a*x)*cosh(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 81 bb:=1/a*log(tanh(a*x)) --R --R log(tanh(a x)) @@ -288,7 +288,7 @@ bb:=1/a*log(tanh(a*x)) --R Type: Expression Integer --E ---S 22 +--S 22 of 81 cc:=aa-bb --R --R (3) @@ -304,7 +304,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 23 +--S 23 of 81 dd:=expandLog cc --R --R - log(tanh(a x)) + log(sinh(a x)) - log(cosh(a x)) @@ -313,7 +313,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 24 +--S 24 of 81 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R --R sinh(x) @@ -322,7 +322,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 25 +--S 25 of 81 ee:=tanhrule dd --R --R sinh(a x) @@ -333,7 +333,7 @@ ee:=tanhrule dd --R Type: Expression Integer --E ---S 26 14:595 Schaums and Axiom agree +--S 26 of 81 14:595 Schaums and Axiom agree ff:=expandLog ee --R --R (7) 0 @@ -349,7 +349,7 @@ $$ <<*>>= )clear all ---S 27 +--S 27 of 81 aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)),x) --R --R (1) @@ -365,7 +365,7 @@ aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 28 +--S 28 of 81 bb:=-1/a*atan(sinh(a*x)-csch(a*x))/a --R --R atan(sinh(a x) - csch(a x)) @@ -375,7 +375,7 @@ bb:=-1/a*atan(sinh(a*x)-csch(a*x))/a --R Type: Expression Integer --E ---S 29 14:596 Axiom cannot simplify this expression +--S 29 of 81 14:596 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -405,7 +405,7 @@ $$ <<*>>= )clear all ---S 30 +--S 30 of 81 aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x) --R --R @@ -427,7 +427,7 @@ aa:=integrate(1/(sinh(a*x)*cosh(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 31 +--S 31 of 81 bb:=sech(a*x)/a+1/a*log(tanh((a*x)/2)) --R --R a x @@ -438,7 +438,7 @@ bb:=sech(a*x)/a+1/a*log(tanh((a*x)/2)) --R Type: Expression Integer --E ---S 32 +--S 32 of 81 cc:=aa-bb --R --R (3) @@ -467,7 +467,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 33 +--S 33 of 81 sechrule:=rule(sech(x) == 1/cosh(x)) --R --R 1 @@ -476,7 +476,7 @@ sechrule:=rule(sech(x) == 1/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 34 +--S 34 of 81 dd:=sechrule cc --R --R (5) @@ -505,7 +505,7 @@ dd:=sechrule cc --R Type: Expression Integer --E ---S 35 +--S 35 of 81 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R --R sinh(x) @@ -514,7 +514,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 36 +--S 36 of 81 ee:=tanhrule dd --R --R (7) @@ -547,7 +547,7 @@ ee:=tanhrule dd --R Type: Expression Integer --E ---S 37 +--S 37 of 81 coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x)) --R --R 3 cosh(3x) - 3cosh(x) @@ -556,7 +556,7 @@ coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 38 +--S 38 of 81 ff:=coshcuberule ee --R --R (9) @@ -595,7 +595,7 @@ ff:=coshcuberule ee --R Type: Expression Integer --E ---S 39 +--S 39 of 81 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -604,7 +604,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 40 +--S 40 of 81 gg:=coshsqrrule ff --R --R (11) @@ -645,7 +645,7 @@ gg:=coshsqrrule ff --R Type: Expression Integer --E ---S 41 +--S 41 of 81 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -654,7 +654,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 42 +--S 42 of 81 hh:=sinhsqrrule gg --R --R (13) @@ -672,7 +672,7 @@ hh:=sinhsqrrule gg --R Type: Expression Integer --E ---S 43 +--S 43 of 81 ii:=expandLog hh --R --R (14) @@ -686,7 +686,7 @@ ii:=expandLog hh --R Type: Expression Integer --E ---S 44 14:597 Schaums and Axiom agree +--S 44 of 81 14:597 Schaums and Axiom agree jj:=complexNormalize ii --R --R (15) 0 @@ -702,7 +702,7 @@ $$ <<*>>= )clear all ---S 45 +--S 45 of 81 aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x) --R --R @@ -718,7 +718,7 @@ aa:=integrate(1/(sinh(a*x)^2*cosh(a*x)^2),x) --R Type: Union(Expression Integer,...) --E ---S 46 +--S 46 of 81 bb:=-(2*coth(2*a*x))/a --R --R 2coth(2a x) @@ -727,7 +727,7 @@ bb:=-(2*coth(2*a*x))/a --R Type: Expression Integer --E ---S 47 14:598 Axiom cannot simplify this expression +--S 47 of 81 14:598 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -757,7 +757,7 @@ $$ <<*>>= )clear all ---S 48 +--S 48 of 81 aa:=integrate(sinh(a*x)^2/cosh(a*x),x) --R --R @@ -772,7 +772,7 @@ aa:=integrate(sinh(a*x)^2/cosh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 49 +--S 49 of 81 bb:=sinh(a*x)/a-1/a*atan(sinh(a*x)) --R --R - atan(sinh(a x)) + sinh(a x) @@ -781,7 +781,7 @@ bb:=sinh(a*x)/a-1/a*atan(sinh(a*x)) --R Type: Expression Integer --E ---S 50 14:599 Axiom cannot simplify this expression +--S 50 of 81 14:599 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -803,7 +803,7 @@ $$ <<*>>= )clear all ---S 51 +--S 51 of 81 aa:=integrate(cosh(a*x)^2/sinh(a*x),x) --R --R @@ -820,7 +820,7 @@ aa:=integrate(cosh(a*x)^2/sinh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 52 +--S 52 of 81 bb:=cosh(a*x)/a+1/a*log(tanh((a*x)/2)) --R --R a x @@ -831,7 +831,7 @@ bb:=cosh(a*x)/a+1/a*log(tanh((a*x)/2)) --R Type: Expression Integer --E ---S 53 14:600 Axiom cannot simplify this expression +--S 53 of 81 14:600 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -861,7 +861,7 @@ $$ <<*>>= )clear all ---S 54 +--S 54 of 81 aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x) --R --R @@ -876,7 +876,7 @@ aa:=integrate(1/(cosh(a*x)*(1+sinh(a*x))),x) --R Type: Union(Expression Integer,...) --E ---S 55 +--S 55 of 81 bb:=1/(2*a)*log((1+sinh(a*x))/cosh(a*x))+1/a*atan(%e^(a*x)) --R --R sinh(a x) + 1 a x @@ -887,7 +887,7 @@ bb:=1/(2*a)*log((1+sinh(a*x))/cosh(a*x))+1/a*atan(%e^(a*x)) --R Type: Expression Integer --E ---S 56 +--S 56 of 81 cc:=aa-bb --R --R (3) @@ -903,7 +903,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 57 +--S 57 of 81 dd:=expandLog cc --R --R a x @@ -913,7 +913,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 58 +--S 58 of 81 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -924,7 +924,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 59 +--S 59 of 81 ee:=atanrule dd --R --R a x @@ -937,7 +937,7 @@ ee:=atanrule dd --R Type: Expression Complex Integer --E ---S 60 +--S 60 of 81 ff:=expandLog ee --R --R (7) @@ -950,7 +950,7 @@ ff:=expandLog ee --R Type: Expression Complex Integer --E ---S 61 14:601 Schaums and Axiom agree +--S 61 of 81 14:601 Schaums and Axiom agree gg:=complexNormalize ff --R --R (8) 0 @@ -966,7 +966,7 @@ $$ <<*>>= )clear all ---S 62 +--S 62 of 81 aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x) --R --R @@ -992,7 +992,7 @@ aa:=integrate(1/(sinh(a*x)*(cosh(a*x)+1)),x) --R Type: Union(Expression Integer,...) --E ---S 63 +--S 63 of 81 bb:=1/(2*a)*log(tanh((a*x)/2))+1/(2*a*(cosh(a*x)+1)) --R --R a x @@ -1003,7 +1003,7 @@ bb:=1/(2*a)*log(tanh((a*x)/2))+1/(2*a*(cosh(a*x)+1)) --R Type: Expression Integer --E ---S 64 +--S 64 of 81 cc:=aa-bb --R --R (3) @@ -1051,7 +1051,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 65 +--S 65 of 81 coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x)) --R --R 3 cosh(3x) - 3cosh(x) @@ -1060,7 +1060,7 @@ coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 66 +--S 66 of 81 dd:=coshcuberule cc --R --R (5) @@ -1110,7 +1110,7 @@ dd:=coshcuberule cc --R Type: Expression Integer --E ---S 67 +--S 67 of 81 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -1119,7 +1119,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 68 +--S 68 of 81 ee:=sinhsqrrule dd --R --R (7) @@ -1160,7 +1160,7 @@ ee:=sinhsqrrule dd --R Type: Expression Integer --E ---S 69 +--S 69 of 81 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -1169,7 +1169,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 70 +--S 70 of 81 ff:=coshsqrrule ee --R --R (9) @@ -1183,7 +1183,7 @@ ff:=coshsqrrule ee --R Type: Expression Integer --E ---S 71 14:602 Schaums and Axiom agree +--S 71 of 81 14:602 Schaums and Axiom agree gg:=complexNormalize ff --R --R (10) 0 @@ -1199,7 +1199,7 @@ $$ <<*>>= )clear all ---S 72 +--S 72 of 81 aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x) --R --R @@ -1225,7 +1225,7 @@ aa:=integrate(1/(sinh(a*x)*(cosh(a*x)-1)),x) --R Type: Union(Expression Integer,...) --E ---S 73 +--S 73 of 81 bb:=-1/(2*a)*log(tanh((a*x)/2))-1/(2*a*(cosh(a*x)-1)) --R --R a x @@ -1236,7 +1236,7 @@ bb:=-1/(2*a)*log(tanh((a*x)/2))-1/(2*a*(cosh(a*x)-1)) --R Type: Expression Integer --E ---S 74 +--S 74 of 81 cc:=aa-bb --R --R (3) @@ -1282,7 +1282,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 75 +--S 75 of 81 coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x)) --R --R 3 cosh(3x) - 3cosh(x) @@ -1291,7 +1291,7 @@ coshcuberule:=rule(cosh(x)^3 == 1/4*cosh(3*x)-3/4*cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 76 +--S 76 of 81 dd:=coshcuberule cc --R --R (5) @@ -1338,7 +1338,7 @@ dd:=coshcuberule cc --R Type: Expression Integer --E ---S 77 +--S 77 of 81 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -1347,7 +1347,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 78 +--S 78 of 81 ee:=sinhsqrrule dd --R --R (7) @@ -1388,7 +1388,7 @@ ee:=sinhsqrrule dd --R Type: Expression Integer --E ---S 79 +--S 79 of 81 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -1397,7 +1397,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 80 +--S 80 of 81 ff:=coshsqrrule ee --R --R (9) @@ -1411,7 +1411,7 @@ ff:=coshsqrrule ee --R Type: Expression Integer --E ---S 81 14:603 Schaums and Axiom agree +--S 81 of 81 14:603 Schaums and Axiom agree gg:=complexNormalize ff --R --R (10) 0 diff --git a/src/input/schaum3.input.pamphlet b/src/input/schaum3.input.pamphlet index bed98c8..6ad4c38 100644 --- a/src/input/schaum3.input.pamphlet +++ b/src/input/schaum3.input.pamphlet @@ -16,7 +16,7 @@ $$\int{\frac{1}{(ax+b)(px+q)}}= )set message auto off )clear all ---S 1 +--S 1 of 28 aa:=integrate(1/((a*x+b)*(p*x+q)),x) --R --R @@ -26,7 +26,7 @@ aa:=integrate(1/((a*x+b)*(p*x+q)),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 28 bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b)) --R --R @@ -38,7 +38,7 @@ bb:=1/(b*p-a*q)*log((p*x+q)/(a*x+b)) --R Type: Expression Integer --E ---S 3 +--S 3 of 28 cc:=aa-bb --R --R @@ -50,7 +50,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 28 logdiv:=rule(log(a)-log(b) == log(a/b)) --R --R a @@ -59,7 +59,7 @@ logdiv:=rule(log(a)-log(b) == log(a/b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 +--S 5 of 28 dd:=logdiv cc --R --R 1 @@ -70,14 +70,14 @@ dd:=logdiv cc --R Type: Expression Integer --E ---S 6 +--S 6 of 28 logmul:=rule(log(a)+log(b) == log(a*b)) --R --I (6) log(b) + log(a) + %J == log(a b) + %J --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 7 14:105 Schaums and Axiom agree +--S 7 of 28 14:105 Schaums and Axiom agree ee:=logmul dd --R --R (7) 0 @@ -92,7 +92,7 @@ $$\int{\frac{x}{(ax+b)(px+q)}}= <<*>>= )clear all ---S 8 +--S 8 of 28 aa:=integrate(x/((a*x+b)*(p*x+q)),x) --R --R @@ -103,7 +103,7 @@ aa:=integrate(x/((a*x+b)*(p*x+q)),x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 28 bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q)) --R --R @@ -114,7 +114,7 @@ bb:=1/(b*p-a*q)*(b/a*log(a*x+b)-q/p*log(p*x+q)) --R Type: Expression Integer --E ---S 10 14:106 Schaums and Axiom agree +--S 10 of 28 14:106 Schaums and Axiom agree cc:=aa-bb --R --R @@ -131,7 +131,7 @@ $$\int{\frac{1}{(ax+b)^2(px+q)}}= <<*>>= )clear all ---S 11 +--S 11 of 28 aa:=integrate(1/((a*x+b)^2*(p*x+q)),x) --R --R @@ -142,7 +142,7 @@ aa:=integrate(1/((a*x+b)^2*(p*x+q)),x) --R Type: Union(Expression Integer,...) --E ---S 12 +--S 12 of 28 bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b))) --R --R @@ -155,7 +155,7 @@ bb:=1/(b*p-a*q)*(1/(a*x+b)+p/(b*p-a*q)*log((p*x+q)/(a*x+b))) --R Type: Expression Integer --E ---S 13 +--S 13 of 28 cc:=aa-bb --R --R @@ -168,7 +168,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 14 +--S 14 of 28 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -177,7 +177,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 15 14:107 Schaums and Axiom agree +--S 15 of 28 14:107 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -195,7 +195,7 @@ $$\int{\frac{x}{(ax+b)^2(px+q)}}= <<*>>= )clear all ---S 16 +--S 16 of 28 aa:=integrate(x/((a*x+b)^2*(p*x+q)),x) --R --R @@ -208,7 +208,7 @@ aa:=integrate(x/((a*x+b)^2*(p*x+q)),x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 28 bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b))) --R --R @@ -221,7 +221,7 @@ bb:=1/(b*p-a*q)*(q/(b*p-a*q)*log((a*x+b)/(p*x+q))-b/(a*(a*x+b))) --R Type: Expression Integer --E ---S 18 +--S 18 of 28 cc:=aa-bb --R --R @@ -234,7 +234,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 19 +--S 19 of 28 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -243,7 +243,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 20 14:108 Schaums and Axiom agree +--S 20 of 28 14:108 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -259,7 +259,7 @@ $$\frac{b^2}{(bp-aq)a^2(ax+b)}+\frac{1}{(bp-aq)^2} <<*>>= )clear all ---S 21 +--S 21 of 28 aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x) --R --R @@ -275,7 +275,7 @@ aa:=integrate(x^2/((a*x+b)^2*(p*x+q)),x) --R Type: Union(Expression Integer,...) --E ---S 22 +--S 22 of 28 bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_ 1/(b*p-a*q)^2*(q^2/p*log(p*x+q)+((b*(b*p-2*a*q))/a^2)*log(a*x+b)) --R @@ -292,7 +292,7 @@ bb:=b^2/((b*p-a*q)*a^2*(a*x+b))+_ --R Type: Expression Integer --E ---S 23 14:109 Schaums and Axiom agree +--S 23 of 28 14:109 Schaums and Axiom agree cc:=aa-bb --R --R @@ -309,7 +309,7 @@ a(m+n-2)~\int{\frac{1}{(ax+b)^m(px+q)^{n-1}}}\right\}$$ <<*>>= )clear all ---S 24 14:110 Axiom cannot do this integral +--S 24 of 28 14:110 Axiom cannot do this integral aa:=integrate(1/((a*x+b)^m*(p*x+q)^n),x) --R --R @@ -327,7 +327,7 @@ $$\int{\frac{ax+b}{px+q}}=\frac{ax}{p}+\frac{bp-aq}{p^2}~\ln(px+q)$$ <<*>>= )clear all ---S 25 +--S 25 of 28 aa:=integrate((a*x+b)/(p*x+q),x) --R --R @@ -338,7 +338,7 @@ aa:=integrate((a*x+b)/(p*x+q),x) --R Type: Union(Expression Integer,...) --E ---S 26 +--S 26 of 28 bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q) --R --R @@ -349,7 +349,7 @@ bb:=(a*x)/p+(b*p-a*q)/p^2*log(p*x+q) --R Type: Expression Integer --E ---S 27 14:111 Schaums and Axiom agree +--S 27 of 28 14:111 Schaums and Axiom agree cc:=aa-bb --R --R @@ -373,7 +373,7 @@ $$\int{\frac{(ax+b)^m}{(px+q)^n}}=\left\{ <<*>>= )clear all ---S 28 14:112 Axiom cannot do this integral +--S 28 of 28 14:112 Axiom cannot do this integral aa:=integrate((a*x+b)^m/(p*x+q)^n,x) --R --R diff --git a/src/input/schaum30.input.pamphlet b/src/input/schaum30.input.pamphlet index 5df48bc..5f5a26b 100644 --- a/src/input/schaum30.input.pamphlet +++ b/src/input/schaum30.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 46 aa:=integrate(tanh(a*x),x) --R --R @@ -30,7 +30,7 @@ aa:=integrate(tanh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 46 bb:=1/a*log(cosh(a*x)) --R --R log(cosh(a x)) @@ -39,7 +39,7 @@ bb:=1/a*log(cosh(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 46 cc:=aa-bb --R --R 2cosh(a x) @@ -50,7 +50,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 46 dd:=expandLog cc --R --R - log(sinh(a x) - cosh(a x)) + log(- 2) - a x @@ -59,7 +59,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 5 14:604 Schaums and Axiom differ by a constant +--S 5 of 46 14:604 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R - log(- 1) + log(- 2) @@ -77,7 +77,7 @@ $$ <<*>>= )clear all ---S 6 +--S 6 of 46 aa:=integrate(tanh(a*x)^2,x) --R --R @@ -87,7 +87,7 @@ aa:=integrate(tanh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 7 +--S 7 of 46 bb:=x-tanh(a*x)/a --R --R - tanh(a x) + a x @@ -96,7 +96,7 @@ bb:=x-tanh(a*x)/a --R Type: Expression Integer --E ---S 8 +--S 8 of 46 cc:=aa-bb --R --R cosh(a x)tanh(a x) - sinh(a x) + cosh(a x) @@ -105,7 +105,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 9 +--S 9 of 46 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R --R sinh(x) @@ -114,7 +114,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 10 14:605 Schaums and Axiom differ by a constant +--S 10 of 46 14:605 Schaums and Axiom differ by a constant dd:=tanhrule cc --R --R 1 @@ -132,7 +132,7 @@ $$ <<*>>= )clear all ---S 11 +--S 11 of 46 aa:=integrate(tanh(a*x)^3,x) --R --R @@ -167,7 +167,7 @@ aa:=integrate(tanh(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 12 +--S 12 of 46 bb:=1/a*log(cosh(a*x))-tanh(a*x)^2/(2*a) --R --R 2 @@ -177,7 +177,7 @@ bb:=1/a*log(cosh(a*x))-tanh(a*x)^2/(2*a) --R Type: Expression Integer --E ---S 13 14:606 Axiom cannot simplify this expression +--S 13 of 46 14:606 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -239,7 +239,7 @@ $$ <<*>>= )clear all ---S 14 +--S 14 of 46 aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x) --R --R @@ -251,7 +251,7 @@ aa:=integrate(tanh(a*x)^n*sech(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 15 +--S 15 of 46 bb:=tanh(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -261,7 +261,7 @@ bb:=tanh(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 16 14:607 Axiom cannot simplify this expression +--S 16 of 46 14:607 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -285,7 +285,7 @@ $$ <<*>>= )clear all ---S 17 +--S 17 of 46 aa:=integrate(sech(a*x)^2/tanh(a*x),x) --R --R @@ -297,7 +297,7 @@ aa:=integrate(sech(a*x)^2/tanh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 18 +--S 18 of 46 bb:=1/a*log(tanh(a*x)) --R --R log(tanh(a x)) @@ -306,7 +306,7 @@ bb:=1/a*log(tanh(a*x)) --R Type: Expression Integer --E ---S 19 +--S 19 of 46 cc:=aa-bb --R --R (3) @@ -322,7 +322,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 20 +--S 20 of 46 tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R --R sinh(x) @@ -331,7 +331,7 @@ tanhrule:=rule(tanh(x) == sinh(x)/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 21 +--S 21 of 46 dd:=tanhrule cc --R --R (5) @@ -347,7 +347,7 @@ dd:=tanhrule cc --R Type: Expression Integer --E ---S 22 14:608 Schaums and Axiom agree +--S 22 of 46 14:608 Schaums and Axiom agree ee:=expandLog dd --R --R (6) 0 @@ -363,7 +363,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 46 aa:=integrate(1/tanh(a*x),x) --R --R @@ -375,7 +375,7 @@ aa:=integrate(1/tanh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 46 bb:=1/a*log(sinh(a*x)) --R --R log(sinh(a x)) @@ -384,7 +384,7 @@ bb:=1/a*log(sinh(a*x)) --R Type: Expression Integer --E ---S 25 +--S 25 of 46 cc:=aa-bb --R --R 2sinh(a x) @@ -395,7 +395,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 26 +--S 26 of 46 dd:=expandLog cc --R --R - log(sinh(a x) - cosh(a x)) + log(- 2) - a x @@ -404,7 +404,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 27 14:609 Schaums and Axiom differ by a constant +--S 27 of 46 14:609 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R - log(- 1) + log(- 2) @@ -424,7 +424,7 @@ $$ <<*>>= )clear all ---S 28 14:610 Axiom cannot compute this integral +--S 28 of 46 14:610 Axiom cannot compute this integral aa:=integrate(x*tanh(a*x),x) --R --R @@ -444,7 +444,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 46 aa:=integrate(x*tanh(a*x)^2,x) --R --R @@ -467,7 +467,7 @@ aa:=integrate(x*tanh(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 46 bb:=x^2/2-(x*tanh(a*x))/a+1/a^2*log(cosh(a*x)) --R --R 2 2 @@ -478,7 +478,7 @@ bb:=x^2/2-(x*tanh(a*x))/a+1/a^2*log(cosh(a*x)) --R Type: Expression Integer --E ---S 31 +--S 31 of 46 cc:=aa-bb --R --R (3) @@ -505,7 +505,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 +--S 32 of 46 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -514,7 +514,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 33 +--S 33 of 46 dd:=sinhsqrrule cc --R --R (5) @@ -541,7 +541,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 34 +--S 34 of 46 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -550,7 +550,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 35 +--S 35 of 46 ee:=coshsqrrule dd --R --R (7) @@ -569,7 +569,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 36 +--S 36 of 46 ff:=expandLog ee --R --R (8) @@ -586,7 +586,7 @@ ff:=expandLog ee --R Type: Expression Integer --E ---S 37 +--S 37 of 46 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %N sinh(y + x) - %N sinh(y - x) @@ -595,7 +595,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 38 +--S 38 of 46 gg:=sinhcoshrule ff --R --R (10) @@ -610,7 +610,7 @@ gg:=sinhcoshrule ff --R Type: Expression Integer --E ---S 39 14:611 Schaums and Axiom differ by a constant +--S 39 of 46 14:611 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R - log(- 1) + log(- 2) @@ -630,7 +630,7 @@ $$ <<*>>= )clear all ---S 40 14:612 Axiom cannot compute this integral +--S 40 of 46 14:612 Axiom cannot compute this integral aa:=integrate(tanh(a*x)/x,x) --R --R @@ -650,7 +650,7 @@ $$ <<*>>= )clear all ---S 41 +--S 41 of 46 aa:=integrate(1/(p+q*tanh(a*x)),x) --R --R @@ -663,7 +663,7 @@ aa:=integrate(1/(p+q*tanh(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 46 bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(q*sinh(a*x)+p*cosh(a*x)) --R --R q log(q sinh(a x) + p cosh(a x)) - a p x @@ -673,7 +673,7 @@ bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(q*sinh(a*x)+p*cosh(a*x)) --R Type: Expression Integer --E ---S 43 +--S 43 of 46 cc:=aa-bb --R --R (3) @@ -688,7 +688,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 44 +--S 44 of 46 dd:=expandLog cc --R --R (4) @@ -701,7 +701,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 45 14:613 Schaums and Axiom differ by a constant +--S 45 of 46 14:613 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R q log(2) - 2q log(- 1) @@ -720,7 +720,7 @@ $$ <<*>>= )clear all ---S 46 14:614 Axiom cannot compute this integral +--S 46 of 46 14:614 Axiom cannot compute this integral aa:=integrate(tanh(a*x)^n,x) --R --R diff --git a/src/input/schaum31.input.pamphlet b/src/input/schaum31.input.pamphlet index 343aa2a..36eb793 100644 --- a/src/input/schaum31.input.pamphlet +++ b/src/input/schaum31.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 46 aa:=integrate(coth(a*x),x) --R --R @@ -30,7 +30,7 @@ aa:=integrate(coth(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 46 bb:=1/a*log(sinh(a*x)) --R --R log(sinh(a x)) @@ -39,7 +39,7 @@ bb:=1/a*log(sinh(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 46 cc:=aa-bb --R --R 2sinh(a x) @@ -50,7 +50,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 46 dd:=expandLog cc --R --R - log(sinh(a x) - cosh(a x)) + log(- 2) - a x @@ -59,7 +59,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 5 14:615 Schaums and Axiom differ by a constant +--S 5 of 46 14:615 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R - log(- 1) + log(- 2) @@ -77,7 +77,7 @@ $$ <<*>>= )clear all ---S 6 +--S 6 of 46 aa:=integrate(coth(a*x)^2,x) --R --R @@ -87,7 +87,7 @@ aa:=integrate(coth(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 7 +--S 7 of 46 bb:=x-coth(a*x)/a --R --R - coth(a x) + a x @@ -96,7 +96,7 @@ bb:=x-coth(a*x)/a --R Type: Expression Integer --E ---S 8 +--S 8 of 46 cc:=aa-bb --R --R (coth(a x) + 1)sinh(a x) - cosh(a x) @@ -105,7 +105,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 9 14:616 Schaums and Axiom differ by a constant +--S 9 of 46 14:616 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 1 @@ -123,7 +123,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 46 aa:=integrate(coth(a*x)^3,x) --R --R @@ -158,7 +158,7 @@ aa:=integrate(coth(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 46 bb:=1/a*log(sinh(a*x)-coth(a*x)^2)/(2*a) --R --R 2 @@ -169,7 +169,7 @@ bb:=1/a*log(sinh(a*x)-coth(a*x)^2)/(2*a) --R Type: Expression Integer --E ---S 12 14:617 Axiom cannot simplify this expression +--S 12 of 46 14:617 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -230,7 +230,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 46 aa:=integrate(coth(a*x)^n*csch(a*x)^2,x) --R --R @@ -242,7 +242,7 @@ aa:=integrate(coth(a*x)^n*csch(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 46 bb:=-coth(a*x)^(n+1)/((n+1)*a) --R --R n + 1 @@ -252,7 +252,7 @@ bb:=-coth(a*x)^(n+1)/((n+1)*a) --R Type: Expression Integer --E ---S 15 +--S 15 of 46 cc:=aa-bb --R --R (3) @@ -267,7 +267,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 16 +--S 16 of 46 dd:=expandLog cc --R --R (4) @@ -282,7 +282,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 17 14:618 Schaums and Axiom agree +--S 17 of 46 14:618 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -298,7 +298,7 @@ $$ <<*>>= )clear all ---S 18 +--S 18 of 46 aa:=integrate(csch(a*x)^2/coth(a*x),x) --R --R @@ -310,7 +310,7 @@ aa:=integrate(csch(a*x)^2/coth(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 19 +--S 19 of 46 bb:=-1/a*log(coth(a*x)) --R --R log(coth(a x)) @@ -319,7 +319,7 @@ bb:=-1/a*log(coth(a*x)) --R Type: Expression Integer --E ---S 20 +--S 20 of 46 cc:=aa-bb --R --R (3) @@ -331,7 +331,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 21 +--S 21 of 46 dd:=expandLog cc --R --R log(sinh(a x)) + log(coth(a x)) - log(cosh(a x)) @@ -340,7 +340,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 22 14:619 Schaums and Axiom agree +--S 22 of 46 14:619 Schaums and Axiom agree ee:=complexNormalize dd --R --R (5) 0 @@ -356,7 +356,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 46 aa:=integrate(1/coth(a*x),x) --R --R @@ -368,7 +368,7 @@ aa:=integrate(1/coth(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 46 bb:=1/a*log(cosh(a*x)) --R --R log(cosh(a x)) @@ -377,7 +377,7 @@ bb:=1/a*log(cosh(a*x)) --R Type: Expression Integer --E ---S 25 +--S 25 of 46 cc:=aa-bb --R --R 2cosh(a x) @@ -388,7 +388,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 26 +--S 26 of 46 dd:=expandLog cc --R --R - log(sinh(a x) - cosh(a x)) + log(- 2) - a x @@ -397,7 +397,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 27 14:620 Schaums and Axiom differ by a constant +--S 27 of 46 14:620 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R - log(- 1) + log(- 2) @@ -417,7 +417,7 @@ $$ <<*>>= )clear all ---S 28 14:621 Axiom cannot compute this integral +--S 28 of 46 14:621 Axiom cannot compute this integral aa:=integrate(x*coth(a*x),x) --R --R @@ -437,7 +437,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 46 aa:=integrate(x*coth(a*x)^2,x) --R --R @@ -460,7 +460,7 @@ aa:=integrate(x*coth(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 46 bb:=x^2/2-(x*coth(a*x)/a)+1/a^2*log(sinh(a*x)) --R --R 2 2 @@ -471,7 +471,7 @@ bb:=x^2/2-(x*coth(a*x)/a)+1/a^2*log(sinh(a*x)) --R Type: Expression Integer --E ---S 31 +--S 31 of 46 cc:=aa-bb --R --R (3) @@ -498,7 +498,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 +--S 32 of 46 dd:=expandLog cc --R --R (4) @@ -520,7 +520,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 33 +--S 33 of 46 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -529,7 +529,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 34 +--S 34 of 46 ee:=sinhsqrrule dd --R --R (6) @@ -553,7 +553,7 @@ ee:=sinhsqrrule dd --R Type: Expression Integer --E ---S 35 +--S 35 of 46 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -562,7 +562,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 36 +--S 36 of 46 ff:=coshsqrrule ee --R --R (8) @@ -577,7 +577,7 @@ ff:=coshsqrrule ee --R Type: Expression Integer --E ---S 37 +--S 37 of 46 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %L sinh(y + x) - %L sinh(y - x) @@ -586,7 +586,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 38 +--S 38 of 46 gg:=sinhcoshrule ff --R --R (10) @@ -601,7 +601,7 @@ gg:=sinhcoshrule ff --R Type: Expression Integer --E ---S 39 14:622 Schaums and Axiom differ by a constant +--S 39 of 46 14:622 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R - log(- 1) + log(- 2) @@ -621,7 +621,7 @@ $$ <<*>>= )clear all ---S 40 14:623 Axiom cannot compute this integral +--S 40 of 46 14:623 Axiom cannot compute this integral aa:=integrate(coth(a*x)/x,x) --R --R @@ -641,7 +641,7 @@ $$ <<*>>= )clear all ---S 41 +--S 41 of 46 aa:=integrate(1/(p+q*coth(a*x)),x) --R --R @@ -654,7 +654,7 @@ aa:=integrate(1/(p+q*coth(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 46 bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(p*sinh(a*x)+q*cosh(a*x)) --R --R q log(p sinh(a x) + q cosh(a x)) - a p x @@ -664,7 +664,7 @@ bb:=(p*x)/(p^2-q^2)-q/(a*(p^2-q^2))*log(p*sinh(a*x)+q*cosh(a*x)) --R Type: Expression Integer --E ---S 43 +--S 43 of 46 cc:=aa-bb --R --R (3) @@ -679,7 +679,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 44 +--S 44 of 46 dd:=expandLog cc --R --R (4) @@ -692,7 +692,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 45 14:624 Schaums and Axiom differ by a constant +--S 45 of 46 14:624 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R q log(2) - 2q log(- 1) @@ -711,7 +711,7 @@ $$ <<*>>= )clear all ---S 46 14:625 Axiom cannot compute this integral +--S 46 of 46 14:625 Axiom cannot compute this integral aa:=integrate(coth(a*x)^n,x) --R --R diff --git a/src/input/schaum32.input.pamphlet b/src/input/schaum32.input.pamphlet index e5b2409..d5ce6f4 100644 --- a/src/input/schaum32.input.pamphlet +++ b/src/input/schaum32.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 52 aa:=integrate(sech(a*x),x) --R --R @@ -28,7 +28,7 @@ aa:=integrate(sech(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 52 bb:=2/a*atan(%e^(a*x)) --R --R a x @@ -38,7 +38,7 @@ bb:=2/a*atan(%e^(a*x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 52 cc:=aa-bb --R --R a x @@ -48,7 +48,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 52 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -59,7 +59,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 5 +--S 5 of 52 dd:=atanrule cc --R --R a x @@ -72,7 +72,7 @@ dd:=atanrule cc --R Type: Expression Complex Integer --E ---S 6 +--S 6 of 52 ee:=expandLog dd --R --R (6) @@ -85,7 +85,7 @@ ee:=expandLog dd --R Type: Expression Complex Integer --E ---S 7 14:626 Schaums and Axiom agree +--S 7 of 52 14:626 Schaums and Axiom agree ff:=complexNormalize ee --R --R (7) 0 @@ -101,7 +101,7 @@ $$ <<*>>= )clear all ---S 8 +--S 8 of 52 aa:=integrate(sech(a*x)^2,x) --R --R @@ -112,7 +112,7 @@ aa:=integrate(sech(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 52 bb:=tanh(a*x)/a --R --R tanh(a x) @@ -121,7 +121,7 @@ bb:=tanh(a*x)/a --R Type: Expression Integer --E ---S 10 +--S 10 of 52 cc:=aa-bb --R --R 2 2 @@ -132,7 +132,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 11 +--S 11 of 52 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -141,7 +141,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 12 +--S 12 of 52 dd:=sinhsqrrule cc --R --R 2 @@ -152,7 +152,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 13 +--S 13 of 52 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -161,7 +161,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 14 +--S 14 of 52 ee:=coshsqrrule dd --R --R (- 2cosh(a x)sinh(a x) - cosh(2a x) - 1)tanh(a x) - 2 @@ -170,7 +170,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 15 +--S 15 of 52 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %L sinh(y + x) - %L sinh(y - x) @@ -179,7 +179,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 16 +--S 16 of 52 ff:=sinhcoshrule ee --R --R (- sinh(2a x) - cosh(2a x) - 1)tanh(a x) - 2 @@ -188,7 +188,7 @@ ff:=sinhcoshrule ee --R Type: Expression Integer --E ---S 17 14:627 Schaums and Axiom differ by a constant +--S 17 of 52 14:627 Schaums and Axiom differ by a constant gg:=complexNormalize ff --R --R 1 @@ -206,7 +206,7 @@ $$ <<*>>= )clear all ---S 18 +--S 18 of 52 aa:=integrate(sech(a*x)^3,x) --R --R @@ -233,7 +233,7 @@ aa:=integrate(sech(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 19 +--S 19 of 52 bb:=(sech(a*x)*tanh(a*x))/(2*a)+1/(2*a)*atan(sinh(a*x)) --R --R atan(sinh(a x)) + sech(a x)tanh(a x) @@ -242,7 +242,7 @@ bb:=(sech(a*x)*tanh(a*x))/(2*a)+1/(2*a)*atan(sinh(a*x)) --R Type: Expression Integer --E ---S 20 14:628 Axiom cannot simplify this expression +--S 20 of 52 14:628 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -301,7 +301,7 @@ $$ <<*>>= )clear all ---S 21 +--S 21 of 52 aa:=integrate(sech(a*x)^n*tanh(a*x),x) --R --R @@ -320,7 +320,7 @@ aa:=integrate(sech(a*x)^n*tanh(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 22 +--S 22 of 52 bb:=-sech(a*x)^n/(n*a) --R --R n @@ -330,7 +330,7 @@ bb:=-sech(a*x)^n/(n*a) --R Type: Expression Integer --E ---S 23 +--S 23 of 52 cc:=aa-bb --R --R (3) @@ -351,7 +351,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 24 +--S 24 of 52 sechrule:=rule(sech(x) == 1/cosh(x)) --R --R 1 @@ -360,7 +360,7 @@ sechrule:=rule(sech(x) == 1/cosh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 25 +--S 25 of 52 dd:=sechrule cc --R --R (5) @@ -382,7 +382,7 @@ dd:=sechrule cc --R Type: Expression Integer --E ---S 26 +--S 26 of 52 ee:=expandLog dd --R --R (6) @@ -407,7 +407,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 27 14:629 Schaums and Axiom agree +--S 27 of 52 14:629 Schaums and Axiom agree ff:=complexNormalize ee --R --R (7) 0 @@ -423,7 +423,7 @@ $$ <<*>>= )clear all ---S 28 +--S 28 of 52 aa:=integrate(1/sech(a*x),x) --R --R @@ -433,7 +433,7 @@ aa:=integrate(1/sech(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 29 +--S 29 of 52 bb:=sinh(a*x)/a --R --R sinh(a x) @@ -442,7 +442,7 @@ bb:=sinh(a*x)/a --R Type: Expression Integer --E ---S 30 14:630 Schaums and Axiom agree +--S 30 of 52 14:630 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -460,7 +460,7 @@ $$ <<*>>= )clear all ---S 31 14:631 Axiom cannot compute this integral +--S 31 of 52 14:631 Axiom cannot compute this integral aa:=integrate(x*sech(a*x),x) --R --R @@ -480,7 +480,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 52 aa:=integrate(x*sech(a*x)^2,x) --R --R @@ -500,7 +500,7 @@ aa:=integrate(x*sech(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 52 bb:=(x*tanh(a*x))/a-1/a^2*log(cosh(a*x)) --R --R - log(cosh(a x)) + a x tanh(a x) @@ -510,7 +510,7 @@ bb:=(x*tanh(a*x))/a-1/a^2*log(cosh(a*x)) --R Type: Expression Integer --E ---S 34 +--S 34 of 52 cc:=aa-bb --R --R (3) @@ -537,7 +537,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 35 +--S 35 of 52 dd:=expandLog cc --R --R (4) @@ -562,7 +562,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 36 +--S 36 of 52 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -571,7 +571,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 37 +--S 37 of 52 ee:=sinhsqrrule dd --R --R (6) @@ -595,7 +595,7 @@ ee:=sinhsqrrule dd --R Type: Expression Integer --E ---S 38 +--S 38 of 52 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -604,7 +604,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 39 +--S 39 of 52 ff:=coshsqrrule ee --R --R (8) @@ -621,7 +621,7 @@ ff:=coshsqrrule ee --R Type: Expression Integer --E ---S 40 +--S 40 of 52 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %P sinh(y + x) - %P sinh(y - x) @@ -630,7 +630,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 41 +--S 41 of 52 gg:=sinhcoshrule ff --R --R (10) @@ -645,7 +645,7 @@ gg:=sinhcoshrule ff --R Type: Expression Integer --E ---S 42 14:632 Schaums and Axiom differ by a constant +--S 42 of 52 14:632 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R log(- 1) - log(- 2) @@ -665,7 +665,7 @@ $$ <<*>>= )clear all ---S 43 14:633 Axiom cannot compute this integral +--S 43 of 52 14:633 Axiom cannot compute this integral aa:=integrate(sech(a*x)/x,x) --R --R @@ -685,7 +685,7 @@ $$ <<*>>= )clear all ---S 44 +--S 44 of 52 aa:=integrate(1/(q+p*sech(a*x)),x) --R --R @@ -733,7 +733,7 @@ aa:=integrate(1/(q+p*sech(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 45 +--S 45 of 52 t1:=integrate(1/(p+q*cosh(a*x)),x) --R --R (2) @@ -774,7 +774,7 @@ t1:=integrate(1/(p+q*cosh(a*x)),x) --R Type: Union(List Expression Integer,...) --E ---S 46 +--S 46 of 52 bb1:=x/q-p/q*t1.1 --R --R (3) @@ -810,7 +810,7 @@ bb1:=x/q-p/q*t1.1 --R Type: Expression Integer --E ---S 47 +--S 47 of 52 bb2:=x/q-p/q*t1.2 --R --R +-------+ @@ -826,7 +826,7 @@ bb2:=x/q-p/q*t1.2 --R Type: Expression Integer --E ---S 48 +--S 48 of 52 cc1:=aa.1-bb1 --R --R (5) @@ -878,7 +878,7 @@ cc1:=aa.1-bb1 --R Type: Expression Integer --E ---S 49 +--S 49 of 52 cc2:=aa.2-bb1 --R --R (6) @@ -918,7 +918,7 @@ cc2:=aa.2-bb1 --R Type: Expression Integer --E ---S 50 +--S 50 of 52 cc3:=aa.1-bb2 --R --R (7) @@ -958,7 +958,7 @@ cc3:=aa.1-bb2 --R Type: Expression Integer --E ---S 51 14:634 Schaums and Axiom agree +--S 51 of 52 14:634 Schaums and Axiom agree cc4:=aa.2-bb2 --R --R (8) 0 @@ -975,7 +975,7 @@ $$ <<*>>= )clear all ---S 52 14:635 Axiom cannot compute this integral +--S 52 of 52 14:635 Axiom cannot compute this integral aa:=integrate(sech(a*x)^n,x) --R --R diff --git a/src/input/schaum33.input.pamphlet b/src/input/schaum33.input.pamphlet index 61506d7..7a33dd1 100644 --- a/src/input/schaum33.input.pamphlet +++ b/src/input/schaum33.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 49 aa:=integrate(csch(a*x),x) --R --R @@ -28,7 +28,7 @@ aa:=integrate(csch(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 49 bb:=1/a*log(tanh((a*x)/2)) --R --R a x @@ -39,7 +39,7 @@ bb:=1/a*log(tanh((a*x)/2)) --R Type: Expression Integer --E ---S 3 +--S 3 of 49 cc:=aa-bb --R --R (3) @@ -53,7 +53,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 14:636 Schaums and Axiom agree +--S 4 of 49 14:636 Schaums and Axiom agree dd:=complexNormalize cc --R --R (4) 0 @@ -69,7 +69,7 @@ $$ <<*>>= )clear all ---S 5 +--S 5 of 49 aa:=integrate(csch(a*x)^2,x) --R --R @@ -80,7 +80,7 @@ aa:=integrate(csch(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 6 +--S 6 of 49 bb:=-coth(a*x)/a --R --R coth(a x) @@ -89,7 +89,7 @@ bb:=-coth(a*x)/a --R Type: Expression Integer --E ---S 7 14:637 Axiom cannot simplify this expression +--S 7 of 49 14:637 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -113,7 +113,7 @@ $$ <<*>>= )clear all ---S 8 +--S 8 of 49 aa:=integrate(csch(a*x)^3,x) --R --R @@ -150,7 +150,7 @@ aa:=integrate(csch(a*x)^3,x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 49 bb:=-(csch(a*x)*coth(a*x))/(2*a)-1/(2*a)*log(tanh((a*x)/2)) --R --R a x @@ -161,7 +161,7 @@ bb:=-(csch(a*x)*coth(a*x))/(2*a)-1/(2*a)*log(tanh((a*x)/2)) --R Type: Expression Integer --E ---S 10 14:638 Axiom cannot simplify this expression +--S 10 of 49 14:638 Axiom cannot simplify this expression cc:=aa-bb --R --R (3) @@ -225,7 +225,7 @@ $$ <<*>>= )clear all ---S 11 +--S 11 of 49 aa:=integrate(csch(a*x)^n*coth(a*x),x) --R --R @@ -244,7 +244,7 @@ aa:=integrate(csch(a*x)^n*coth(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 12 +--S 12 of 49 bb:=-csch(a*x)^n/(n*a) --R --R n @@ -254,7 +254,7 @@ bb:=-csch(a*x)^n/(n*a) --R Type: Expression Integer --E ---S 13 +--S 13 of 49 cc:=aa-bb --R --R (3) @@ -275,7 +275,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 14 +--S 14 of 49 cschrule:=rule(csch(x) == 1/sinh(x)) --R --R 1 @@ -284,7 +284,7 @@ cschrule:=rule(csch(x) == 1/sinh(x)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 15 +--S 15 of 49 dd:=cschrule cc --R --R (5) @@ -306,7 +306,7 @@ dd:=cschrule cc --R Type: Expression Integer --E ---S 16 +--S 16 of 49 ee:=expandLog dd --R --R (6) @@ -331,7 +331,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 17 +--S 17 of 49 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -340,7 +340,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 18 +--S 18 of 49 ff:=sinhsqrrule ee --R --R (8) @@ -369,7 +369,7 @@ ff:=sinhsqrrule ee --R Type: Expression Integer --E ---S 19 +--S 19 of 49 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -378,7 +378,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 20 +--S 20 of 49 gg:=coshsqrrule ff --R --R (10) @@ -401,7 +401,7 @@ gg:=coshsqrrule ff --R Type: Expression Integer --E ---S 21 +--S 21 of 49 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %O sinh(y + x) - %O sinh(y - x) @@ -410,7 +410,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 22 +--S 22 of 49 hh:=sinhcoshrule gg --R --R (12) @@ -433,7 +433,7 @@ hh:=sinhcoshrule gg --R Type: Expression Integer --E ---S 23 14:639 Schaums and Axiom agree +--S 23 of 49 14:639 Schaums and Axiom agree ii:=complexNormalize hh --R --R (13) 0 @@ -449,7 +449,7 @@ $$ <<*>>= )clear all ---S 24 +--S 24 of 49 aa:=integrate(1/csch(a*x),x) --R --R @@ -459,7 +459,7 @@ aa:=integrate(1/csch(a*x),x) --R Type: Union(Expression Integer,...) --E ---S 25 +--S 25 of 49 bb:=1/a*cosh(a*x) --R --R cosh(a x) @@ -468,7 +468,7 @@ bb:=1/a*cosh(a*x) --R Type: Expression Integer --E ---S 26 14:640 Schaums and Axiom agree +--S 26 of 49 14:640 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -486,7 +486,7 @@ $$ <<*>>= )clear all ---S 27 14:641 Axiom cannot compute this integral +--S 27 of 49 14:641 Axiom cannot compute this integral aa:=integrate(x*csch(a*x),x) --R --R @@ -506,7 +506,7 @@ $$ <<*>>= )clear all ---S 28 +--S 28 of 49 aa:=integrate(x*csch(a*x)^2,x) --R --R @@ -526,7 +526,7 @@ aa:=integrate(x*csch(a*x)^2,x) --R Type: Union(Expression Integer,...) --E ---S 29 +--S 29 of 49 bb:=-(x*coth(a*x))/a+1/a^2*log(sinh(a*x)) --R --R log(sinh(a x)) - a x coth(a x) @@ -536,7 +536,7 @@ bb:=-(x*coth(a*x))/a+1/a^2*log(sinh(a*x)) --R Type: Expression Integer --E ---S 30 +--S 30 of 49 cc:=aa-bb --R --R (3) @@ -563,7 +563,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 31 +--S 31 of 49 dd:=expandLog cc --R --R (4) @@ -585,7 +585,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 32 +--S 32 of 49 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -594,7 +594,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 33 +--S 33 of 49 ee:=sinhsqrrule dd --R --R (6) @@ -618,7 +618,7 @@ ee:=sinhsqrrule dd --R Type: Expression Integer --E ---S 34 +--S 34 of 49 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -627,7 +627,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 35 +--S 35 of 49 ff:=coshsqrrule ee --R --R (8) @@ -642,7 +642,7 @@ ff:=coshsqrrule ee --R Type: Expression Integer --E ---S 36 +--S 36 of 49 sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R --I %P sinh(y + x) - %P sinh(y - x) @@ -651,7 +651,7 @@ sinhcoshrule:=rule(sinh(x)*cosh(y) == 1/2*(sinh(x+y)+sinh(x-y))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 37 +--S 37 of 49 gg:=sinhcoshrule ff --R --R (10) @@ -666,7 +666,7 @@ gg:=sinhcoshrule ff --R Type: Expression Integer --E ---S 38 14:642 Schaums and Axiom differ by a constant +--S 38 of 49 14:642 Schaums and Axiom differ by a constant hh:=complexNormalize gg --R --R - log(- 1) + log(- 2) @@ -686,7 +686,7 @@ $$ <<*>>= )clear all ---S 39 14:643 Axiom cannot compute this integral +--S 39 of 49 14:643 Axiom cannot compute this integral aa:=integrate(csch(a*x)/x,x) --R --R @@ -706,7 +706,7 @@ $$ <<*>>= )clear all ---S 40 +--S 40 of 49 aa:=integrate(1/(q+p*csch(a*x)),x) --R --R @@ -742,7 +742,7 @@ aa:=integrate(1/(q+p*csch(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 41 +--S 41 of 49 t1:=integrate(1/(p+q*sinh(a*x)),x) --R --R (2) @@ -771,7 +771,7 @@ t1:=integrate(1/(p+q*sinh(a*x)),x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 49 bb:=x/q-p/q*t1 --R --R (3) @@ -807,7 +807,7 @@ bb:=x/q-p/q*t1 --R Type: Expression Integer --E ---S 43 +--S 43 of 49 cc:=aa-bb --R --R (4) @@ -859,7 +859,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 44 +--S 44 of 49 sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R --R 2 cosh(2x) - 1 @@ -868,7 +868,7 @@ sinhsqrrule:=rule(sinh(x)^2 == 1/2*cosh(2*x)-1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 45 +--S 45 of 49 dd:=sinhsqrrule cc --R --R (6) @@ -920,7 +920,7 @@ dd:=sinhsqrrule cc --R Type: Expression Integer --E ---S 46 +--S 46 of 49 coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R --R 2 cosh(2x) + 1 @@ -929,7 +929,7 @@ coshsqrrule:=rule(cosh(x)^2 == 1/2*cosh(2*x)+1/2) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 47 +--S 47 of 49 ee:=coshsqrrule dd --R --R (8) @@ -975,7 +975,7 @@ ee:=coshsqrrule dd --R Type: Expression Integer --E ---S 48 14:644 Schaums and Axiom differ by a constant +--S 48 of 49 14:644 Schaums and Axiom differ by a constant ff:=complexNormalize ee --R --R 4 2 2 @@ -997,7 +997,7 @@ $$ <<*>>= )clear all ---S 49 14:645 Axiom cannot compute this integral +--S 49 of 49 14:645 Axiom cannot compute this integral aa:=integrate(csch(a*x)^n,x) --R --R diff --git a/src/input/schaum34.input.pamphlet b/src/input/schaum34.input.pamphlet index d61b757..10ef92b 100644 --- a/src/input/schaum34.input.pamphlet +++ b/src/input/schaum34.input.pamphlet @@ -18,7 +18,7 @@ $$ )set message auto off )clear all ---S 1 +--S 1 of 156 aa:=integrate(asinh(x/a),x) --R --R @@ -34,7 +34,7 @@ aa:=integrate(asinh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 156 bb:=x*asinh(x/a)-sqrt(x^2+a^2) --R --R +-------+ @@ -44,7 +44,7 @@ bb:=x*asinh(x/a)-sqrt(x^2+a^2) --R Type: Expression Integer --E ---S 3 +--S 3 of 156 cc:=aa-bb --R --R +-------+ @@ -55,7 +55,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 156 asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R --R +------+ @@ -64,7 +64,7 @@ asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 +--S 5 of 156 dd:=asinhlogrule cc --R --R +-------+ @@ -78,7 +78,7 @@ dd:=asinhlogrule cc --R Type: Expression Integer --E ---S 6 +--S 6 of 156 ee:=expandLog dd --R --R +-------+ @@ -90,7 +90,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 7 14:646 Schaums and Axiom agree +--S 7 of 156 14:646 Schaums and Axiom agree ff:=rootSimp ee --R --R (7) 0 @@ -107,7 +107,7 @@ $$ <<*>>= )clear all ---S 8 +--S 8 of 156 aa:=integrate(x*asinh(x/a),x) --R --R @@ -128,7 +128,7 @@ aa:=integrate(x*asinh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 156 bb:=(x^2/2+a^2/4)*asinh(x/a)-(x*sqrt(x^2+a^2))/4 --R --R +-------+ @@ -140,7 +140,7 @@ bb:=(x^2/2+a^2/4)*asinh(x/a)-(x*sqrt(x^2+a^2))/4 --R Type: Expression Integer --E ---S 10 +--S 10 of 156 cc:=aa-bb --R --R +-------+ @@ -153,7 +153,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 11 +--S 11 of 156 asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R --R +------+ @@ -162,7 +162,7 @@ asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 12 +--S 12 of 156 dd:=asinhlogrule cc --R --R +-------+ @@ -178,7 +178,7 @@ dd:=asinhlogrule cc --R Type: Expression Integer --E ---S 13 +--S 13 of 156 ee:=expandLog dd --R --R +-------+ @@ -192,7 +192,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 14 14:647 Schaums and Axiom agree +--S 14 of 156 14:647 Schaums and Axiom agree ff:=rootSimp ee --R --R (7) 0 @@ -208,7 +208,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 156 aa:=integrate(x^2*asinh(x/a),x) --R --R @@ -229,7 +229,7 @@ aa:=integrate(x^2*asinh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 16 +--S 16 of 156 bb:=x^3/3*asinh(x/a)+((2*a^2-x^2)*sqrt(x^2+a^2))/9 --R --R +-------+ @@ -241,7 +241,7 @@ bb:=x^3/3*asinh(x/a)+((2*a^2-x^2)*sqrt(x^2+a^2))/9 --R Type: Expression Integer --E ---S 17 +--S 17 of 156 cc:=aa-bb --R --R +-------+ @@ -254,7 +254,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 18 +--S 18 of 156 asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R --R +------+ @@ -263,7 +263,7 @@ asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 19 +--S 19 of 156 dd:=asinhlogrule cc --R --R +-------+ @@ -279,7 +279,7 @@ dd:=asinhlogrule cc --R Type: Expression Integer --E ---S 20 +--S 20 of 156 ee:=expandLog dd --R --R +-------+ @@ -293,7 +293,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 21 14:648 Schaums and Axiom agree +--S 21 of 156 14:648 Schaums and Axiom agree ff:=rootSimp ee --R --R (7) 0 @@ -329,7 +329,7 @@ $$ <<*>>= )clear all ---S 22 14:649 Axiom cannot compute this integral +--S 22 of 156 14:649 Axiom cannot compute this integral aa:=integrate(asinh(x/a)/x,x) --R --R @@ -351,7 +351,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 156 aa:=integrate(asinh(x/a)/x^2,x) --R --R @@ -370,7 +370,7 @@ aa:=integrate(asinh(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 156 bb:=-asinh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -383,7 +383,7 @@ bb:=-asinh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 25 +--S 25 of 156 cc:=aa-bb --R --R (3) @@ -401,7 +401,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 26 +--S 26 of 156 asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R --R +------+ @@ -410,7 +410,7 @@ asinhlogrule:=rule(asinh(x) == log(x+sqrt(x^2+1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 27 +--S 27 of 156 dd:=asinhlogrule cc --R --R (5) @@ -431,7 +431,7 @@ dd:=asinhlogrule cc --R Type: Expression Integer --E ---S 28 +--S 28 of 156 ee:=expandLog dd --R --R (6) @@ -454,7 +454,7 @@ ee:=expandLog dd --R Type: Expression Integer --E ---S 29 +--S 29 of 156 ff:=rootSimp ee --R --R (7) @@ -468,7 +468,7 @@ ff:=rootSimp ee --R Type: Expression Integer --E ---S 30 14:650 Schaums and Axiom differ by a constant +--S 30 of 156 14:650 Schaums and Axiom differ by a constant gg:=complexNormalize ff --R --R log(- 1) @@ -494,7 +494,7 @@ $$ <<*>>= )clear all ---S 31 +--S 31 of 156 aa:=integrate(acosh(x/a),x) --R --R @@ -510,7 +510,7 @@ aa:=integrate(acosh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 32 +--S 32 of 156 bb1:=x*acosh(x/a)-sqrt(x^2-a^2) --R --R +-------+ @@ -520,7 +520,7 @@ bb1:=x*acosh(x/a)-sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 33 +--S 33 of 156 bb2:=x*acosh(x/a)+sqrt(x^2-a^2) --R --R +-------+ @@ -530,7 +530,7 @@ bb2:=x*acosh(x/a)+sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 34 +--S 34 of 156 cc1:=aa-bb1 --R --R +-------+ @@ -541,7 +541,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 35 +--S 35 of 156 cc2:=aa-bb2 --R --R (5) @@ -561,7 +561,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 36 +--S 36 of 156 acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1))) --R --R +------+ @@ -570,7 +570,7 @@ acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 37 +--S 37 of 156 dd1:=acoshlogrule cc1 --R --R +-------+ @@ -584,7 +584,7 @@ dd1:=acoshlogrule cc1 --R Type: Expression Integer --E ---S 38 +--S 38 of 156 ee1:=expandLog dd1 --R --R +-------+ @@ -596,7 +596,7 @@ ee1:=expandLog dd1 --R Type: Expression Integer --E ---S 39 14:651 Schaums and Axiom agree +--S 39 of 156 14:651 Schaums and Axiom agree ff1:=rootSimp ee1 --R --R (9) 0 @@ -623,7 +623,7 @@ $$ <<*>>= )clear all ---S 40 +--S 40 of 156 aa:=integrate(x*acosh(x/a),x) --R --R @@ -644,7 +644,7 @@ aa:=integrate(x*acosh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 41 +--S 41 of 156 bb1:=1/4*(2*x^2-a^2)*acosh(x/a)-1/4*x*sqrt(x^2-a^2) --R --R +-------+ @@ -656,7 +656,7 @@ bb1:=1/4*(2*x^2-a^2)*acosh(x/a)-1/4*x*sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 42 +--S 42 of 156 bb2:=1/4*(2*x^2-a^2)*acosh(x/a)+1/4*x*sqrt(x^2-a^2) --R --R +-------+ @@ -668,7 +668,7 @@ bb2:=1/4*(2*x^2-a^2)*acosh(x/a)+1/4*x*sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 43 +--S 43 of 156 cc1:=aa-bb1 --R --R +-------+ @@ -681,7 +681,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 44 +--S 44 of 156 cc2:=aa-bb2 --R --R (5) @@ -706,7 +706,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 45 +--S 45 of 156 acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1))) --R --R +------+ @@ -715,7 +715,7 @@ acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 46 +--S 46 of 156 dd1:=acoshlogrule cc1 --R --R +-------+ @@ -731,7 +731,7 @@ dd1:=acoshlogrule cc1 --R Type: Expression Integer --E ---S 47 +--S 47 of 156 ee1:=expandLog dd1 --R --R +-------+ @@ -745,7 +745,7 @@ ee1:=expandLog dd1 --R Type: Expression Integer --E ---S 48 14:652 Schaums and Axiom agree +--S 48 of 156 14:652 Schaums and Axiom agree ff1:=rootSimp ee1 --R --R (9) 0 @@ -771,7 +771,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 156 aa:=integrate(x^2*acosh(x/a),x) --R --R @@ -792,7 +792,7 @@ aa:=integrate(x^2*acosh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 50 +--S 50 of 156 bb1:=1/3*x^3*acosh(x/a)-1/9*(x^2+2*a^2)*sqrt(x^2-a^2) --R --R +-------+ @@ -804,7 +804,7 @@ bb1:=1/3*x^3*acosh(x/a)-1/9*(x^2+2*a^2)*sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 51 +--S 51 of 156 bb2:=1/3*x^3*acosh(x/a)+1/9*(x^2+2*a^2)*sqrt(x^2-a^2) --R --R +-------+ @@ -816,7 +816,7 @@ bb2:=1/3*x^3*acosh(x/a)+1/9*(x^2+2*a^2)*sqrt(x^2-a^2) --R Type: Expression Integer --E ---S 52 +--S 52 of 156 cc1:=aa-bb1 --R --R +-------+ @@ -829,7 +829,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 53 +--S 53 of 156 cc2:=aa-bb2 --R --R (5) @@ -854,7 +854,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 54 +--S 54 of 156 acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1))) --R --R +------+ @@ -863,7 +863,7 @@ acoshlogrule:=rule(acosh(x) == log(x+sqrt(x^2-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 55 +--S 55 of 156 dd1:=acoshlogrule cc1 --R --R +-------+ @@ -879,7 +879,7 @@ dd1:=acoshlogrule cc1 --R Type: Expression Integer --E ---S 56 +--S 56 of 156 ee1:=expandLog dd1 --R --R +-------+ @@ -893,7 +893,7 @@ ee1:=expandLog dd1 --R Type: Expression Integer --E ---S 57 14:653 Schaums and Axiom agree +--S 57 of 156 14:653 Schaums and Axiom agree ff1:=rootSimp ee1 --R --R (9) 0 @@ -918,7 +918,7 @@ $$ <<*>>= )clear all ---S 58 14:654 Axiom cannot compute this integral +--S 58 of 156 14:654 Axiom cannot compute this integral aa:=integrate(acosh(x/a)/x,x) --R --R @@ -947,7 +947,7 @@ $$ <<*>>= )clear all ---S 59 +--S 59 of 156 aa:=integrate(acosh(x/a)/x^2,x) --R --R @@ -961,7 +961,7 @@ aa:=integrate(acosh(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 60 +--S 60 of 156 bb1:=-acosh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -974,7 +974,7 @@ bb1:=-acosh(x/a)/x-1/a*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 61 +--S 61 of 156 bb2:=-acosh(x/a)/x+1/a*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -987,7 +987,7 @@ bb2:=-acosh(x/a)/x+1/a*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 62 +--S 62 of 156 cc1:=aa-bb1 --R --R (4) @@ -1005,7 +1005,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 63 14:655 Axiom cannot simplify these expressions +--S 63 of 156 14:655 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -1032,7 +1032,7 @@ $$ <<*>>= )clear all ---S 64 +--S 64 of 156 aa:=integrate(atanh(x/a),x) --R --R @@ -1044,7 +1044,7 @@ aa:=integrate(atanh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 65 +--S 65 of 156 bb:=x*atanh(x/a)+a/2*log(a^2-x^2) --R --R 2 2 x @@ -1055,7 +1055,7 @@ bb:=x*atanh(x/a)+a/2*log(a^2-x^2) --R Type: Expression Integer --E ---S 66 +--S 66 of 156 cc:=aa-bb --R --R 2 2 - x - a 2 2 x @@ -1066,7 +1066,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 67 +--S 67 of 156 atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R --R - x - 1 @@ -1077,7 +1077,7 @@ atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 68 +--S 68 of 156 dd:=atanhrule cc --R --R 2 2 2 2 @@ -1087,7 +1087,7 @@ dd:=atanhrule cc --R Type: Expression Integer --E ---S 69 14:656 Schaums and Axiom differ by a constant +--S 69 of 156 14:656 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R a log(- 1) @@ -1105,7 +1105,7 @@ $$ <<*>>= )clear all ---S 70 +--S 70 of 156 aa:=integrate(x*atanh(x/a),x) --R --R @@ -1117,7 +1117,7 @@ aa:=integrate(x*atanh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 71 +--S 71 of 156 bb:=(a*x)/2+1/2*(x^2-a^2)*atanh(x/a) --R --R 2 2 x @@ -1128,7 +1128,7 @@ bb:=(a*x)/2+1/2*(x^2-a^2)*atanh(x/a) --R Type: Expression Integer --E ---S 72 +--S 72 of 156 cc:=aa-bb --R --R 2 2 - x - a 2 2 x @@ -1139,7 +1139,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 73 +--S 73 of 156 atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R --R - x - 1 @@ -1150,7 +1150,7 @@ atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 74 14:657 Schaums and Axiom agree +--S 74 of 156 14:657 Schaums and Axiom agree dd:=atanhrule cc --R --R (5) 0 @@ -1167,7 +1167,7 @@ $$ <<*>>= )clear all ---S 75 +--S 75 of 156 aa:=integrate(x^2*atanh(x/a),x) --R --R @@ -1179,7 +1179,7 @@ aa:=integrate(x^2*atanh(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 76 +--S 76 of 156 bb:=(a*x^2)/6+x^3/3*atanh(x/a)+a^3/6*log(a^2-x^2) --R --R 3 2 2 3 x 2 @@ -1190,7 +1190,7 @@ bb:=(a*x^2)/6+x^3/3*atanh(x/a)+a^3/6*log(a^2-x^2) --R Type: Expression Integer --E ---S 77 +--S 77 of 156 cc:=aa-bb --R --R 3 2 2 3 - x - a 3 2 2 3 x @@ -1201,7 +1201,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 78 +--S 78 of 156 atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R --R - x - 1 @@ -1212,7 +1212,7 @@ atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 79 +--S 79 of 156 dd:=atanhrule cc --R --R 3 2 2 3 2 2 @@ -1222,7 +1222,7 @@ dd:=atanhrule cc --R Type: Expression Integer --E ---S 80 14:658 Schaums and Axiom differ by a constant +--S 80 of 156 14:658 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R 3 @@ -1241,7 +1241,7 @@ $$ <<*>>= )clear all ---S 81 14:659 Axiom cannot compute this integral +--S 81 of 156 14:659 Axiom cannot compute this integral aa:=integrate(atanh(x/a)/x,x) --R --R @@ -1262,7 +1262,7 @@ $$ <<*>>= )clear all ---S 82 +--S 82 of 156 aa:=integrate(atanh(x/a)/x^2,x) --R --R @@ -1274,7 +1274,7 @@ aa:=integrate(atanh(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 83 +--S 83 of 156 bb:=-atanh(x/a)/x+1/(2*a)*log(x^2/(a^2-x^2)) --R --R 2 @@ -1287,7 +1287,7 @@ bb:=-atanh(x/a)/x+1/(2*a)*log(x^2/(a^2-x^2)) --R Type: Expression Integer --E ---S 84 +--S 84 of 156 cc:=aa-bb --R --R (3) @@ -1305,7 +1305,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 85 +--S 85 of 156 atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R --R - x - 1 @@ -1316,7 +1316,7 @@ atanhrule:=rule(atanh(x) == 1/2*log((1+x)/(1-x))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 86 +--S 86 of 156 dd:=atanhrule cc --R --R 2 @@ -1329,7 +1329,7 @@ dd:=atanhrule cc --R Type: Expression Integer --E ---S 87 14:660 Schaums and Axiom agree +--S 87 of 156 14:660 Schaums and Axiom agree ee:=expandLog dd --R --R log(- 1) @@ -1352,7 +1352,7 @@ $$ <<*>>= )clear all ---S 88 +--S 88 of 156 aa:=integrate(acoth(x/a),x) --R --R @@ -1364,7 +1364,7 @@ aa:=integrate(acoth(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 89 +--S 89 of 156 bb:=x*acoth(x/a)+a/2*log(x^2-a^2) --R --R 2 2 x @@ -1375,7 +1375,7 @@ bb:=x*acoth(x/a)+a/2*log(x^2-a^2) --R Type: Expression Integer --E ---S 90 +--S 90 of 156 cc:=aa-bb --R --R x + a x @@ -1386,7 +1386,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 91 +--S 91 of 156 acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R --R x + 1 @@ -1397,7 +1397,7 @@ acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 92 14:661 Schaums and Axiom agree +--S 92 of 156 14:661 Schaums and Axiom agree dd:=acothrule cc --R --R (5) 0 @@ -1413,7 +1413,7 @@ $$ <<*>>= )clear all ---S 93 +--S 93 of 156 aa:=integrate(x*acoth(x/a),x) --R --R @@ -1425,7 +1425,7 @@ aa:=integrate(x*acoth(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 94 +--S 94 of 156 bb:=(a*x)/2+1/2*(x^2-a^2)*acoth(x/a) --R --R 2 2 x @@ -1436,7 +1436,7 @@ bb:=(a*x)/2+1/2*(x^2-a^2)*acoth(x/a) --R Type: Expression Integer --E ---S 95 +--S 95 of 156 cc:=aa-bb --R --R 2 2 x + a 2 2 x @@ -1447,7 +1447,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 96 +--S 96 of 156 acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R --R x + 1 @@ -1458,7 +1458,7 @@ acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 97 14:662 Schaums and Axiom agree +--S 97 of 156 14:662 Schaums and Axiom agree dd:=acothrule cc --R --R (5) 0 @@ -1475,7 +1475,7 @@ $$ <<*>>= )clear all ---S 98 +--S 98 of 156 aa:=integrate(x^2*acoth(x/a),x) --R --R @@ -1487,7 +1487,7 @@ aa:=integrate(x^2*acoth(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 99 +--S 99 of 156 bb:=(a*x^2)/6+x^3/3*acoth(x/a)+a^3/6*log(x^2-a^2) --R --R 3 2 2 3 x 2 @@ -1498,7 +1498,7 @@ bb:=(a*x^2)/6+x^3/3*acoth(x/a)+a^3/6*log(x^2-a^2) --R Type: Expression Integer --E ---S 100 +--S 100 of 156 cc:=aa-bb --R --R 3 x + a 3 x @@ -1509,7 +1509,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 101 +--S 101 of 156 acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R --R x + 1 @@ -1520,7 +1520,7 @@ acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 102 14:663 Schaums and Axiom agree +--S 102 of 156 14:663 Schaums and Axiom agree dd:=acothrule cc --R --R (5) 0 @@ -1536,7 +1536,7 @@ $$ <<*>>= )clear all ---S 103 14:664 Axiom cannot compute this integral +--S 103 of 156 14:664 Axiom cannot compute this integral aa:=integrate(acoth(x/a)/x,x) --R --R @@ -1557,7 +1557,7 @@ $$ <<*>>= )clear all ---S 104 +--S 104 of 156 aa:=integrate(acoth(x/a)/x^2,x) --R --R @@ -1569,7 +1569,7 @@ aa:=integrate(acoth(x/a)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 105 +--S 105 of 156 bb:=-acoth(x/a)/x+1/(2*a)*log(x^2/(x^2-a^2)) --R --R 2 @@ -1582,7 +1582,7 @@ bb:=-acoth(x/a)/x+1/(2*a)*log(x^2/(x^2-a^2)) --R Type: Expression Integer --E ---S 106 +--S 106 of 156 cc:=aa-bb --R --R (3) @@ -1596,7 +1596,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 107 +--S 107 of 156 acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R --R x + 1 @@ -1607,7 +1607,7 @@ acothrule:=rule(acoth(x) == 1/2*log((x+1)/(x-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 108 +--S 108 of 156 dd:=acothrule cc --R --R 2 @@ -1620,7 +1620,7 @@ dd:=acothrule cc --R Type: Expression Integer --E ---S 109 14:665 Schaums and Axiom agree +--S 109 of 156 14:665 Schaums and Axiom agree ee:=expandLog dd --R --R (6) 0 @@ -1644,7 +1644,7 @@ $$ <<*>>= )clear all ---S 110 +--S 110 of 156 aa:=integrate(asech(x/a),x) --R --R @@ -1656,7 +1656,7 @@ aa:=integrate(asech(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 111 +--S 111 of 156 bb1:=x*asech(x/a)+a*asin(x/a) --R --R x x @@ -1665,7 +1665,7 @@ bb1:=x*asech(x/a)+a*asin(x/a) --R Type: Expression Integer --E ---S 112 +--S 112 of 156 bb2:=x*asech(x/a)-a*asin(x/a) --R --R x x @@ -1674,7 +1674,7 @@ bb2:=x*asech(x/a)-a*asin(x/a) --R Type: Expression Integer --E ---S 113 +--S 113 of 156 cc1:=aa-bb1 --R --R (4) @@ -1686,7 +1686,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 114 +--S 114 of 156 cc2:=aa-bb2 --R --R (5) @@ -1698,7 +1698,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 115 +--S 115 of 156 asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1))) --R --R +--------+ @@ -1712,7 +1712,7 @@ asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 116 +--S 116 of 156 dd1:=asechrule cc1 --R --R (7) @@ -1733,7 +1733,7 @@ dd1:=asechrule cc1 --R Type: Expression Integer --E ---S 117 +--S 117 of 156 asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R --R +--------+ @@ -1742,7 +1742,7 @@ asinrule:=rule(asin(x) == %i*log(-%i*x+sqrt(1-x^2))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 118 +--S 118 of 156 ee1:=asinrule dd1 --R --R (9) @@ -1763,7 +1763,7 @@ ee1:=asinrule dd1 --R Type: Expression Complex Integer --E ---S 119 +--S 119 of 156 atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R --R - x + %i @@ -1774,7 +1774,7 @@ atanrule:=rule(atan(x) == -%i/2*log((1+%i*x)/(1-%i*x))) --R Type: RewriteRule(Integer,Complex Integer,Expression Complex Integer) --E ---S 120 +--S 120 of 156 ff1:=atanrule ee1 --R --R (11) @@ -1797,7 +1797,7 @@ ff1:=atanrule ee1 --R Type: Expression Complex Integer --E ---S 121 +--S 121 of 156 gg1:=expandLog ff1 --R --R (12) @@ -1818,7 +1818,7 @@ gg1:=expandLog ff1 --R Type: Expression Complex Integer --E ---S 122 +--S 122 of 156 hh1:=rootSimp gg1 --R --R (13) @@ -1832,7 +1832,7 @@ hh1:=rootSimp gg1 --R Type: Expression Complex Integer --E ---S 123 14:666 Schaums and Axiom agree +--S 123 of 156 14:666 Schaums and Axiom agree ii1:=complexNormalize hh1 --R --R (14) 0 @@ -1844,7 +1844,7 @@ Note that Axiom has a built-in assumption about the sign of asech(x/a). We can see this if we simplify the cc2 value and show that it differs by a complex value of x. <<*>>= ---S 124 +--S 124 of 156 dd2:=asechrule cc2 --R --R (15) @@ -1865,7 +1865,7 @@ dd2:=asechrule cc2 --R Type: Expression Integer --E ---S 125 +--S 125 of 156 ee2:=asinrule dd2 --R --R (16) @@ -1886,7 +1886,7 @@ ee2:=asinrule dd2 --R Type: Expression Complex Integer --E ---S 126 +--S 126 of 156 ff2:=atanrule ee2 --R --R (17) @@ -1909,7 +1909,7 @@ ff2:=atanrule ee2 --R Type: Expression Complex Integer --E ---S 127 +--S 127 of 156 gg2:=expandLog ff2 --R --R (18) @@ -1930,7 +1930,7 @@ gg2:=expandLog ff2 --R Type: Expression Complex Integer --E ---S 128 +--S 128 of 156 hh2:=rootSimp gg2 --R --R (19) @@ -1944,7 +1944,7 @@ hh2:=rootSimp gg2 --R Type: Expression Complex Integer --E ---S 129 +--S 129 of 156 ii2:=complexNormalize hh2 --R --R +-------+ @@ -1976,7 +1976,7 @@ $$ <<*>>= )clear all ---S 130 +--S 130 of 156 aa:=integrate(x*asech(x/a),x) --R --R @@ -1992,7 +1992,7 @@ aa:=integrate(x*asech(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 131 +--S 131 of 156 bb1:=1/2*x^2*asech(x/a)-1/2*a*sqrt(a^2-x^2) --R --R +---------+ @@ -2004,7 +2004,7 @@ bb1:=1/2*x^2*asech(x/a)-1/2*a*sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 132 +--S 132 of 156 bb2:=1/2*x^2*asech(x/a)+1/2*a*sqrt(a^2-x^2) --R --R +---------+ @@ -2016,7 +2016,7 @@ bb2:=1/2*x^2*asech(x/a)+1/2*a*sqrt(a^2-x^2) --R Type: Expression Integer --E ---S 133 +--S 133 of 156 cc1:=aa-bb1 --R --R +---------+ @@ -2029,7 +2029,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 134 +--S 134 of 156 cc2:=aa-bb2 --R --R (5) @@ -2050,7 +2050,7 @@ cc2:=aa-bb2 --R Type: Expression Integer --E ---S 135 +--S 135 of 156 asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1))) --R --R +--------+ @@ -2064,7 +2064,7 @@ asechrule:=rule(asech(x) == log(1/x+sqrt(1/x^2-1))) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 136 +--S 136 of 156 dd1:=asechrule cc1 --R --R +---------+ @@ -2080,7 +2080,7 @@ dd1:=asechrule cc1 --R Type: Expression Integer --E ---S 137 +--S 137 of 156 ee1:=expandLog dd1 --R --R +---------+ @@ -2094,7 +2094,7 @@ ee1:=expandLog dd1 --R Type: Expression Integer --E ---S 138 14:667 Schaums and Axiom differ by a constant +--S 138 of 156 14:667 Schaums and Axiom differ by a constant ff1:=rootSimp ee1 --R --R 2 @@ -2128,7 +2128,7 @@ solution to the problem but Schaums gives a series solution. <<*>>= )clear all ---S 139 14:668 Axiom cannot compute this integral +--S 139 of 156 14:668 Axiom cannot compute this integral aa:=integrate(asech(x/a)/x,x) --R --R @@ -2150,7 +2150,7 @@ $$ <<*>>= )clear all ---S 140 +--S 140 of 156 aa:=integrate(acsch(x/a),x) --R --R @@ -2162,7 +2162,7 @@ aa:=integrate(acsch(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 141 +--S 141 of 156 bb1:=x*acsch(x/a)+a*asinh(x/a) --R --R x x @@ -2171,7 +2171,7 @@ bb1:=x*acsch(x/a)+a*asinh(x/a) --R Type: Expression Integer --E ---S 142 +--S 142 of 156 bb2:=x*acsch(x/a)-a*asinh(x/a) --R --R x x @@ -2180,7 +2180,7 @@ bb2:=x*acsch(x/a)-a*asinh(x/a) --R Type: Expression Integer --E ---S 143 +--S 143 of 156 cc1:=aa-bb1 --R --R (4) @@ -2192,7 +2192,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 144 14:669 Axiom cannot simplify these expressions +--S 144 of 156 14:669 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -2214,7 +2214,7 @@ $$ <<*>>= )clear all ---S 145 +--S 145 of 156 aa:=integrate(x*acsch(x/a),x) --R --R @@ -2230,7 +2230,7 @@ aa:=integrate(x*acsch(x/a),x) --R Type: Union(Expression Integer,...) --E ---S 146 +--S 146 of 156 bb1:=x^2/2*acsch(x/a)+(a*sqrt(x^2+a^2))/2 --R --R +-------+ @@ -2242,7 +2242,7 @@ bb1:=x^2/2*acsch(x/a)+(a*sqrt(x^2+a^2))/2 --R Type: Expression Integer --E ---S 147 +--S 147 of 156 bb2:=x^2/2*acsch(x/a)-(a*sqrt(x^2+a^2))/2 --R --R +-------+ @@ -2254,7 +2254,7 @@ bb2:=x^2/2*acsch(x/a)-(a*sqrt(x^2+a^2))/2 --R Type: Expression Integer --E ---S 148 +--S 148 of 156 cc1:=aa-bb1 --R --R +-------+ @@ -2267,7 +2267,7 @@ cc1:=aa-bb1 --R Type: Expression Integer --E ---S 149 14:670 Axiom cannot simplify these expressions +--S 149 of 156 14:670 Axiom cannot simplify these expressions cc2:=aa-bb2 --R --R (5) @@ -2316,7 +2316,7 @@ but Axiom has computed a closed form. <<*>>= )clear all ---S 150 14:671 Axiom cannot compute this integral +--S 150 of 156 14:671 Axiom cannot compute this integral aa:=integrate(acsch(x/a)/x,x) --R --R @@ -2339,7 +2339,7 @@ $$ <<*>>= )clear all ---S 151 14:672 Axiom cannot compute this integral +--S 151 of 156 14:672 Axiom cannot compute this integral aa:=integrate(x^m*asinh(x/a),x) --R --R @@ -2371,7 +2371,7 @@ $$ <<*>>= )clear all ---S 152 14:673 Axiom cannot compute this integral +--S 152 of 156 14:673 Axiom cannot compute this integral aa:=integrate(x^m*acosh(x/a),x) --R --R @@ -2392,7 +2392,7 @@ $$ <<*>>= )clear all ---S 153 14:674 Axiom cannot compute this integral +--S 153 of 156 14:674 Axiom cannot compute this integral aa:=integrate(x^m*atanh(x/a),x) --R --R @@ -2413,7 +2413,7 @@ $$ <<*>>= )clear all ---S 154 14:675 Axiom cannot compute this integral +--S 154 of 156 14:675 Axiom cannot compute this integral aa:=integrate(x^m*acoth(x/a),x) --R --R @@ -2445,7 +2445,7 @@ $$ <<*>>= )clear all ---S 155 14:676 Axiom cannot compute this integral +--S 155 of 156 14:676 Axiom cannot compute this integral aa:=integrate(x^m*asech(x/a),x) --R --R @@ -2468,7 +2468,7 @@ $$ <<*>>= )clear all ---S 156 14:677 Axiom cannot compute this integral +--S 156 of 156 14:677 Axiom cannot compute this integral aa:=integrate(x^m*acsch(x/a),x) --R --R diff --git a/src/input/schaum4.input.pamphlet b/src/input/schaum4.input.pamphlet index 0edbbf9..26dd9f9 100644 --- a/src/input/schaum4.input.pamphlet +++ b/src/input/schaum4.input.pamphlet @@ -16,7 +16,7 @@ $$\int{\frac{px+q}{\sqrt{ax+b}}}= )set message auto off )clear all ---S 1 +--S 1 of 25 aa:=integrate((p*x+q)/sqrt(a*x+b),x) --R --R @@ -28,7 +28,7 @@ aa:=integrate((p*x+q)/sqrt(a*x+b),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 25 bb:=(2*(a*p*x+3*a*q-2*b*p))/(3*a^2)*sqrt(a*x+b) --R --R +-------+ @@ -39,7 +39,7 @@ bb:=(2*(a*p*x+3*a*q-2*b*p))/(3*a^2)*sqrt(a*x+b) --R Type: Expression Integer --E ---S 3 14:113 Schaums and Axiom agree +--S 3 of 25 14:113 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -61,7 +61,7 @@ $$ <<*>>= )clear all ---S 4 +--S 4 of 25 aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x) --R --R @@ -87,7 +87,7 @@ aa:=integrate(1/((p*x+q)*sqrt(a*x+b)),x) --R Type: Union(List Expression Integer,...) --E ---S 5 +--S 5 of 25 aa1:=aa.1 --R --R (2) @@ -103,7 +103,7 @@ aa1:=aa.1 --R Type: Expression Integer --E ---S 6 +--S 6 of 25 aa2:=aa.2 --R --R +------------+ @@ -118,7 +118,7 @@ aa2:=aa.2 --R Type: Expression Integer --E ---S 7 +--S 7 of 25 bb1:=1/sqrt(b*p-a*q)*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q))) --R --R +-----------+ +-----------+ @@ -132,7 +132,7 @@ bb1:=1/sqrt(b*p-a*q)*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b --R Type: Expression Integer --E ---S 8 +--S 8 of 25 bb2:=2/(sqrt(a*q-b*p)*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p))) --R --R +-----------+ @@ -145,7 +145,7 @@ bb2:=2/(sqrt(a*q-b*p)*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p))) --R Type: Expression Integer --E ---S 9 +--S 9 of 25 cc1:=aa1-bb1 --R --R (6) @@ -170,7 +170,7 @@ cc1:=aa1-bb1 --R Type: Expression Integer --E ---S 10 +--S 10 of 25 cc2:=aa1-bb2 --R --R (7) @@ -194,7 +194,7 @@ cc2:=aa1-bb2 --R Type: Expression Integer --E ---S 11 +--S 11 of 25 cc3:=aa2-bb1 --R --R (8) @@ -216,7 +216,7 @@ cc3:=aa2-bb1 --R Type: Expression Integer --E ---S 12 14:114 Axiom cannot simplify these answers +--S 12 of 25 14:114 Axiom cannot simplify these answers cc4:=aa2-bb2 --R --R (9) @@ -252,7 +252,7 @@ $$\int{\frac{\sqrt{ax+b}}{px+q}}= <<*>>= )clear all ---S 13 +--S 13 of 25 aa:=integrate(sqrt(a*x+b)/(p*x+q),x) --R --R @@ -282,7 +282,7 @@ aa:=integrate(sqrt(a*x+b)/(p*x+q),x) --R Type: Union(List Expression Integer,...) --E ---S 14 +--S 14 of 25 aa1:=aa.1 --R --R (2) @@ -300,7 +300,7 @@ aa1:=aa.1 --R Type: Expression Integer --E ---S 15 +--S 15 of 25 aa2:=aa.2 --R --R +---------+ +-------+ @@ -315,7 +315,7 @@ aa2:=aa.2 --R Type: Expression Integer --E ---S 16 +--S 16 of 25 bb1:=(2*sqrt(a*x+b))/p+sqrt(b*p-a*q)/(p*sqrt(p))*log((sqrt(p*(a*x+b))-sqrt(b*p-a*q))/(sqrt(p*(a*x+b))+sqrt(b*p-a*q))) --R --R +-----------+ +-----------+ @@ -329,7 +329,7 @@ bb1:=(2*sqrt(a*x+b))/p+sqrt(b*p-a*q)/(p*sqrt(p))*log((sqrt(p*(a*x+b))-sqrt(b*p-a --R Type: Expression Integer --E ---S 17 +--S 17 of 25 bb2:=(2*sqrt(a*x+b))/p-(2*sqrt(a*q-b*p))/(p*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q-b*p))) --R --R +-----------+ @@ -342,7 +342,7 @@ bb2:=(2*sqrt(a*x+b))/p-(2*sqrt(a*q-b*p))/(p*sqrt(p))*atan(sqrt((p*(a*x+b))/(a*q- --R Type: Expression Integer --E ---S 18 +--S 18 of 25 cc1:=aa1-bb1 --R --R (6) @@ -364,7 +364,7 @@ cc1:=aa1-bb1 --R Type: Expression Integer --E ---S 19 +--S 19 of 25 cc2:=aa1-bb2 --R --R (7) @@ -385,7 +385,7 @@ cc2:=aa1-bb2 --R Type: Expression Integer --E ---S 20 +--S 20 of 25 cc3:=aa2-bb1 --R --R (8) @@ -408,7 +408,7 @@ cc3:=aa2-bb1 --R Type: Expression Integer --E ---S 21 14:115 Axiom cannot simplify these answers +--S 21 of 25 14:115 Axiom cannot simplify these answers cc4:=aa2-bb2 --R --R (9) @@ -435,7 +435,7 @@ $$\int{(px+b)^n\sqrt{ax+b}}= <<*>>= )clear all ---S 22 14:116 Axiom cannot compute this integral +--S 22 of 25 14:116 Axiom cannot compute this integral aa:=integrate((p*x+q)^n*sqrt(a*x+b),x) --R --R @@ -457,7 +457,7 @@ $$\int{\frac{1}{(px+b)^n\sqrt{ax+b}}}= <<*>>= )clear all ---S 23 14:117 Axiom cannot compute this integral +--S 23 of 25 14:117 Axiom cannot compute this integral aa:=integrate(1/((p*x+q)^n*sqrt(a*x+b)),x) --R --R @@ -479,7 +479,7 @@ $$\int{\frac{(px+q)^n}{\sqrt{ax+b}}}= <<*>>= )clear all ---S 24 14:118 Axiom cannot compute this integral +--S 24 of 25 14:118 Axiom cannot compute this integral aa:=integrate((p*x+q)^n/sqrt(a*x+b),x) --R --R @@ -500,7 +500,7 @@ $$\int{\frac{\sqrt{ax+b}}{(px+q)^n}}= <<*>>= )clear all ---S 25 14:119 Axiom cannot compute this integral +--S 25 of 25 14:119 Axiom cannot compute this integral aa:=integrate(sqrt(a*x+b)/(p*x+q)^n,x) --R --R diff --git a/src/input/schaum5.input.pamphlet b/src/input/schaum5.input.pamphlet index a5d3fc3..81784b7 100644 --- a/src/input/schaum5.input.pamphlet +++ b/src/input/schaum5.input.pamphlet @@ -22,7 +22,7 @@ $$\int{\frac{1}{\sqrt{(ax+b)(px+q)}}}= )set message auto off )clear all ---S 1 +--S 1 of 45 aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x) --R --R @@ -54,7 +54,7 @@ aa:=integrate(1/sqrt((a*x+b)*(p*x+q)),x) --R Type: Union(List Expression Integer,...) --E ---S 2 +--S 2 of 45 aa1:=aa.1 --R --R (2) @@ -75,7 +75,7 @@ aa1:=aa.1 --R Type: Expression Integer --E ---S 3 +--S 3 of 45 aa2:=aa.2 --R --R +---------------------------+ @@ -89,7 +89,7 @@ aa2:=aa.2 --R Type: Expression Integer --E ---S 4 +--S 4 of 45 bb1:=2/sqrt(a*p)*log(sqrt(a*(p*x+q))+sqrt(p*(a*x+b))) --R --R +-----------+ +-----------+ @@ -100,7 +100,7 @@ bb1:=2/sqrt(a*p)*log(sqrt(a*(p*x+q))+sqrt(p*(a*x+b))) --R Type: Expression Integer --E ---S 5 +--S 5 of 45 bb2:=2/sqrt(-a*p)*atan(sqrt((-p*(a*x+b))/(a*(p*x+q)))) --R --R +-------------+ @@ -113,7 +113,7 @@ bb2:=2/sqrt(-a*p)*atan(sqrt((-p*(a*x+b))/(a*(p*x+q)))) --R Type: Expression Integer --E ---S 6 +--S 6 of 45 cc1:=aa1-bb1 --R --R (6) @@ -137,7 +137,7 @@ cc1:=aa1-bb1 --R Type: Expression Integer --E ---S 7 +--S 7 of 45 cc2:=aa1-bb2 --R --R (7) @@ -166,7 +166,7 @@ cc2:=aa1-bb2 --R Type: Expression Integer --E ---S 8 +--S 8 of 45 cc3:=aa2-bb1 --R --R (8) @@ -184,7 +184,7 @@ cc3:=aa2-bb1 --R Type: Expression Integer --E ---S 9 14:120 Axiom cannot simplify these answers +--S 9 of 45 14:120 Axiom cannot simplify these answers cc4:=aa2-bb2 --R --R (9) @@ -215,7 +215,7 @@ $$ <<*>>= )clear all ---S 10 +--S 10 of 45 aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x) --R --R @@ -285,7 +285,7 @@ aa:=integrate(x/sqrt((a*x+b)*(p*x+q)),x) --R Type: Union(List Expression Integer,...) --E ---S 11 +--S 11 of 45 bb1:=integrate(1/(sqrt(a*x+b)*(p*x+q)),x) --R --R (2) @@ -310,7 +310,7 @@ bb1:=integrate(1/(sqrt(a*x+b)*(p*x+q)),x) --R Type: Union(List Expression Integer,...) --E ---S 12 +--S 12 of 45 bb2:=sqrt((a*x+b)*(p*x+q))/(a*p)-(b*p+a*q)/(2*a*p) --R --R +---------------------------+ @@ -321,7 +321,7 @@ bb2:=sqrt((a*x+b)*(p*x+q))/(a*p)-(b*p+a*q)/(2*a*p) --R Type: Expression Integer --E ---S 13 +--S 13 of 45 bb:=bb2*bb1 --R --R (4) @@ -353,7 +353,7 @@ bb:=bb2*bb1 --R Type: Vector Expression Integer --E ---S 14 14:121 Axiom cannot simplify this answer +--S 14 of 45 14:121 Axiom cannot simplify this answer cc:=aa-bb --R --R (5) @@ -475,7 +475,7 @@ $$ <<*>>= )clear all ---S 15 +--S 15 of 45 aa:=integrate(sqrt((a*x+b)*(p*x+q)),x) --R --R @@ -625,7 +625,7 @@ aa:=integrate(sqrt((a*x+b)*(p*x+q)),x) @ Since there are two parts to the aa variable we split them: <<*>>= ---S 16 +--S 16 of 45 aa1:=aa.1 --R --R (2) @@ -703,7 +703,7 @@ aa1:=aa.1 --R Type: Expression Integer --E ---S 17 +--S 17 of 45 aa2:=aa.2 --R --R (3) @@ -778,7 +778,7 @@ aa2:=aa.2 We break the books answer into 3 parts, the first term, the coefficient of the second term, and the integral. <<*>>= ---S 18 +--S 18 of 45 bba:=((2*a*p*x+b*p+a*q)/(4*a*p))*sqrt((a*x+b)*(p*x+q)) --R --R +---------------------------+ @@ -789,7 +789,7 @@ bba:=((2*a*p*x+b*p+a*q)/(4*a*p))*sqrt((a*x+b)*(p*x+q)) --R Type: Expression Integer --E ---S 19 +--S 19 of 45 bbb:=-(b*p-a*q)^2/(8*a*p) --R --R 2 2 2 2 @@ -799,7 +799,7 @@ bbb:=-(b*p-a*q)^2/(8*a*p) --R Type: Fraction Polynomial Integer --E ---S 20 +--S 20 of 45 bbc:=integrate(1/sqrt((a*x+b)*(p*x+q)),x) --R --R (6) @@ -832,7 +832,7 @@ bbc:=integrate(1/sqrt((a*x+b)*(p*x+q)),x) @ Since the integral has two parts, we break them apart <<*>>= ---S 21 +--S 21 of 45 bbc1:=bbc.1 --R --R (7) @@ -853,7 +853,7 @@ bbc1:=bbc.1 --R Type: Expression Integer --E ---S 22 +--S 22 of 45 bbc2:=bbc.2 --R --R +---------------------------+ @@ -869,7 +869,7 @@ bbc2:=bbc.2 @ And now we construct the two bb answers based on the integral parts <<*>>= ---S 23 +--S 23 of 45 bb1:=bba+bbb*bbc1 --R --R (9) @@ -897,7 +897,7 @@ bb1:=bba+bbb*bbc1 --R Type: Expression Integer --E ---S 24 +--S 24 of 45 bb2:=bba+bbb*bbc2 --R --R (10) @@ -922,7 +922,7 @@ bb2:=bba+bbb*bbc2 So there are 4 possible combinations that might yield an answer. We construct all four. <<*>>= ---S 25 +--S 25 of 45 cc1:=aa1-bb1 --R --R (11) @@ -1022,7 +1022,7 @@ cc1:=aa1-bb1 --R Type: Expression Integer --E ---S 26 +--S 26 of 45 cc2:=aa1-bb2 --R --R (12) @@ -1122,7 +1122,7 @@ cc2:=aa1-bb2 --R Type: Expression Integer --E ---S 27 +--S 27 of 45 cc3:=aa1-bb1 --R --R (13) @@ -1222,7 +1222,7 @@ cc3:=aa1-bb1 --R Type: Expression Integer --E ---S 28 14:122 Axiom cannot simplify this answer +--S 28 of 45 14:122 Axiom cannot simplify this answer cc4:=aa2-bb2 --R --R (14) @@ -1264,7 +1264,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 45 aa:=integrate(sqrt((p*x+q)/(a*x+b)),x) --R --R @@ -1297,7 +1297,7 @@ aa:=integrate(sqrt((p*x+q)/(a*x+b)),x) --R Type: Union(List Expression Integer,...) --E ---S 30 +--S 30 of 45 aa1:=aa.1 --R --R (2) @@ -1316,7 +1316,7 @@ aa1:=aa.1 --R Type: Expression Integer --E ---S 31 +--S 31 of 45 aa2:=aa.2 --R --R +-------+ @@ -1331,7 +1331,7 @@ aa2:=aa.2 --R Type: Expression Integer --E ---S 32 +--S 32 of 45 bba:=sqrt((a*x+b)*(p*x+q))/a --R --R +---------------------------+ @@ -1342,7 +1342,7 @@ bba:=sqrt((a*x+b)*(p*x+q))/a --R Type: Expression Integer --E ---S 33 +--S 33 of 45 bbb:=(a*q-b*p)/(2*a) --R --R a q - b p @@ -1351,7 +1351,7 @@ bbb:=(a*q-b*p)/(2*a) --R Type: Fraction Polynomial Integer --E ---S 34 +--S 34 of 45 bbc:=integrate(1/(sqrt((a*x+b)*(p*x+q))),x) --R --R (6) @@ -1382,7 +1382,7 @@ bbc:=integrate(1/(sqrt((a*x+b)*(p*x+q))),x) --R Type: Union(List Expression Integer,...) --E ---S 35 +--S 35 of 45 bbc1:=bbc.1 --R --R (7) @@ -1403,7 +1403,7 @@ bbc1:=bbc.1 --R Type: Expression Integer --E ---S 36 +--S 36 of 45 bbc2:=bbc.2 --R --R +---------------------------+ @@ -1417,7 +1417,7 @@ bbc2:=bbc.2 --R Type: Expression Integer --E ---S 37 +--S 37 of 45 bb1:=bba+bbb*bbc1 --R --R (9) @@ -1444,7 +1444,7 @@ bb1:=bba+bbb*bbc1 --R Type: Expression Integer --E ---S 38 +--S 38 of 45 bb2:=bba+bbb*bbc2 --R --R (10) @@ -1463,7 +1463,7 @@ bb2:=bba+bbb*bbc2 --R Type: Expression Integer --E ---S 39 +--S 39 of 45 cc1:=aa1-bb1 --R --R (11) @@ -1496,7 +1496,7 @@ cc1:=aa1-bb1 --R Type: Expression Integer --E ---S 40 +--S 40 of 45 cc2:=aa1-bb2 --R --R (12) @@ -1531,7 +1531,7 @@ cc2:=aa1-bb2 --R Type: Expression Integer --E ---S 41 +--S 41 of 45 cc3:=aa2-bb1 --R --R (13) @@ -1571,7 +1571,7 @@ cc3:=aa2-bb1 --R Type: Expression Integer --E ---S 42 14:123 Axiom cannot simplify these results +--S 42 of 45 14:123 Axiom cannot simplify these results cc4:=aa2-bb2 --R --R (14) @@ -1610,7 +1610,7 @@ $$ <<*>>= )clear all ---S 43 +--S 43 of 45 aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x) --R --R @@ -1622,7 +1622,7 @@ aa:=integrate(1/((p*x+q)*sqrt((a*x+b)*(p*x+q))),x) --R Type: Union(Expression Integer,...) --E ---S 44 +--S 44 of 45 bb:=(2*sqrt(a*x+b))/((a*q-b*p)*sqrt(p*x+q)) --R --R +-------+ @@ -1633,7 +1633,7 @@ bb:=(2*sqrt(a*x+b))/((a*q-b*p)*sqrt(p*x+q)) --R Type: Expression Integer --E ---S 45 14:124 Axiom cannot simplify this result +--S 45 of 45 14:124 Axiom cannot simplify this result cc:=aa-bb --R --R (3) diff --git a/src/input/schaum6.input.pamphlet b/src/input/schaum6.input.pamphlet index ca2c6aa..82b1d2b 100644 --- a/src/input/schaum6.input.pamphlet +++ b/src/input/schaum6.input.pamphlet @@ -15,7 +15,7 @@ $$\int{\frac{1}{x^2+a^2}}=\frac{1}{a}\tan^{-1}\frac{x}{a}$$ )set message auto off )clear all ---S 1 +--S 1 of 68 aa:=integrate(1/(x^2+a^2),x) --R --R @@ -27,7 +27,7 @@ aa:=integrate(1/(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 68 bb:=(1/a)*atan(x/a) --R --R x @@ -38,7 +38,7 @@ bb:=(1/a)*atan(x/a) --R Type: Expression Integer --E ---S 3 14:125 Schaums and Axiom agree +--S 3 of 68 14:125 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -52,7 +52,7 @@ $$\int{\frac{x}{x^2+a^2}}=\frac{1}{2}\ln(x^2+a^2)$$ <<*>>= )clear all ---S 4 +--S 4 of 68 aa:=integrate(x/(x^2+a^2),x) --R --R @@ -63,7 +63,7 @@ aa:=integrate(x/(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 5 +--S 5 of 68 bb:=(1/2)*log(x^2+a^2) --R --R 2 2 @@ -73,7 +73,7 @@ bb:=(1/2)*log(x^2+a^2) --R Type: Expression Integer --E ---S 6 14:126 Schaums and Axiom agree +--S 6 of 68 14:126 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -86,7 +86,7 @@ $$\int{\frac{x^2}{x^2+a^2}}=x-a\tan^{-1}\frac{x}{a}$$ <<*>>= )clear all ---S 7 +--S 7 of 68 aa:=integrate(x^2/(x^2+a^2),x) --R --R @@ -96,7 +96,7 @@ aa:=integrate(x^2/(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 8 +--S 8 of 68 bb:=x-a*atan(x/a) --R --R x @@ -105,7 +105,7 @@ bb:=x-a*atan(x/a) --R Type: Expression Integer --E ---S 9 14:127 Schaums and Axiom agree +--S 9 of 68 14:127 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -120,7 +120,7 @@ $$\int{\frac{x^3}{x^2+a^2}}=\frac{x^2}{2}-\frac{a^2}{2}\ln(x^2+a^2)$$ <<*>>= )clear all ---S 10 +--S 10 of 68 aa:=integrate(x^3/(x^2+a^2),x) --R --R @@ -131,7 +131,7 @@ aa:=integrate(x^3/(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 11 +--S 11 of 68 bb:=x^2/2-a^2/2*log(x^2+a^2) --R --R 2 2 2 2 @@ -141,7 +141,7 @@ bb:=x^2/2-a^2/2*log(x^2+a^2) --R Type: Expression Integer --E ---S 12 14:128 Schaums and Axiom agree +--S 12 of 68 14:128 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -156,7 +156,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 68 aa:=integrate(1/(x*(x^2+a^2)),x) --R --R @@ -168,7 +168,7 @@ aa:=integrate(1/(x*(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 68 bb:=1/(2*a^2)*log(x^2/(x^2+a^2)) --R --R 2 @@ -182,7 +182,7 @@ bb:=1/(2*a^2)*log(x^2/(x^2+a^2)) --R Type: Expression Integer --E ---S 15 +--S 15 of 68 cc:=aa-bb --R --R 2 @@ -196,7 +196,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 16 +--S 16 of 68 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -205,7 +205,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 17 +--S 17 of 68 dd:=divlog cc --R --R 2 @@ -216,7 +216,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 18 +--S 18 of 68 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -224,7 +224,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 19 14:129 Schaums and Axiom agree +--S 19 of 68 14:129 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -240,7 +240,7 @@ $$ <<*>>= )clear all ---S 20 +--S 20 of 68 aa:=integrate(1/(x^2*(x^2+a^2)),x) --R --R @@ -253,7 +253,7 @@ aa:=integrate(1/(x^2*(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 68 bb:=-1/(a^2*x)-1/a^3*atan(x/a) --R --R x @@ -265,7 +265,7 @@ bb:=-1/(a^2*x)-1/a^3*atan(x/a) --R Type: Expression Integer --E ---S 22 14:130 Schaums and Axiom agree +--S 22 of 68 14:130 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -281,7 +281,7 @@ $$ <<*>>= )clear all ---S 23 +--S 23 of 68 aa:=integrate(1/(x^3*(x^2+a^2)),x) --R --R @@ -293,7 +293,7 @@ aa:=integrate(1/(x^3*(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 24 +--S 24 of 68 bb:=-1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2+a^2)) --R --R 2 @@ -307,7 +307,7 @@ bb:=-1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2+a^2)) --R Type: Expression Integer --E ---S 25 +--S 25 of 68 cc:=aa-bb --R --R 2 @@ -321,7 +321,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 26 +--S 26 of 68 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -330,7 +330,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 27 +--S 27 of 68 dd:=divlog cc --R --R 2 @@ -341,7 +341,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 28 +--S 28 of 68 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -349,7 +349,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 29 14:131 Schaums and Axiom agree +--S 29 of 68 14:131 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -365,7 +365,7 @@ $$ <<*>>= )clear all ---S 30 +--S 30 of 68 aa:=integrate(1/((x^2+a^2)^2),x) --R --R @@ -378,7 +378,7 @@ aa:=integrate(1/((x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 31 +--S 31 of 68 bb:=x/(2*a^2*(x^2+a^2))+1/(2*a^3)*atan(x/a) --R --R 2 2 x @@ -390,7 +390,7 @@ bb:=x/(2*a^2*(x^2+a^2))+1/(2*a^3)*atan(x/a) --R Type: Expression Integer --E ---S 32 14:132 Schaums and Axiom agree +--S 32 of 68 14:132 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -406,7 +406,7 @@ $$ <<*>>= )clear all ---S 33 +--S 33 of 68 aa:=integrate(x/((x^2+a^2)^2),x) --R --R @@ -417,7 +417,7 @@ aa:=integrate(x/((x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 34 +--S 34 of 68 bb:=-1/(2*(x^2+a^2)) --R --R 1 @@ -427,7 +427,7 @@ bb:=-1/(2*(x^2+a^2)) --R Type: Fraction Polynomial Integer --E ---S 35 14:133 Schaums and Axiom agree +--S 35 of 68 14:133 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -442,7 +442,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 68 aa:=integrate(x^2/((x^2+a^2)^2),x) --R --R @@ -455,7 +455,7 @@ aa:=integrate(x^2/((x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 68 bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a) --R --R 2 2 x @@ -467,7 +467,7 @@ bb:=-x/(2*(x^2+a^2))+1/(2*a)*atan(x/a) --R Type: Expression Integer --E ---S 38 14:134 Schaums and Axiom agree +--S 38 of 68 14:134 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -482,7 +482,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 68 aa:=integrate(x^3/((x^2+a^2)^2),x) --R --R @@ -494,7 +494,7 @@ aa:=integrate(x^3/((x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 68 bb:=a^2/(2*(x^2+a^2))+1/2*log(x^2+a^2) --R --R 2 2 2 2 2 @@ -505,7 +505,7 @@ bb:=a^2/(2*(x^2+a^2))+1/2*log(x^2+a^2) --R Type: Expression Integer --E ---S 41 14:135 Schaums and Axiom agree +--S 41 of 68 14:135 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -520,7 +520,7 @@ $$ <<*>>= )clear all ---S 42 +--S 42 of 68 aa:=integrate(1/(x*(x^2+a^2)^2),x) --R --R @@ -532,7 +532,7 @@ aa:=integrate(1/(x*(x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 43 +--S 43 of 68 bb:=1/(2*a^2*(x^2+a^2))+1/(2*a^4)*log(x^2/(x^2+a^2)) --R --R 2 @@ -546,7 +546,7 @@ bb:=1/(2*a^2*(x^2+a^2))+1/(2*a^4)*log(x^2/(x^2+a^2)) --R Type: Expression Integer --E ---S 44 +--S 44 of 68 cc:=aa-bb --R --R 2 @@ -560,7 +560,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 45 +--S 45 of 68 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -569,7 +569,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 46 +--S 46 of 68 dd:=divlog cc --R --R 2 @@ -580,7 +580,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 47 +--S 47 of 68 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -588,7 +588,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 48 14:136 Schaums and Axiom agree +--S 48 of 68 14:136 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -603,7 +603,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 68 aa:=integrate(1/(x^2*(x^2+a^2)^2),x) --R --R 3 2 x 2 3 @@ -615,7 +615,7 @@ aa:=integrate(1/(x^2*(x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 50 +--S 50 of 68 bb:=-1/(a^4*x)-x/(2*a^4*(x^2+a^2))-3/(2*a^5)*atan(x/a) --R --R 3 2 x 2 3 @@ -627,7 +627,7 @@ bb:=-1/(a^4*x)-x/(2*a^4*(x^2+a^2))-3/(2*a^5)*atan(x/a) --R Type: Expression Integer --E ---S 51 14:137 Schaums and Axiom agree +--S 51 of 68 14:137 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -643,7 +643,7 @@ $$ <<*>>= )clear all ---S 52 +--S 52 of 68 aa:=integrate(1/(x^3*(x^2+a^2)^2),x) --R --R @@ -655,7 +655,7 @@ aa:=integrate(1/(x^3*(x^2+a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 53 +--S 53 of 68 bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2+a^2))-1/a^6*log(x^2/(x^2+a^2)) --R --R 2 @@ -669,7 +669,7 @@ bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2+a^2))-1/a^6*log(x^2/(x^2+a^2)) --R Type: Expression Integer --E ---S 54 +--S 54 of 68 cc:=aa-bb --R --R 2 @@ -683,7 +683,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 55 +--S 55 of 68 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -692,7 +692,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 56 +--S 56 of 68 dd:=divlog cc --R --R 2 @@ -703,7 +703,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 57 +--S 57 of 68 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -711,7 +711,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 58 14:138 Schaums and Axiom agree +--S 58 of 68 14:138 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -728,7 +728,7 @@ $$ <<*>>= )clear all ---S 59 14:139 Axiom cannot do this integral +--S 59 of 68 14:139 Axiom cannot do this integral aa:=integrate(1/((x^2+a^2)^n),x) --R --R @@ -748,7 +748,7 @@ $$ <<*>>= )clear all ---S 60 +--S 60 of 68 aa:=integrate(x/((x^2+a^2)^n),x) --R --R @@ -761,7 +761,7 @@ aa:=integrate(x/((x^2+a^2)^n),x) --R Type: Union(Expression Integer,...) --E ---S 61 +--S 61 of 68 bb:=-1/(2*(n-1)*(x^2+a^2)^(n-1)) --R --R 1 @@ -771,7 +771,7 @@ bb:=-1/(2*(n-1)*(x^2+a^2)^(n-1)) --R Type: Expression Integer --E ---S 62 +--S 62 of 68 cc:=aa-bb --R --R 2 2 @@ -784,7 +784,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 63 +--S 63 of 68 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -792,7 +792,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 64 +--S 64 of 68 dd:=explog cc --R --R 2 2 n 2 2 2 2 n - 1 @@ -803,7 +803,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 65 14:140 Schaums and Axiom agree +--S 65 of 68 14:140 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -819,7 +819,7 @@ $$ <<*>>= )clear all ---S 66 14:141 Axiom cannot do this integral +--S 66 of 68 14:141 Axiom cannot do this integral aa:=integrate(1/(x*(x^2+a^2)^n),x) --R --R @@ -840,7 +840,7 @@ $$ <<*>>= )clear all ---S 67 14:142 Axiom cannot do this integral +--S 67 of 68 14:142 Axiom cannot do this integral aa:=integrate(x^m/((x^2+a^2)^n),x) --R --R @@ -861,7 +861,7 @@ $$ <<*>>= )clear all ---S 68 14:143 Axiom cannot do this integral +--S 68 of 68 14:143 Axiom cannot do this integral aa:=integrate(1/(x^m*(x^2+a^2)^n),x) --R --R diff --git a/src/input/schaum7.input.pamphlet b/src/input/schaum7.input.pamphlet index 52e0b97..3b64f8e 100644 --- a/src/input/schaum7.input.pamphlet +++ b/src/input/schaum7.input.pamphlet @@ -16,7 +16,7 @@ $$\int{\frac{1}{x^2-a^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$ )set message auto off )clear all ---S 1 +--S 1 of 80 aa:=integrate(1/(x^2-a^2),x) --R --R @@ -26,7 +26,7 @@ aa:=integrate(1/(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 80 bb:=1/(2*a)*log((x-a)/(x+a)) --R --R x - a @@ -37,7 +37,7 @@ bb:=1/(2*a)*log((x-a)/(x+a)) --R Type: Expression Integer --E ---S 3 +--S 3 of 80 cc:=aa-bb --R --R x - a @@ -48,7 +48,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -57,7 +57,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 14:144 Schaums and Axiom agree +--S 5 of 80 14:144 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -71,7 +71,7 @@ $$\int{\frac{x}{x^2-a^2}}=\frac{1}{2}\ln(x^2-a^2)$$ <<*>>= )clear all ---S 6 +--S 6 of 80 aa:=integrate(x/(x^2-a^2),x) --R --R @@ -82,7 +82,7 @@ aa:=integrate(x/(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 7 +--S 7 of 80 bb:=1/2*log(x^2-a^2) --R --R 2 2 @@ -92,7 +92,7 @@ bb:=1/2*log(x^2-a^2) --R Type: Expression Integer --E ---S 8 14:145 Schaums and Axiom agree +--S 8 of 80 14:145 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -106,7 +106,7 @@ $$\int{\frac{x^2}{x^2-a^2}}=x+\frac{a}{2}\ln\left(\frac{x-a}{x+a}\right)$$ <<*>>= )clear all ---S 9 +--S 9 of 80 aa:=integrate(x^2/(x^2-a^2),x) --R --R @@ -116,7 +116,7 @@ aa:=integrate(x^2/(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 10 +--S 10 of 80 bb:=x+a/2*log((x-a)/(x+a)) --R --R x - a @@ -127,7 +127,7 @@ bb:=x+a/2*log((x-a)/(x+a)) --R Type: Expression Integer --E ---S 11 +--S 11 of 80 cc:=aa-bb --R --R x - a @@ -138,7 +138,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 12 +--S 12 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -147,7 +147,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 13 14:146 Schaums and Axiom agree +--S 13 of 80 14:146 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -162,7 +162,7 @@ $$\int{\frac{x^3}{x^2-a^2}}=\frac{x^2}{2}+\frac{a^2}{2}\ln(x^2-a^2)$$ <<*>>= )clear all ---S 14 +--S 14 of 80 aa:=integrate(x^3/(x^2-a^2),x) --R --R @@ -173,7 +173,7 @@ aa:=integrate(x^3/(x^2-a^2),x) --R Type: Union(Expression Integer,...) --E ---S 15 +--S 15 of 80 bb:=x^2/2+a^2/2*log(x^2-a^2) --R --R 2 2 2 2 @@ -183,7 +183,7 @@ bb:=x^2/2+a^2/2*log(x^2-a^2) --R Type: Expression Integer --E ---S 16 14:147 Schaums and Axiom agree +--S 16 of 80 14:147 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -199,7 +199,7 @@ $$ <<*>>= )clear all ---S 17 +--S 17 of 80 aa:=integrate(1/(x*(x^2-a^2)),x) --R --R @@ -211,7 +211,7 @@ aa:=integrate(1/(x*(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 18 +--S 18 of 80 bb:=1/(2*a^2)*log((x^2-a^2)/x^2) --R --R 2 2 @@ -225,7 +225,7 @@ bb:=1/(2*a^2)*log((x^2-a^2)/x^2) --R Type: Expression Integer --E ---S 19 +--S 19 of 80 cc:=aa-bb --R --R 2 2 @@ -239,7 +239,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 20 +--S 20 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -248,7 +248,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 21 +--S 21 of 80 dd:=divlog cc --R --R 2 @@ -259,7 +259,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 22 +--S 22 of 80 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -267,7 +267,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 23 14:148 Schaums and Axiom agree +--S 23 of 80 14:148 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -283,7 +283,7 @@ $$ <<*>>= )clear all ---S 24 +--S 24 of 80 aa:=integrate(1/(x^2*(x^2-a^2)),x) --R --R @@ -294,7 +294,7 @@ aa:=integrate(1/(x^2*(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 25 +--S 25 of 80 bb:=1/(a^2*x)+1/(2*a^3)*log((x-a)/(x+a)) --R --R x - a @@ -306,7 +306,7 @@ bb:=1/(a^2*x)+1/(2*a^3)*log((x-a)/(x+a)) --R Type: Expression Integer --E ---S 26 +--S 26 of 80 cc:=aa-bb --R --R x - a @@ -318,7 +318,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 27 +--S 27 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -327,7 +327,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 28 14:149 Schaums and Axiom agree +--S 28 of 80 14:149 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -343,7 +343,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 80 aa:=integrate(1/(x^3*(x^2-a^2)),x) --R --R @@ -355,7 +355,7 @@ aa:=integrate(1/(x^3*(x^2-a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 80 bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2)) --R --R 2 @@ -369,7 +369,7 @@ bb:=1/(2*a^2*x^2)-1/(2*a^4)*log(x^2/(x^2-a^2)) --R Type: Expression Integer --E ---S 31 +--S 31 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -378,7 +378,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 32 +--S 32 of 80 t1:=divlog bb --R --R 2 2 2 2 2 2 @@ -389,7 +389,7 @@ t1:=divlog bb --R Type: Expression Integer --E ---S 33 +--S 33 of 80 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -397,7 +397,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 34 +--S 34 of 80 t2:=logpow t1 --R --R 2 2 2 2 2 @@ -408,7 +408,7 @@ t2:=logpow t1 --R Type: Expression Integer --E ---S 35 14:150 Schaums and Axiom agree +--S 35 of 80 14:150 Schaums and Axiom agree cc:=aa-t2 --R --R (7) 0 @@ -423,7 +423,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 80 aa:=integrate(1/((x^2-a^2)^2),x) --R --R @@ -435,7 +435,7 @@ aa:=integrate(1/((x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 80 bb:=-x/(2*a^2*(x^2-a^2))-1/(4*a^3)*log((x-a)/(x+a)) --R --R 2 2 x - a @@ -447,7 +447,7 @@ bb:=-x/(2*a^2*(x^2-a^2))-1/(4*a^3)*log((x-a)/(x+a)) --R Type: Expression Integer --E ---S 38 +--S 38 of 80 cc:=aa-bb --R --R x - a @@ -459,7 +459,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 39 +--S 39 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -468,7 +468,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 40 14:151 Schaums and Axiom agree +--S 40 of 80 14:151 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -484,7 +484,7 @@ $$ <<*>>= )clear all ---S 41 +--S 41 of 80 aa:=integrate(x/((x^2-a^2)^2),x) --R --R @@ -495,7 +495,7 @@ aa:=integrate(x/((x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 42 +--S 42 of 80 bb:=-1/(2*(x^2-a^2)) --R --R 1 @@ -505,7 +505,7 @@ bb:=-1/(2*(x^2-a^2)) --R Type: Fraction Polynomial Integer --E ---S 43 14:152 Schaums and Axiom agree +--S 43 of 80 14:152 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -521,7 +521,7 @@ $$ <<*>>= )clear all ---S 44 +--S 44 of 80 aa:=integrate(x^2/((x^2-a^2)^2),x) --R --R @@ -533,7 +533,7 @@ aa:=integrate(x^2/((x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 45 +--S 45 of 80 bb:=-x/(2*(x^2-a^2))+1/(4*a)*log((x-a)/(x+a)) --R --R 2 2 x - a @@ -545,7 +545,7 @@ bb:=-x/(2*(x^2-a^2))+1/(4*a)*log((x-a)/(x+a)) --R Type: Expression Integer --E ---S 46 +--S 46 of 80 cc:=aa-bb --R --R x - a @@ -556,7 +556,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 47 +--S 47 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -565,7 +565,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 48 14:153 Schaums and Axiom agree +--S 48 of 80 14:153 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -581,7 +581,7 @@ $$ <<*>>= )clear all ---S 49 +--S 49 of 80 aa:=integrate(x^3/((x^2-a^2)^2),x) --R --R @@ -593,7 +593,7 @@ aa:=integrate(x^3/((x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 50 +--S 50 of 80 bb:=-a^2/(2*(x^2-a^2))+1/2*log(x^2-a^2) --R --R 2 2 2 2 2 @@ -604,7 +604,7 @@ bb:=-a^2/(2*(x^2-a^2))+1/2*log(x^2-a^2) --R Type: Expression Integer --E ---S 51 14:154 Schaums and Axiom agree +--S 51 of 80 14:154 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -620,7 +620,7 @@ $$ <<*>>= )clear all ---S 52 +--S 52 of 80 aa:=integrate(1/(x*(x^2-a^2)^2),x) --R --R @@ -632,7 +632,7 @@ aa:=integrate(1/(x*(x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 53 +--S 53 of 80 bb:=-1/(2*a^2*(x^2-a^2))+1/(2*a^4)*log(x^2/(x^2-a^2)) --R --R 2 @@ -646,7 +646,7 @@ bb:=-1/(2*a^2*(x^2-a^2))+1/(2*a^4)*log(x^2/(x^2-a^2)) --R Type: Expression Integer --E ---S 54 +--S 54 of 80 cc:=aa-bb --R --R 2 @@ -660,7 +660,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 55 +--S 55 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -669,7 +669,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 56 +--S 56 of 80 dd:=divlog cc --R --R 2 @@ -680,7 +680,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 57 +--S 57 of 80 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -688,7 +688,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 58 14:155 Schaums and Axiom agree +--S 58 of 80 14:155 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -705,7 +705,7 @@ $$ <<*>>= )clear all ---S 59 +--S 59 of 80 aa:=integrate(1/(x^2*(x^2-a^2)^2),x) --R --R 3 2 3 2 2 3 @@ -716,7 +716,7 @@ aa:=integrate(1/(x^2*(x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 60 +--S 60 of 80 bb:=-1/(a^4*x)-x/(2*a^4*(x^2-a^2))-3/(4*a^5)*log((x-a)/(x+a)) --R --R 3 2 x - a 2 3 @@ -728,7 +728,7 @@ bb:=-1/(a^4*x)-x/(2*a^4*(x^2-a^2))-3/(4*a^5)*log((x-a)/(x+a)) --R Type: Expression Integer --E ---S 61 +--S 61 of 80 cc:=aa-bb --R --R x - a @@ -740,7 +740,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 62 +--S 62 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -749,7 +749,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 63 14:156 Schaums and Axiom agree +--S 63 of 80 14:156 Schaums and Axiom agree dd:=divlog cc --R --R (5) 0 @@ -766,7 +766,7 @@ $$ <<*>>= )clear all ---S 64 +--S 64 of 80 aa:=integrate(1/(x^3*(x^2-a^2)^2),x) --R --R @@ -778,7 +778,7 @@ aa:=integrate(1/(x^3*(x^2-a^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 65 +--S 65 of 80 bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2-a^2))+1/a^6*log(x^2/(x^2-a^2)) --R --R 2 @@ -792,7 +792,7 @@ bb:=-1/(2*a^4*x^2)-1/(2*a^4*(x^2-a^2))+1/a^6*log(x^2/(x^2-a^2)) --R Type: Expression Integer --E ---S 66 +--S 66 of 80 cc:=aa-bb --R --R 2 @@ -806,7 +806,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 67 +--S 67 of 80 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -815,7 +815,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 68 +--S 68 of 80 dd:=divlog cc --R --R 2 @@ -826,7 +826,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 69 +--S 69 of 80 logpow:=rule(log(a^n) == n*log(a)) --R --R n @@ -834,7 +834,7 @@ logpow:=rule(log(a^n) == n*log(a)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 70 14:157 Schaums and Axiom agree +--S 70 of 80 14:157 Schaums and Axiom agree ee:=logpow dd --R --R (7) 0 @@ -851,7 +851,7 @@ $$ <<*>>= )clear all ---S 71 14:158 Axiom cannot do this integral +--S 71 of 80 14:158 Axiom cannot do this integral aa:=integrate(1/((x^2-a^2)^n),x) --R --R @@ -871,7 +871,7 @@ $$ <<*>>= )clear all ---S 72 +--S 72 of 80 aa:=integrate(x/((x^2-a^2)^n),x) --R --R @@ -884,7 +884,7 @@ aa:=integrate(x/((x^2-a^2)^n),x) --R Type: Union(Expression Integer,...) --E ---S 73 +--S 73 of 80 bb:=-1/(2*(n-1)*(x^2-a^2)^(n-1)) --R --R 1 @@ -894,7 +894,7 @@ bb:=-1/(2*(n-1)*(x^2-a^2)^(n-1)) --R Type: Expression Integer --E ---S 74 +--S 74 of 80 cc:=aa-bb --R --R 2 2 @@ -907,7 +907,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 75 +--S 75 of 80 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -915,7 +915,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 76 +--S 76 of 80 dd:=explog cc --R --R 2 2 n 2 2 2 2 n - 1 @@ -926,7 +926,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 77 14:159 Schaums and Axiom agree +--S 77 of 80 14:159 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -942,7 +942,7 @@ $$ <<*>>= )clear all ---S 78 14:160 Axiom cannot compute this integral +--S 78 of 80 14:160 Axiom cannot compute this integral aa:=integrate(1/(x*(x^2-a^2)^n),x) --R --R @@ -963,7 +963,7 @@ $$ <<*>>= )clear all ---S 79 14:161 Axiom cannot compute this integral +--S 79 of 80 14:161 Axiom cannot compute this integral aa:=integrate(x^m/((x^2-a^2)^n),x) --R --R @@ -984,7 +984,7 @@ $$ <<*>>= )clear all ---S 80 14:162 Axiom cannot compute this integral +--S 80 of 80 14:162 Axiom cannot compute this integral aa:=integrate(1/(x^m*(x^2-a^2)^n),x) --R --R diff --git a/src/input/schaum8.input.pamphlet b/src/input/schaum8.input.pamphlet index 10d9ef5..b633686 100644 --- a/src/input/schaum8.input.pamphlet +++ b/src/input/schaum8.input.pamphlet @@ -16,7 +16,7 @@ $$\int{\frac{1}{a^2-x^2}}=-\frac{1}{a}\coth^{-1}\frac{x}{a}$$ )set message auto off )clear all ---S 1 +--S 1 of 99 aa:=integrate(1/(a^2-x^2),x) --R --R @@ -26,7 +26,7 @@ aa:=integrate(1/(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 99 bb:=1/(2*a)*log((a+x)/(a-x)) --R --R - x - a @@ -37,7 +37,7 @@ bb:=1/(2*a)*log((a+x)/(a-x)) --R Type: Expression Integer --E ---S 3 +--S 3 of 99 cc:=aa-bb --R --R - x - a @@ -48,7 +48,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 +--S 4 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -57,7 +57,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 5 +--S 5 of 99 dd:=divlog cc --R --R log(x + a) - log(- x - a) @@ -66,14 +66,14 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 6 +--S 6 of 99 logminus:=rule(log(x + a) - log(- x - a) == log(-1)) --R --I (6) log(x + a) - log(- x - a) + %I == log(- 1) + %I --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 7 14:163 Schaums and Axiom differ by a constant +--S 7 of 99 14:163 Schaums and Axiom differ by a constant ee:=logminus dd --R --R log(- 1) @@ -89,7 +89,7 @@ $$\int{\frac{x}{a^2-x^2}}=-\frac{1}{2}\ln(a^2-x^2)$$ <<*>>= )clear all ---S 8 +--S 8 of 99 aa:=integrate(x/(a^2-x^2),x) --R --R @@ -100,7 +100,7 @@ aa:=integrate(x/(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 99 bb:=-1/2*log(a^2-x^2) --R --R 2 2 @@ -110,7 +110,7 @@ bb:=-1/2*log(a^2-x^2) --R Type: Expression Integer --E ---S 10 +--S 10 of 99 cc:=aa-bb --R --R 2 2 2 2 @@ -120,7 +120,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 11 +--S 11 of 99 logminus1:=rule(-log(x^2-a^2)+log(-x^2+a^2) == log(-1)) --R --R 2 2 2 2 @@ -128,7 +128,7 @@ logminus1:=rule(-log(x^2-a^2)+log(-x^2+a^2) == log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 12 14:164 Schaums and Axiom differ by a constant +--S 12 of 99 14:164 Schaums and Axiom differ by a constant dd:=logminus1 cc --R --R log(- 1) @@ -143,7 +143,7 @@ $$\int{\frac{x^2}{a^2-x^2}}=-x+\frac{a}{2}\ln\left(\frac{a+x}{a-x}\right)$$ <<*>>= )clear all ---S 13 +--S 13 of 99 aa:=integrate(x^2/(a^2-x^2),x) --R --R @@ -153,7 +153,7 @@ aa:=integrate(x^2/(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 99 bb:=-x+a/2*log((a+x)/(a-x)) --R --R - x - a @@ -164,7 +164,7 @@ bb:=-x+a/2*log((a+x)/(a-x)) --R Type: Expression Integer --E ---S 15 +--S 15 of 99 cc:=aa-bb --R --R - x - a @@ -175,7 +175,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 16 +--S 16 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -184,7 +184,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 17 +--S 17 of 99 dd:=divlog cc --R --R a log(x + a) - a log(- x - a) @@ -193,14 +193,14 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 18 +--S 18 of 99 logminusa:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1)) --R --I (6) b log(x + a) - b log(- x - a) + %M == b log(- 1) + %M --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 19 14:165 Schaums and Axiom differ by a constant +--S 19 of 99 14:165 Schaums and Axiom differ by a constant ee:=logminusa dd --R --R a log(- 1) @@ -216,7 +216,7 @@ $$\int{\frac{x^3}{a^2-x^2}}=-\frac{x^2}{2}-\frac{a^2}{2}\ln(a^2-x^2)$$ <<*>>= )clear all ---S 20 +--S 20 of 99 aa:=integrate(x^3/(a^2-x^2),x) --R --R @@ -227,7 +227,7 @@ aa:=integrate(x^3/(a^2-x^2),x) --R Type: Union(Expression Integer,...) --E ---S 21 +--S 21 of 99 bb:=-x^2/2-a^2/2*log(a^2-x^2) --R --R 2 2 2 2 @@ -237,7 +237,7 @@ bb:=-x^2/2-a^2/2*log(a^2-x^2) --R Type: Expression Integer --E ---S 22 +--S 22 of 99 cc:=aa-bb --R --R 2 2 2 2 2 2 @@ -247,7 +247,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 23 +--S 23 of 99 logminus1b:=rule(-b*log(x^2-a^2)+b*log(-x^2+a^2) == b*log(-1)) --R --R 2 2 2 2 @@ -255,7 +255,7 @@ logminus1b:=rule(-b*log(x^2-a^2)+b*log(-x^2+a^2) == b*log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 24 14:166 Schaums and Axiom differ by a constant +--S 24 of 99 14:166 Schaums and Axiom differ by a constant dd:=logminus1b cc --R --R 2 @@ -274,7 +274,7 @@ $$ <<*>>= )clear all ---S 25 +--S 25 of 99 aa:=integrate(1/(x*(a^2-x^2)),x) --R --R @@ -286,7 +286,7 @@ aa:=integrate(1/(x*(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 26 +--S 26 of 99 bb:=1/(2*a^2)*log(x^2/(a^2-x^2)) --R --R 2 @@ -300,7 +300,7 @@ bb:=1/(2*a^2)*log(x^2/(a^2-x^2)) --R Type: Expression Integer --E ---S 27 +--S 27 of 99 cc:=aa-bb --R --R 2 @@ -314,7 +314,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 28 +--S 28 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -323,7 +323,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 29 +--S 29 of 99 dd:=divlog cc --R --R 2 @@ -334,7 +334,7 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 30 +--S 30 of 99 logpowminus:=rule(log(-a^n) == n*log(a)+log(-1)) --R --R n @@ -342,7 +342,7 @@ logpowminus:=rule(log(-a^n) == n*log(a)+log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 31 14:167 Schaums and Axiom differ by a constant +--S 31 of 99 14:167 Schaums and Axiom differ by a constant ee:=logpowminus dd --R --R log(- 1) @@ -360,7 +360,7 @@ $$ <<*>>= )clear all ---S 32 +--S 32 of 99 aa:=integrate(1/(x^2*(a^2-x^2)),x) --R --R @@ -371,7 +371,7 @@ aa:=integrate(1/(x^2*(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 33 +--S 33 of 99 bb:=-1/(a^2*x)+1/(2*a^3)*log((a+x)/(a-x)) --R --R - x - a @@ -383,7 +383,7 @@ bb:=-1/(a^2*x)+1/(2*a^3)*log((a+x)/(a-x)) --R Type: Expression Integer --E ---S 34 +--S 34 of 99 cc:=aa-bb --R --R - x - a @@ -395,7 +395,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 35 +--S 35 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -404,7 +404,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 36 +--S 36 of 99 dd:=divlog cc --R --R log(x + a) - log(- x - a) @@ -414,14 +414,14 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 37 +--S 37 of 99 logminus:=rule(log(x + a) - log(- x - a) == log(-1)) --R --I (6) log(x + a) - log(- x - a) + %O == log(- 1) + %O --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 38 14:168 Schaums and Axiom differ by a constant +--S 38 of 99 14:168 Schaums and Axiom differ by a constant ee:=logminus dd --R --R log(- 1) @@ -440,7 +440,7 @@ $$ <<*>>= )clear all ---S 39 +--S 39 of 99 aa:=integrate(1/(x^3*(a^2-x^2)),x) --R --R @@ -452,7 +452,7 @@ aa:=integrate(1/(x^3*(a^2-x^2)),x) --R Type: Union(Expression Integer,...) --E ---S 40 +--S 40 of 99 bb:=-1/(2*a^2*x^2)+1/(2*a^4)*log(x^2/(a^2-x^2)) --R --R 2 @@ -466,7 +466,7 @@ bb:=-1/(2*a^2*x^2)+1/(2*a^4)*log(x^2/(a^2-x^2)) --R Type: Expression Integer --E ---S 41 +--S 41 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -475,7 +475,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 42 +--S 42 of 99 bb1:=divlog bb --R --R 2 2 2 2 2 2 @@ -486,7 +486,7 @@ bb1:=divlog bb --R Type: Expression Integer --E ---S 43 +--S 43 of 99 cc:=aa-bb1 --R --R 2 @@ -497,7 +497,7 @@ cc:=aa-bb1 --R Type: Expression Integer --E ---S 44 +--S 44 of 99 logminuspow:=rule(log(-x^n) == n*log(x)+log(-1)) --R --R n @@ -505,7 +505,7 @@ logminuspow:=rule(log(-x^n) == n*log(x)+log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 45 14:169 Schaums and Axiom differ by a constant +--S 45 of 99 14:169 Schaums and Axiom differ by a constant dd:=logminuspow cc --R --R log(- 1) @@ -524,7 +524,7 @@ $$ <<*>>= )clear all ---S 46 +--S 46 of 99 aa:=integrate(1/((a^2-x^2)^2),x) --R --R @@ -536,7 +536,7 @@ aa:=integrate(1/((a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 47 +--S 47 of 99 bb:=x/(2*a^2*(a^2-x^2))+1/(4*a^3)*log((a+x)/(a-x)) --R --R 2 2 - x - a @@ -548,7 +548,7 @@ bb:=x/(2*a^2*(a^2-x^2))+1/(4*a^3)*log((a+x)/(a-x)) --R Type: Expression Integer --E ---S 48 +--S 48 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -557,7 +557,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 49 +--S 49 of 99 bb1:=divlog bb --R --R 2 2 2 2 @@ -568,7 +568,7 @@ bb1:=divlog bb --R Type: Expression Integer --E ---S 50 +--S 50 of 99 cc:=aa-bb1 --R --R log(x + a) - log(- x - a) @@ -578,14 +578,14 @@ cc:=aa-bb1 --R Type: Expression Integer --E ---S 51 +--S 51 of 99 logminus:=rule(log(x + a) - log(- x - a) == log(-1)) --R --I (6) log(x + a) - log(- x - a) + %P == log(- 1) + %P --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 52 14:170 Schaums and Axiom differ by a constant +--S 52 of 99 14:170 Schaums and Axiom differ by a constant dd:=logminus cc --R --R log(- 1) @@ -604,7 +604,7 @@ $$ <<*>>= )clear all ---S 53 +--S 53 of 99 aa:=integrate(x/((a^2-x^2)^2),x) --R --R @@ -615,7 +615,7 @@ aa:=integrate(x/((a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 54 +--S 54 of 99 bb:=1/(2*(a^2-x^2)) --R --R 1 @@ -625,7 +625,7 @@ bb:=1/(2*(a^2-x^2)) --R Type: Fraction Polynomial Integer --E ---S 55 14:171 Schaums and Axiom agree +--S 55 of 99 14:171 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -641,7 +641,7 @@ $$ <<*>>= )clear all ---S 56 +--S 56 of 99 aa:=integrate(x^2/((a^2-x^2)^2),x) --R --R @@ -653,7 +653,7 @@ aa:=integrate(x^2/((a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 57 +--S 57 of 99 bb:=x/(2*(a^2-x^2))-1/(4*a)*log((a+x)/(a-x)) --R --R 2 2 - x - a @@ -665,7 +665,7 @@ bb:=x/(2*(a^2-x^2))-1/(4*a)*log((a+x)/(a-x)) --R Type: Expression Integer --E ---S 58 +--S 58 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -674,7 +674,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 59 +--S 59 of 99 bb1:=divlog bb --R --R 2 2 2 2 @@ -685,7 +685,7 @@ bb1:=divlog bb --R Type: Expression Integer --E ---S 60 +--S 60 of 99 cc:=aa-bb1 --R --R - log(x + a) + log(- x - a) @@ -694,14 +694,14 @@ cc:=aa-bb1 --R Type: Expression Integer --E ---S 61 +--S 61 of 99 logminus2:=rule(-log(x + a) + log(- x - a) == log(-1)) --R --I (6) - log(x + a) + log(- x - a) + %S == log(- 1) + %S --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 62 14:172 Schaums and Axiom differ by a constant +--S 62 of 99 14:172 Schaums and Axiom differ by a constant dd:=logminus2 cc --R --R log(- 1) @@ -718,7 +718,7 @@ $$ <<*>>= )clear all ---S 63 +--S 63 of 99 aa:=integrate(x^3/((a^2-x^2)^2),x) --R --R @@ -730,7 +730,7 @@ aa:=integrate(x^3/((a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 64 +--S 64 of 99 bb:=a^2/(2*(a^2-x^2))+1/2*log(a^2-x^2) --R --R 2 2 2 2 2 @@ -741,7 +741,7 @@ bb:=a^2/(2*(a^2-x^2))+1/2*log(a^2-x^2) --R Type: Expression Integer --E ---S 65 +--S 65 of 99 cc:=aa-bb --R --R 2 2 2 2 @@ -751,7 +751,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 66 +--S 66 of 99 logminus3:=rule(log(x^2-a^2)-log(-x^2+a^2) == log(-1)) --R --R 2 2 2 2 @@ -759,7 +759,7 @@ logminus3:=rule(log(x^2-a^2)-log(-x^2+a^2) == log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 67 14:173 Schaums and Axiom differ by a constant +--S 67 of 99 14:173 Schaums and Axiom differ by a constant dd:=logminus3 cc --R --R log(- 1) @@ -777,7 +777,7 @@ $$ <<*>>= )clear all ---S 68 +--S 68 of 99 aa:=integrate(1/(x*(a^2-x^2)^2),x) --R --R @@ -789,7 +789,7 @@ aa:=integrate(1/(x*(a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 69 +--S 69 of 99 bb:=1/(2*a^2*(a^2-x^2))+1/(2*a^4)*log(x^2/(a^2-x^2)) --R --R 2 @@ -803,7 +803,7 @@ bb:=1/(2*a^2*(a^2-x^2))+1/(2*a^4)*log(x^2/(a^2-x^2)) --R Type: Expression Integer --E ---S 70 +--S 70 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -812,7 +812,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 71 +--S 71 of 99 bb1:=divlog bb --R --R 2 2 2 2 2 2 2 2 @@ -823,7 +823,7 @@ bb1:=divlog bb --R Type: Expression Integer --E ---S 72 +--S 72 of 99 cc:=aa-bb1 --R --R 2 @@ -834,7 +834,7 @@ cc:=aa-bb1 --R Type: Expression Integer --E ---S 73 +--S 73 of 99 logpowminus:=rule(log(-a^n) == n*log(a)+log(-1)) --R --R n @@ -842,7 +842,7 @@ logpowminus:=rule(log(-a^n) == n*log(a)+log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 74 14:174 Schaums and Axiom differ by a constant +--S 74 of 99 14:174 Schaums and Axiom differ by a constant dd:=logpowminus cc --R --R log(- 1) @@ -862,7 +862,7 @@ $$ <<*>>= )clear all ---S 75 +--S 75 of 99 aa:=integrate(1/(x^2*(a^2-x^2)^2),x) --R --R 3 2 3 2 2 3 @@ -873,7 +873,7 @@ aa:=integrate(1/(x^2*(a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 76 +--S 76 of 99 bb:=-1/(a^4*x)+x/(2*a^4*(a^2-x^2))+3/(4*a^5)*log((a+x)/(a-x)) --R --R 3 2 - x - a 2 3 @@ -885,7 +885,7 @@ bb:=-1/(a^4*x)+x/(2*a^4*(a^2-x^2))+3/(4*a^5)*log((a+x)/(a-x)) --R Type: Expression Integer --E ---S 77 +--S 77 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -894,7 +894,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 78 +--S 78 of 99 bb1:=divlog bb --R --R 3 2 3 2 2 3 @@ -905,7 +905,7 @@ bb1:=divlog bb --R Type: Expression Integer --E ---S 79 +--S 79 of 99 cc:=aa-bb --R --R - x - a @@ -917,7 +917,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 80 +--S 80 of 99 dd:=divlog cc --R --R 3log(x + a) - 3log(- x - a) @@ -927,14 +927,14 @@ dd:=divlog cc --R Type: Expression Integer --E ---S 81 +--S 81 of 99 logminusb:=rule(b*log(x + a) - b*log(- x - a) == b*log(-1)) --R --I (7) b log(x + a) - b log(- x - a) + %U == b log(- 1) + %U --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 82 14:175 Schaums and Axiom differ by a constant +--S 82 of 99 14:175 Schaums and Axiom differ by a constant ee:=logminusb dd --R --R 3log(- 1) @@ -954,7 +954,7 @@ $$ <<*>>= )clear all ---S 83 +--S 83 of 99 aa:=integrate(1/(x^3*(a^2-x^2)^2),x) --R --R @@ -966,7 +966,7 @@ aa:=integrate(1/(x^3*(a^2-x^2)^2),x) --R Type: Union(Expression Integer,...) --E ---S 84 +--S 84 of 99 bb:=-1/(2*a^4*x^2)+1/(2*a^4*(a^2-x^2))+1/a^6*log(x^2/(a^2-x^2)) --R --R 2 @@ -980,7 +980,7 @@ bb:=-1/(2*a^4*x^2)+1/(2*a^4*(a^2-x^2))+1/a^6*log(x^2/(a^2-x^2)) --R Type: Expression Integer --E ---S 85 +--S 85 of 99 divlog:=rule(log(a/b) == log(a) - log(b)) --R --R a @@ -989,7 +989,7 @@ divlog:=rule(log(a/b) == log(a) - log(b)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 86 +--S 86 of 99 bb1:=divlog bb --R --R 4 2 2 2 2 4 2 2 2 2 2 4 @@ -1000,7 +1000,7 @@ bb1:=divlog bb --R Type: Expression Integer --E ---S 87 +--S 87 of 99 cc:=aa-bb1 --R --R 2 @@ -1011,7 +1011,7 @@ cc:=aa-bb1 --R Type: Expression Integer --E ---S 88 +--S 88 of 99 logpowminus:=rule(log(-a^n) == n*log(a)+log(-1)) --R --R n @@ -1019,7 +1019,7 @@ logpowminus:=rule(log(-a^n) == n*log(a)+log(-1)) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 89 14:176 Schaums and Axiom differ by a constant +--S 89 of 99 14:176 Schaums and Axiom differ by a constant dd:=logpowminus cc --R --R log(- 1) @@ -1039,7 +1039,7 @@ $$ <<*>>= )clear all ---S 90 14:177 Axiom cannot do this integration +--S 90 of 99 14:177 Axiom cannot do this integration aa:=integrate(1/((a^2-x^2)^n),x) --R --R @@ -1059,7 +1059,7 @@ $$ <<*>>= )clear all ---S 91 +--S 91 of 99 aa:=integrate(x/((a^2-x^2)^n),x) --R --R @@ -1072,7 +1072,7 @@ aa:=integrate(x/((a^2-x^2)^n),x) --R Type: Union(Expression Integer,...) --E ---S 92 +--S 92 of 99 bb:=1/(2*(n-1)*(a^2-x^2)^(n-1)) --R --R 1 @@ -1082,7 +1082,7 @@ bb:=1/(2*(n-1)*(a^2-x^2)^(n-1)) --R Type: Expression Integer --E ---S 93 +--S 93 of 99 cc:=aa-bb --R --R 2 2 @@ -1095,7 +1095,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 94 +--S 94 of 99 explog:=rule(%e^(n*log(x)) == x^n) --R --R n log(x) n @@ -1103,7 +1103,7 @@ explog:=rule(%e^(n*log(x)) == x^n) --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 95 +--S 95 of 99 dd:=explog cc --R --R 2 2 n 2 2 2 2 n - 1 @@ -1114,7 +1114,7 @@ dd:=explog cc --R Type: Expression Integer --E ---S 96 14:178 Schaums and Axiom agree +--S 96 of 99 14:178 Schaums and Axiom agree ee:=complexNormalize dd --R --R (6) 0 @@ -1131,7 +1131,7 @@ $$ <<*>>= )clear all ---S 97 14:179 Axiom cannot integrate this expression +--S 97 of 99 14:179 Axiom cannot integrate this expression aa:=integrate(1/(x*(a^2-x^2)^n),x) --R --R @@ -1152,7 +1152,7 @@ $$ <<*>>= )clear all ---S 98 14:180 Axiom cannot integrate this expression +--S 98 of 99 14:180 Axiom cannot integrate this expression aa:=integrate(x^m/((a^2-x^2)^n),x) --R --R @@ -1173,7 +1173,7 @@ $$ <<*>>= )clear all ---S 99 14:181 Axiom cannot integrate this expression +--S 99 of 99 14:181 Axiom cannot integrate this expression aa:=integrate(1/(x^m*(a^2-x^2)^n),x) --R --R diff --git a/src/input/schaum9.input.pamphlet b/src/input/schaum9.input.pamphlet index fa7d4f2..79f959b 100644 --- a/src/input/schaum9.input.pamphlet +++ b/src/input/schaum9.input.pamphlet @@ -16,7 +16,7 @@ $$\int{\frac{1}{\sqrt{x^2+a^2}}}=\sinh^{-1}\frac{x}{a}$$ )set message auto off )clear all ---S 1 +--S 1 of 110 aa:=integrate(1/(sqrt(x^2+a^2)),x) --R --R @@ -26,7 +26,7 @@ aa:=integrate(1/(sqrt(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 2 +--S 2 of 110 bb:=log(x+sqrt(x^2+a^2)) --R --R +-------+ @@ -35,7 +35,7 @@ bb:=log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 3 +--S 3 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -44,7 +44,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 4 14:182 Schaums and Axiom differ by a constant +--S 4 of 110 14:182 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 @@ -60,7 +60,7 @@ $$\int{\frac{x}{\sqrt{x^2+a^2}}}=\sqrt{x^2+a^2}$$ <<*>>= )clear all ---S 5 +--S 5 of 110 aa:=integrate(x/(sqrt(x^2+a^2)),x) --R --R @@ -74,7 +74,7 @@ aa:=integrate(x/(sqrt(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 6 +--S 6 of 110 bb:=sqrt(x^2+a^2) --R --R +-------+ @@ -83,7 +83,7 @@ bb:=sqrt(x^2+a^2) --R Type: Expression Integer --E ---S 7 14:183 Schaums and Axiom agree +--S 7 of 110 14:183 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -99,7 +99,7 @@ $$ <<*>>= )clear all ---S 8 +--S 8 of 110 aa:=integrate(x^2/sqrt(x^2+a^2),x) --R --R @@ -118,7 +118,7 @@ aa:=integrate(x^2/sqrt(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 9 +--S 9 of 110 bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -129,7 +129,7 @@ bb:=(x*sqrt(x^2+a^2))/2-a^2/2*log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 10 +--S 10 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -140,14 +140,14 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 11 +--S 11 of 110 logmul1:=rule(c*log(a)+c*log(b) == c*log(a*b)) --R --I (4) c log(b) + c log(a) + %K == c log(a b) + %K --R Type: RewriteRule(Integer,Integer,Expression Integer) --E ---S 12 14:184 Schaums and Axiom differ by a constant +--S 12 of 110 14:184 Schaums and Axiom differ by a constant dd:=logmul1 cc --R --R 2 2 @@ -167,7 +167,7 @@ $$ <<*>>= )clear all ---S 13 +--S 13 of 110 aa:=integrate(x^3/sqrt(x^2+a^2),x) --R --R @@ -181,7 +181,7 @@ aa:=integrate(x^3/sqrt(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 14 +--S 14 of 110 bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2) --R --R +-------+ @@ -192,7 +192,7 @@ bb:=(x^2+a^2)^(3/2)/3-a^2*sqrt(x^2+a^2) --R Type: Expression Integer --E ---S 15 14:185 Schaums and Axiom agree +--S 15 of 110 14:185 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -207,7 +207,7 @@ $$ <<*>>= )clear all ---S 16 +--S 16 of 110 aa:=integrate(1/(x*sqrt(x^2+a^2)),x) --R --R @@ -219,7 +219,7 @@ aa:=integrate(1/(x*sqrt(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 17 +--S 17 of 110 bb:=-1/a*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -232,7 +232,7 @@ bb:=-1/a*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 18 +--S 18 of 110 cc:=aa-bb --R --R (3) @@ -246,7 +246,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 19 +--S 19 of 110 dd:=expandLog cc --R --R (4) @@ -260,7 +260,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 20 14:186 Schaums and Axiom differ by a constant +--S 20 of 110 14:186 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R log(- 1) @@ -279,7 +279,7 @@ $$ <<*>>= )clear all ---S 21 +--S 21 of 110 aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x) --R --R @@ -291,7 +291,7 @@ aa:=integrate(1/(x^2*sqrt(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 22 +--S 22 of 110 bb:=-sqrt(x^2+a^2)/(a^2*x) --R --R +-------+ @@ -303,7 +303,7 @@ bb:=-sqrt(x^2+a^2)/(a^2*x) --R Type: Expression Integer --E ---S 23 14:187 Schaums and Axiom differ by a constant +--S 23 of 110 14:187 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 1 @@ -323,7 +323,7 @@ $$ <<*>>= )clear all ---S 24 +--S 24 of 110 aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x) --R --R @@ -346,7 +346,7 @@ aa:=integrate(1/(x^3*sqrt(x^2+a^2)),x) --R Type: Union(Expression Integer,...) --E ---S 25 +--S 25 of 110 bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -360,7 +360,7 @@ bb:=-sqrt(x^2+a^2)/(2*a^2*x^2)+1/(2*a^3)*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 26 +--S 26 of 110 cc:=aa-bb --R --R (3) @@ -375,7 +375,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 27 +--S 27 of 110 dd:=expandLog cc --R --R (4) @@ -390,7 +390,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 28 14:188 Schaums and Axiom differ by a constant +--S 28 of 110 14:188 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R log(- 1) @@ -409,7 +409,7 @@ $$ <<*>>= )clear all ---S 29 +--S 29 of 110 aa:=integrate(sqrt(x^2+a^2),x) --R --R @@ -428,7 +428,7 @@ aa:=integrate(sqrt(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 30 +--S 30 of 110 bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -439,7 +439,7 @@ bb:=(x*sqrt(x^2+a^2))/2+a^2/2*log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 31 +--S 31 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -450,7 +450,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 32 14:189 Schaums and Axiom differ by a constant +--S 32 of 110 14:189 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 2 @@ -469,7 +469,7 @@ $$ <<*>>= )clear all ---S 33 +--S 33 of 110 aa:=integrate(x*sqrt(x^2+a^2),x) --R --R @@ -483,7 +483,7 @@ aa:=integrate(x*sqrt(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 34 +--S 34 of 110 bb:=(x^2+a^2)^(3/2)/3 --R --R +-------+ @@ -494,7 +494,7 @@ bb:=(x^2+a^2)^(3/2)/3 --R Type: Expression Integer --E ---S 35 14:190 Schaums and Axiom agree +--S 35 of 110 14:190 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -511,7 +511,7 @@ $$ <<*>>= )clear all ---S 36 +--S 36 of 110 aa:=integrate(x^2*sqrt(x^2+a^2),x) --R --R @@ -530,7 +530,7 @@ aa:=integrate(x^2*sqrt(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 37 +--S 37 of 110 bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -541,7 +541,7 @@ bb:=(x*(x^2+a^2)^(3/2))/4-(a^2*x*sqrt(x^2+a^2))/8-a^4/8*log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 38 +--S 38 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -552,7 +552,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 39 14:191 Schaums and Axiom differ by a constant +--S 39 of 110 14:191 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 4 2 @@ -571,7 +571,7 @@ $$ <<*>>= )clear all ---S 40 +--S 40 of 110 aa:=integrate(x^3*sqrt(x^2+a^2),x) --R --R @@ -589,7 +589,7 @@ aa:=integrate(x^3*sqrt(x^2+a^2),x) --R Type: Union(Expression Integer,...) --E ---S 41 +--S 41 of 110 bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3 --R --R +-------+ @@ -600,7 +600,7 @@ bb:=(x^2+a^2)^(5/2)/5-(a^2*(x^2+a^2)^(3/2))/3 --R Type: Expression Integer --E ---S 42 14:192 Schaums and Axiom agree +--S 42 of 110 14:192 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -616,7 +616,7 @@ $$ <<*>>= )clear all ---S 43 +--S 43 of 110 aa:=integrate(sqrt(x^2+a^2)/x,x) --R --R @@ -635,7 +635,7 @@ aa:=integrate(sqrt(x^2+a^2)/x,x) --R Type: Union(Expression Integer,...) --E ---S 44 +--S 44 of 110 bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -646,7 +646,7 @@ bb:=sqrt(x^2+a^2)-a*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 45 +--S 45 of 110 cc:=aa-bb --R --R (3) @@ -662,7 +662,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 46 +--S 46 of 110 dd:=expandLog cc --R --R (4) @@ -676,7 +676,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 47 14:193 Schaums and Axiom differ by a constant +--S 47 of 110 14:193 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R (5) - a log(- 1) @@ -692,7 +692,7 @@ $$ <<*>>= )clear all ---S 48 +--S 48 of 110 aa:=integrate(sqrt(x^2+a^2)/x^2,x) --R --R @@ -706,7 +706,7 @@ aa:=integrate(sqrt(x^2+a^2)/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 49 +--S 49 of 110 bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -717,7 +717,7 @@ bb:=-sqrt(x^2+a^2)/x+log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 50 +--S 50 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -726,7 +726,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 51 14:194 Schaums and Axiom differ by a constant +--S 51 of 110 14:194 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 @@ -745,7 +745,7 @@ $$ <<*>>= )clear all ---S 52 +--S 52 of 110 aa:=integrate(sqrt(x^2+a^2)/x^3,x) --R --R @@ -768,7 +768,7 @@ aa:=integrate(sqrt(x^2+a^2)/x^3,x) --R Type: Union(Expression Integer,...) --E ---S 53 +--S 53 of 110 bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -782,7 +782,7 @@ bb:=-sqrt(x^2+a^2)/(2*x^2)-1/(2*a)*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 54 +--S 54 of 110 cc:=aa-bb --R --R (3) @@ -796,7 +796,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 55 +--S 55 of 110 dd:=expandLog cc --R --R (4) @@ -810,7 +810,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 56 14:195 Schaums and Axiom differ by a constant +--S 56 of 110 14:195 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R log(- 1) @@ -827,7 +827,7 @@ $$ <<*>>= )clear all ---S 57 +--S 57 of 110 aa:=integrate(1/(x^2+a^2)^(3/2),x) --R --R @@ -839,7 +839,7 @@ aa:=integrate(1/(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 58 +--S 58 of 110 bb:=x/(a^2*sqrt(x^2+a^2)) --R --R x @@ -850,7 +850,7 @@ bb:=x/(a^2*sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 59 14:196 Schaums and Axiom differ by a constant +--S 59 of 110 14:196 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 1 @@ -869,7 +869,7 @@ $$ <<*>>= )clear all ---S 60 +--S 60 of 110 aa:=integrate(x/(x^2+a^2)^(3/2),x) --R --R @@ -883,7 +883,7 @@ aa:=integrate(x/(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 61 +--S 61 of 110 bb:=-1/sqrt(x^2+a^2) --R --R 1 @@ -894,7 +894,7 @@ bb:=-1/sqrt(x^2+a^2) --R Type: Expression Integer --E ---S 62 14:197 Schaums and Axiom agree +--S 62 of 110 14:197 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -911,7 +911,7 @@ $$ <<*>>= )clear all ---S 63 +--S 63 of 110 aa:=integrate(x^2/(x^2+a^2)^(3/2),x) --R --R @@ -925,7 +925,7 @@ aa:=integrate(x^2/(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 64 +--S 64 of 110 bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -938,7 +938,7 @@ bb:=-x/sqrt(x^2+a^2)+log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 65 +--S 65 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -947,7 +947,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 66 14:198 Schaums and Axiom differ by a constant +--S 66 of 110 14:198 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 @@ -964,7 +964,7 @@ $$ <<*>>= )clear all ---S 67 +--S 67 of 110 aa:=integrate(x^3/(x^2+a^2)^(3/2),x) --R --R @@ -978,7 +978,7 @@ aa:=integrate(x^3/(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 68 +--S 68 of 110 bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2) --R --R 2 2 @@ -990,7 +990,7 @@ bb:=sqrt(x^2+a^2)+a^2/sqrt(x^2+a^2) --R Type: Expression Integer --E ---S 69 14:199 Schaums and Axiom agree +--S 69 of 110 14:199 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1007,7 +1007,7 @@ $$ <<*>>= )clear all ---S 70 +--S 70 of 110 aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x) --R --R @@ -1026,7 +1026,7 @@ aa:=integrate(1/(x*(x^2+a^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 71 +--S 71 of 110 bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -1041,7 +1041,7 @@ bb:=1/(a^2*sqrt(x^2+a^2))-1/a^3*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 72 +--S 72 of 110 cc:=aa-bb --R --R (3) @@ -1056,7 +1056,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 73 +--S 73 of 110 dd:=expandLog cc --R --R (4) @@ -1071,7 +1071,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 74 14:200 Schaums and Axiom differ by a constant +--S 74 of 110 14:200 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R log(- 1) @@ -1091,7 +1091,7 @@ $$ <<*>>= )clear all ---S 75 +--S 75 of 110 aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x) --R --R @@ -1103,7 +1103,7 @@ aa:=integrate(1/(x^2*(x^2+a^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 76 +--S 76 of 110 bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2)) --R --R 2 2 @@ -1115,7 +1115,7 @@ bb:=-sqrt(x^2+a^2)/(a^4*x)-x/(a^4*sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 77 14:201 Schaums and Axiom differ by a constant +--S 77 of 110 14:201 Schaums and Axiom differ by a constant cc:=aa-bb --R --R 2 @@ -1136,7 +1136,7 @@ $$ <<*>>= )clear all ---S 78 +--S 78 of 110 aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x) --R --R @@ -1163,7 +1163,7 @@ aa:=integrate(1/(x^3*(x^2+a^2)^(3/2)),x) --R Type: Union(Expression Integer,...) --E ---S 79 +--S 79 of 110 bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -1178,7 +1178,7 @@ bb:=-1/(2*a^2*x^2*sqrt(x^2+a^2))-3/(2*a^4*sqrt(x^2+a^2))+3/(2*a^5)*log((a+sqrt(x --R Type: Expression Integer --E ---S 80 +--S 80 of 110 cc:=aa-bb --R --R (3) @@ -1193,7 +1193,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 81 +--S 81 of 110 dd:=expandLog cc --R --R (4) @@ -1210,7 +1210,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 82 14:202 Schaums and Axiom differ by a constant +--S 82 of 110 14:202 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R 3log(- 1) @@ -1229,7 +1229,7 @@ $$ <<*>>= )clear all ---S 83 +--S 83 of 110 aa:=integrate((x^2+a^2)^(3/2),x) --R --R (1) @@ -1250,7 +1250,7 @@ aa:=integrate((x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 84 +--S 84 of 110 bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -1261,7 +1261,7 @@ bb:=(x*(x^2+a^2)^(3/2))/4+(3*a^2*x*sqrt(x^2+a^2))/8+3/8*a^4*log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 85 +--S 85 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -1272,7 +1272,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 86 14:203 Schaums and Axiom differ by a constant +--S 86 of 110 14:203 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 4 2 @@ -1288,7 +1288,7 @@ $$\int{x(x^2+a^2)^{3/2}}=\frac{(x^2+a^2)^{5/2}}{5}$$ <<*>>= )clear all ---S 87 +--S 87 of 110 aa:=integrate(x*(x^2+a^2)^(3/2),x) --R --R @@ -1306,7 +1306,7 @@ aa:=integrate(x*(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 88 +--S 88 of 110 bb:=(x^2+a^2)^(5/2)/5 --R --R +-------+ @@ -1317,7 +1317,7 @@ bb:=(x^2+a^2)^(5/2)/5 --R Type: Expression Integer --E ---S 89 14:204 Schaums and Axiom agree +--S 89 of 110 14:204 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1334,7 +1334,7 @@ $$ <<*>>= )clear all ---S 90 +--S 90 of 110 aa:=integrate(x^2*(x^2+a^2)^(3/2),x) --R --R @@ -1363,7 +1363,7 @@ aa:=integrate(x^2*(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 91 +--S 91 of 110 bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^6/16*log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -1374,7 +1374,7 @@ bb:=(x*(x^2+a^2)^(5/2))/6-(a^2*x*(x^2+a^2)^(3/2))/24-(a^4*x*sqrt(x^2+a^2))/16-a^ --R Type: Expression Integer --E ---S 92 +--S 92 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -1385,7 +1385,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 93 14:205 Schaums and Axiom differ by a constant +--S 93 of 110 14:205 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 6 2 @@ -1403,7 +1403,7 @@ $$ <<*>>= )clear all ---S 94 +--S 94 of 110 aa:=integrate(x^3*(x^2+a^2)^(3/2),x) --R --R @@ -1433,7 +1433,7 @@ aa:=integrate(x^3*(x^2+a^2)^(3/2),x) --R Type: Union(Expression Integer,...) --E ---S 95 +--S 95 of 110 bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5 --R --R +-------+ @@ -1444,7 +1444,7 @@ bb:=(x^2+a^2)^(7/2)/7-(a^2*(x^2+a^2)^(5/2))/5 --R Type: Expression Integer --E ---S 96 14:206 Schaums and Axiom agree +--S 96 of 110 14:206 Schaums and Axiom agree cc:=aa-bb --R --R (3) 0 @@ -1461,7 +1461,7 @@ $$ <<*>>= )clear all ---S 97 +--S 97 of 110 aa:=integrate((x^2+a^2)^(3/2)/x,x) --R --R @@ -1484,7 +1484,7 @@ aa:=integrate((x^2+a^2)^(3/2)/x,x) --R Type: Union(Expression Integer,...) --E ---S 98 +--S 98 of 110 bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -1497,7 +1497,7 @@ bb:=(x^2+a^2)^(3/2)/3+a^2*sqrt(x^2+a^2)-a^3*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 99 +--S 99 of 110 cc:=aa-bb --R --R (3) @@ -1513,7 +1513,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 100 +--S 100 of 110 dd:=expandLog cc --R --R (4) @@ -1527,7 +1527,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 101 14:207 Schaums and Axiom differ by a constant +--S 101 of 110 14:207 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R 3 @@ -1545,7 +1545,7 @@ $$ <<*>>= )clear all ---S 102 +--S 102 of 110 aa:=integrate((x^2+a^2)^{3/2}/x^2,x) --R --R @@ -1564,7 +1564,7 @@ aa:=integrate((x^2+a^2)^{3/2}/x^2,x) --R Type: Union(Expression Integer,...) --E ---S 103 +--S 103 of 110 bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2)) --R --R +-------+ +-------+ @@ -1575,7 +1575,7 @@ bb:=-(x^2+a^2)^(3/2)/x+(3*x*sqrt(x^2+a^2))/2+3/2*a^2*log(x+sqrt(x^2+a^2)) --R Type: Expression Integer --E ---S 104 +--S 104 of 110 cc:=aa-bb --R --R +-------+ +-------+ @@ -1586,7 +1586,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 105 14:208 Schaums and Axiom differ by a constant +--S 105 of 110 14:208 Schaums and Axiom differ by a constant dd:=complexNormalize cc --R --R 2 2 2 @@ -1607,7 +1607,7 @@ $$ <<*>>= )clear all ---S 106 +--S 106 of 110 aa:=integrate((x^2+a^2)^(3/2)/x^3,x) --R --R @@ -1630,7 +1630,7 @@ aa:=integrate((x^2+a^2)^(3/2)/x^3,x) --R Type: Union(Expression Integer,...) --E ---S 107 +--S 107 of 110 bb:=-(x^2+a^2)^(3/2)/(2*x^2)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x) --R --R +-------+ @@ -1644,7 +1644,7 @@ bb:=-(x^2+a^2)^(3/2)/(2*x^2)+3/2*sqrt(x^2+a^2)-3/2*a*log((a+sqrt(x^2+a^2))/x) --R Type: Expression Integer --E ---S 108 +--S 108 of 110 cc:=aa-bb --R --R (3) @@ -1662,7 +1662,7 @@ cc:=aa-bb --R Type: Expression Integer --E ---S 109 +--S 109 of 110 dd:=expandLog cc --R --R (4) @@ -1678,7 +1678,7 @@ dd:=expandLog cc --R Type: Expression Integer --E ---S 110 14:209 Schaums and Axiom differ by a constant +--S 110 of 110 14:209 Schaums and Axiom differ by a constant ee:=complexNormalize dd --R --R 3a log(- 1) diff --git a/src/input/series.input.pamphlet b/src/input/series.input.pamphlet index 8636c41..bd53d23 100644 --- a/src/input/series.input.pamphlet +++ b/src/input/series.input.pamphlet @@ -18,7 +18,7 @@ )set message test on )set message auto off )clear all ---S 1 +--S 1 of 17 \section{Expression To Power Series} We compute series expansions of various functions using EXPR2UPS. diff --git a/src/input/sersolve.input.pamphlet b/src/input/sersolve.input.pamphlet index 1f910b7..993bb36 100644 --- a/src/input/sersolve.input.pamphlet +++ b/src/input/sersolve.input.pamphlet @@ -55,7 +55,7 @@ seriesSolve(eq,y,x=0,y(0) = 0) )set streams calculate 10 ---S 4 of 10 +--S 4 of 10 R := EXPR INT --R --R diff --git a/src/input/stream2.input.pamphlet b/src/input/stream2.input.pamphlet index 11adb23..514a99f 100644 --- a/src/input/stream2.input.pamphlet +++ b/src/input/stream2.input.pamphlet @@ -22,7 +22,7 @@ )set functions cache all )set functions compile on ---S 1 of 55 +--S 1 of 55 u==[i+j for i in (-4)..10 | i < 5 for j in 4.. | j < 10] --R --R Type: Void @@ -198,7 +198,7 @@ u==[i for i in m..n] )set mes test off ---S 21 of 55 +--S 21 of 55 u --R --R @@ -207,7 +207,7 @@ u )set mes test on ---S 22 of 55 +--S 22 of 55 n:=7 --R --R @@ -303,7 +303,7 @@ u==[[i+j for i in 0..j] for j in 0..n] )set mes test off ---S 33 of 55 +--S 33 of 55 u --R --R @@ -312,7 +312,7 @@ u )set mes test on ---S 34 of 55 +--S 34 of 55 n:=5 --R --R @@ -406,7 +406,7 @@ u )set streams calculate 10 ---S 44 of 55 +--S 44 of 55 u==[[i+j for i in 0..] for j in 0..] --R --R Type: Void @@ -486,7 +486,7 @@ u(3,6) )set streams calculate 3 ---S 51 of 55 +--S 51 of 55 [[[i+j+k for i in 0..] for j in 0..] for k in 0..] --R --R diff --git a/src/input/test.input.pamphlet b/src/input/test.input.pamphlet index 7ffe5b8..1706da0 100644 --- a/src/input/test.input.pamphlet +++ b/src/input/test.input.pamphlet @@ -26,7 +26,7 @@ Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 1 +--S 1 of 188 eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F --R --R @@ -35,7 +35,7 @@ eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F --R Type: Polynomial Integer --E 1 ---S 2 +--S 2 of 188 eq2:= eval(eq1,[x= xdot*cos(t) - ydot*sin(t), y=xdot*sin(t) + ydot*cos(t)]) --R --R @@ -56,7 +56,7 @@ UTS coercions. Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 3 +--S 3 of 188 taylor exp x --R --R @@ -71,7 +71,7 @@ taylor exp x --R Type: UnivariateTaylorSeries(Expression Integer,x,0) --E 3 ---S 4 +--S 4 of 188 s := % --R --R @@ -86,7 +86,7 @@ s := % --R Type: UnivariateTaylorSeries(Expression Integer,x,0) --E 4 ---S 5 +--S 5 of 188 s::(UTS(EXPR FLOAT, x, 0)) --R --R @@ -108,7 +108,7 @@ s::(UTS(EXPR FLOAT, x, 0)) --R Type: UnivariateTaylorSeries(Expression Float,x,0.0) --E 5 ---S 6 +--S 6 of 188 s::(UTS(FLOAT, x, 0)) --R --R @@ -130,7 +130,7 @@ s::(UTS(FLOAT, x, 0)) --R Type: UnivariateTaylorSeries(Float,x,0.0) --E 6 ---S 7 +--S 7 of 188 eval(s,1) --R --R @@ -140,7 +140,7 @@ eval(s,1) --R Type: Stream Expression Integer --E 7 ---S 8 +--S 8 of 188 %::(Stream Float) --R --R @@ -156,7 +156,7 @@ Another bug, fixed by adding UPXS2 package, <<*>>= )clear all ---S 9 +--S 9 of 188 s := series(sin(a*x),x=0) --R --R @@ -167,7 +167,7 @@ s := series(sin(a*x),x=0) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 9 ---S 10 +--S 10 of 188 eval(s, 1.0) --R --R @@ -205,7 +205,7 @@ eval(s, 1.0) --R Type: Stream Expression Float --E 10 ---S 11 +--S 11 of 188 s - a*x --R --R @@ -224,7 +224,7 @@ s - a*x Grand finale, just fixed on 3/23/91 <<*>>= ---S 12 +--S 12 of 188 eval(s, 1.0) --R --R @@ -267,7 +267,7 @@ Generalized resolve. Fixed (enhanced) by SCM in 3/23/91 <<*>>= )clear all ---S 13 +--S 13 of 188 v := vector [1,2,3] --R --R @@ -275,7 +275,7 @@ v := vector [1,2,3] --R Type: Vector PositiveInteger --E 13 ---S 14 +--S 14 of 188 (1/2)*v --R --R @@ -285,7 +285,7 @@ v := vector [1,2,3] --R Type: Vector Fraction Integer --E 14 ---S 15 +--S 15 of 188 eval(x**2, x=1/2) --R --R @@ -295,7 +295,7 @@ eval(x**2, x=1/2) --R Type: Polynomial Fraction Integer --E 15 ---S 16 +--S 16 of 188 eval(x**2, x=0.5) --R --R @@ -303,7 +303,7 @@ eval(x**2, x=0.5) --R Type: Polynomial Float --E 16 ---S 17 +--S 17 of 188 eval(3**x, x=0.5) --R --R @@ -316,19 +316,19 @@ Overloading interpreter maps on arity. Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 18 +--S 18 of 188 f(x) == x+1 --R --R Type: Void --E 18 ---S 19 +--S 19 of 188 f(x,y) == x+y --R --R Type: Void --E 19 ---S 20 +--S 20 of 188 f 3 --R --R Compiling function f with type PositiveInteger -> PositiveInteger @@ -337,7 +337,7 @@ f 3 --R Type: PositiveInteger --E 20 ---S 21 +--S 21 of 188 f(3,4) --R --R Compiling function f with type (PositiveInteger,PositiveInteger) -> @@ -347,7 +347,7 @@ f(3,4) --R Type: PositiveInteger --E 21 ---S 22 +--S 22 of 188 f(5) --R --R @@ -355,7 +355,7 @@ f(5) --R Type: PositiveInteger --E 22 ---S 23 +--S 23 of 188 f(1,x) --R --R Compiling function f with type (PositiveInteger,Variable x) -> @@ -370,7 +370,7 @@ Targetted function requiring a coercion. Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 24 +--S 24 of 188 series(n +-> bernoulli(n)/factorial(n), t=0) --R --R @@ -386,7 +386,7 @@ In-homogeneous list mapping. Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 25 +--S 25 of 188 l := [1,2,-1] --R --R @@ -394,19 +394,19 @@ l := [1,2,-1] --R Type: List Integer --E 25 ---S 26 +--S 26 of 188 f : INT -> FRAC INT --R --R Type: Void --E 26 ---S 27 +--S 27 of 188 f x == x --R --R Type: Void --E 27 ---S 28 +--S 28 of 188 map(f, l) --R --R Compiling function f with type Integer -> Fraction Integer @@ -420,25 +420,25 @@ Function args to interpreter functions. Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 29 +--S 29 of 188 f: INT -> INT --R --R Type: Void --E 29 ---S 30 +--S 30 of 188 f x == x+1 --R --R Type: Void --E 30 ---S 31 +--S 31 of 188 u g == g 3 --R --R Type: Void --E 31 ---S 32 +--S 32 of 188 u f --R --R Compiling function u with type (Integer -> Integer) -> Integer @@ -454,7 +454,7 @@ Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 33 +--S 33 of 188 groebner [x**2 - y, y**3+1] --R --R @@ -469,7 +469,7 @@ Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 34 +--S 34 of 188 factor x --R --R @@ -484,28 +484,28 @@ Bracket parsing and empty-set types. Fixed by SCM, verified on 10/30/90 <<*>>= )clear all ---S 35 +--S 35 of 188 {}$(List INT) --R --RDaly Bug --R The function SEQ is not implemented in List Integer . --E 35 ---S 36 +--S 36 of 188 brace [] -- {} --R --R (1) {} --R Type: Set None --E 36 ---S 37 +--S 37 of 188 brace [1] -- {1} --R --R (2) {1} --R Type: Set PositiveInteger --E 37 ---S 38 +--S 38 of 188 union(brace [], brace [1,2]) -- union({}, {1,2}) --R --R (3) {1,2} @@ -520,7 +520,7 @@ Fixed by SCM, verified on 10/30/90 )set mes test off ---S 39 +--S 39 of 188 map(variable, [x,y]) --R --R @@ -537,19 +537,19 @@ Recursive map type analysis bug. Fixed by SCM, verified on 10/30/90 )set fun recur off ---S 40 +--S 40 of 188 p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x) --R --R Type: Void --E 40 ---S 41 +--S 41 of 188 pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x) --R --R Type: Void --E 41 ---S 42 +--S 42 of 188 pp(-1,x) -- should be 1/(x-1) --R --R Compiling function p with type (Integer,Polynomial Integer) -> @@ -570,7 +570,7 @@ Interpret-code mode for iterators is broken <<*>>= )clear all ---S 43 +--S 43 of 188 f n == for i in 1..n repeat j:=2*i @@ -580,7 +580,7 @@ f n == --R Type: Void --E 43 ---S 44 +--S 44 of 188 g n == j:=2*n m:SQMATRIX(j,?):=1 @@ -589,7 +589,7 @@ g n == --R Type: Void --E 44 ---S 45 +--S 45 of 188 g 3 --R --R Cannot compile the declaration for m because its (possible partial) @@ -609,7 +609,7 @@ g 3 --R Type: Void --E 45 ---S 46 +--S 46 of 188 f 3 --R --R Cannot compile the declaration for m because its (possible partial) @@ -644,7 +644,7 @@ Test interpreter list destructuring <<*>>= )clear all ---S 47 +--S 47 of 188 mp(x,l) == l is [a,:b] => a*x**(#b)+ mp(x,b) @@ -653,7 +653,7 @@ mp(x,l) == --R Type: Void --E 47 ---S 48 +--S 48 of 188 mp(x, [1,3,4, 2]) --R --R Compiling function mp with type (Variable x,List PositiveInteger) @@ -664,7 +664,7 @@ mp(x, [1,3,4, 2]) --R Type: Polynomial Integer --E 48 ---S 49 +--S 49 of 188 mp(x, [1,2,-3, 4]) --R --R Compiling function mp with type (Variable x,List Integer) -> @@ -680,14 +680,14 @@ Tests compilation of recursive functions <<*>>= )clear all ---S 50 +--S 50 of 188 f1 n == if n=0 then 1 else if n=1 then 1 else f1(n-1)+f1(n-2) --R --R Type: Void --E 50 ---S 51 +--S 51 of 188 f2 n == m:=n if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2) @@ -695,7 +695,7 @@ f2 n == --R Type: Void --E 51 ---S 52 +--S 52 of 188 f3 n == n=0 => 1 n=1 => 1 @@ -704,7 +704,7 @@ f3 n == --R Type: Void --E 52 ---S 53 +--S 53 of 188 f4 n == m:=n n=0 => 1 @@ -715,13 +715,13 @@ f4 n == --R Type: Void --E 53 ---S 54 +--S 54 of 188 f5 n == if n=0 or n=1 then 1 else f5(n-1)+f5(n-2) --R --R Type: Void --E 54 ---S 55 +--S 55 of 188 [f1 3,f2 3, f3 3,f4 3,f5 3] --R --R Compiling function f1 with type Integer -> PositiveInteger @@ -739,7 +739,7 @@ Input of GDMP types. Fixed by SCM on 1/22/91 <<*>>= )clear all ---S 56 +--S 56 of 188 g: GDMP([x,y], INT, DIRPROD(2, NNI)) := x**2 + y --R --R @@ -753,7 +753,7 @@ Has test with variables. Fixed by SCM on 1/22/91 <<*>>= )clear all ---S 57 +--S 57 of 188 i := INT --R --R @@ -761,7 +761,7 @@ i := INT --R Type: Domain --E 57 ---S 58 +--S 58 of 188 i has Algebra(i) --R --R @@ -774,13 +774,13 @@ Returns in functions. Fixed by SCM on 1/22/91 <<*>>= )clear all ---S 59 +--S 59 of 188 f x == if x<0 then return x else x+1 --R --R Type: Void --E 59 ---S 60 +--S 60 of 188 f 2 -- should be 3 --R --R Compiling function f with type PositiveInteger -> PositiveInteger @@ -789,7 +789,7 @@ f 2 -- should be 3 --R Type: PositiveInteger --E 60 ---S 61 +--S 61 of 188 f(-2) -- should be -2 --R --R Compiling function f with type Integer -> Integer @@ -803,7 +803,7 @@ resolveTT not returning Any. Fixed by SCM 1/30/91 <<*>>= )clear all ---S 62 +--S 62 of 188 m = [[1,2],[2,3]] -- Should return type EQ POLY SQMATRIX(2, INT) --R --R @@ -813,7 +813,7 @@ m = [[1,2],[2,3]] -- Should return type EQ POLY SQMATRIX(2, INT) --R Type: Equation Polynomial SquareMatrix(2,Integer) --E 62 ---S 63 +--S 63 of 188 [1, "asd"] -- Should be of type List Any --R --R @@ -823,7 +823,7 @@ m = [[1,2],[2,3]] -- Should return type EQ POLY SQMATRIX(2, INT) )set mes test off ---S 64 +--S 64 of 188 1+"asd" -- These should both fail in the same way --R --R There are 12 exposed and 5 unexposed library operations named + @@ -843,7 +843,7 @@ m = [[1,2],[2,3]] -- Should return type EQ POLY SQMATRIX(2, INT) --R or "$" to specify which version of the function you need. --E 64 ---S 65 +--S 65 of 188 1/"asd" --R --R There are 13 exposed and 12 unexposed library operations named / @@ -870,7 +870,7 @@ Passing type variables to )show <<*>>= )clear all ---S 66 +--S 66 of 188 t := MPOLY([x,y], INT) --R --R @@ -878,7 +878,7 @@ t := MPOLY([x,y], INT) --R Type: Domain --E 66 ---S 67 +--S 67 of 188 )show t --R --R MultivariatePolynomial([x,y],Integer) is a domain constructor. @@ -998,19 +998,19 @@ Caching nullary functions <<*>>= )clear all ---S 68 +--S 68 of 188 )set fun cache all --R --R In general, interpreter functions will cache all values. --E 68 ---S 69 +--S 69 of 188 u == 1 --R --R Type: Void --E 69 ---S 70 +--S 70 of 188 u --R --R Compiling body of rule u to compute value of type PositiveInteger @@ -1020,7 +1020,7 @@ u --R Type: PositiveInteger --E 70 ---S 71 +--S 71 of 188 )set fun cache 0 --R --R In general, functions will cache no returned values. @@ -1031,13 +1031,13 @@ Interpreter Only mode on collects. Fixed by SCM on 3/1/91 <<*>>= )clear all ---S 72 +--S 72 of 188 factorp: (UP(x,INT),PositiveInteger,PositiveInteger) -> List(UP(x,INT)) --R --R Type: Void --E 72 ---S 73 +--S 73 of 188 factorp(poly,p,e) == ppoly:UP(x,PF p):=poly pl := [rec.factor for rec in factors factor ppoly] @@ -1046,7 +1046,7 @@ factorp(poly,p,e) == --R Type: Void --E 73 ---S 74 +--S 74 of 188 factorp(x**2+x+5,7,1) --R --R Cannot compile the declaration for ppoly because its (possible @@ -1065,7 +1065,7 @@ Using "by" with segments. Fixed by SCM on 2/14/91 <<*>>= )clear all ---S 75 +--S 75 of 188 b:= 1..10 --R --R @@ -1073,7 +1073,7 @@ b:= 1..10 --R Type: Segment PositiveInteger --E 75 ---S 76 +--S 76 of 188 for i in b by 2 repeat output i --R --R 1 @@ -1089,55 +1089,55 @@ DMP resolve bug. Fixed by SCM 3/7/91 <<*>>= )clear all ---S 77 +--S 77 of 188 macro RN == FRAC INT --R --R Type: Void --E 77 ---S 78 +--S 78 of 188 a51:=x+y+z+t+u; --R --R --R Type: Polynomial Integer --E 78 ---S 79 +--S 79 of 188 a52:=x*y+y*z+z*t+x*u+t*u; --R --R --R Type: Polynomial Integer --E 79 ---S 80 +--S 80 of 188 a53:=x*y*z+y*z*t+x*y*u+x*t*u+z*t*u; --R --R --R Type: Polynomial Integer --E 80 ---S 81 +--S 81 of 188 a54:=x*y*z*t+x*y*z*u+x*y*t*u+x*z*t*u+y*z*t*u; --R --R --R Type: Polynomial Integer --E 81 ---S 82 +--S 82 of 188 a55:=x*y*z*t*u-1; --R --R --R Type: Polynomial Integer --E 82 ---S 83 +--S 83 of 188 arnborg5: List HDMP([x,y,z,t,u],RN):=[a51,a52,a53,a54,a55]; --R --R --RType: List HomogeneousDistributedMultivariatePolynomial([x,y,z,t,u],Fraction Integer) --E 83 ---S 84 +--S 84 of 188 arnborg5l: List DMP([x,y,z,t,u],RN):=[a51,a52,a53,a54,a55]; --R --R @@ -1149,14 +1149,14 @@ Construct in interpret-only mode. Fixed by SCM on 3/7/91 <<*>>= )clear all ---S 85 +--S 85 of 188 factorp(poly,p,e) == [rec.factor for rec in factors factor (poly::UP(x, PF p))]::List UP(x, INT) --R --R Type: Void --E 85 ---S 86 +--S 86 of 188 factorp(x**2+x+5,7,1) --R --R Cannot compile conversion for types involving local variables. In @@ -1173,7 +1173,7 @@ Return in interpret-only mode. fixed by SCM 3/11/91 <<*>>= )clear all ---S 87 +--S 87 of 188 f (x) == y: PF x := 1 x = 3 => return x @@ -1183,7 +1183,7 @@ f (x) == --R Type: Void --E 87 ---S 88 +--S 88 of 188 f 3 --R --R Cannot compile the declaration for y because its (possible partial) @@ -1199,7 +1199,7 @@ Incorrect handling of type of returns. fixed by SCM 3/11/91 <<*>>= )clear all ---S 89 +--S 89 of 188 f (x) == x = 3 => return x x = 4 => return(-x) @@ -1208,7 +1208,7 @@ f (x) == --R Type: Void --E 89 ---S 90 +--S 90 of 188 f 3 --R --R Compiling function f with type PositiveInteger -> Integer @@ -1222,7 +1222,7 @@ SquareMatrix coercion bug. Fixed by SCM on 4/3/91 <<*>>= )clear all ---S 91 +--S 91 of 188 s:SQMATRIX(2, INT) := matrix [[1,2],[2,3]] --R --R @@ -1232,7 +1232,7 @@ s:SQMATRIX(2, INT) := matrix [[1,2],[2,3]] --R Type: SquareMatrix(2,Integer) --E 91 ---S 92 +--S 92 of 188 s::SQMATRIX(2, FRAC INT) --R --R @@ -1247,7 +1247,7 @@ SquareMatric resolve bug <<*>>= )clear all ---S 93 +--S 93 of 188 Mat := SquareMatrix(2, Polynomial Integer) --R --R @@ -1255,7 +1255,7 @@ Mat := SquareMatrix(2, Polynomial Integer) --R Type: Domain --E 93 ---S 94 +--S 94 of 188 s:Mat := matrix [[ 2*x + 1, x], [x, 1]] --R --R @@ -1265,7 +1265,7 @@ s:Mat := matrix [[ 2*x + 1, x], [x, 1]] --R Type: SquareMatrix(2,Polynomial Integer) --E 94 ---S 95 +--S 95 of 188 s**3 --R --R @@ -1277,7 +1277,7 @@ s**3 --R Type: SquareMatrix(2,Polynomial Integer) --E 95 ---S 96 +--S 96 of 188 %::Polynomial(?) --R --R @@ -1292,7 +1292,7 @@ Parsing bug. Fixed by BURGE on 4/18/91 <<*>>= )clear all ---S 97 +--S 97 of 188 -2**2 -- Should return -4 --R --R @@ -1305,7 +1305,7 @@ Parsing bug. Fixed by BURGE on 4/18/91 <<*>>= )clear all ---S 98 +--S 98 of 188 f: DMP([x,y], INT) := x**2-y**2 --R --R @@ -1314,7 +1314,7 @@ f: DMP([x,y], INT) := x**2-y**2 --R Type: DistributedMultivariatePolynomial([x,y],Integer) --E 98 ---S 99 +--S 99 of 188 coefficient(f, degree f) --R --R @@ -1327,7 +1327,7 @@ Retract from EXPR to POLY. fixed by SCM and SUTOR on 5/1/91 <<*>>= )clear all ---S 100 +--S 100 of 188 x+1::EXPR INT --R --R @@ -1335,7 +1335,7 @@ x+1::EXPR INT --R Type: Expression Integer --E 100 ---S 101 +--S 101 of 188 %::POLY INT --R --R @@ -1348,7 +1348,7 @@ Fixed by SCM in May <<*>>= )clear all ---S 102 +--S 102 of 188 solve([[1,2],[2,3]],[-2,3]) --R --R @@ -1361,7 +1361,7 @@ Fixed by several people over a period of time <<*>>= )clear all ---S 103 +--S 103 of 188 eval(m**2, m=[[1,2],[2,3]]) --R --R @@ -1378,14 +1378,14 @@ Filtering various illegal declarations )set mes test off ---S 104 +--S 104 of 188 r: Ring --R --R --R Ring is a category, not a domain, and declarations require domains. --E 104 ---S 105 +--S 105 of 188 w: RF INT --R --R @@ -1400,7 +1400,7 @@ Correct representation of length 1 records <<*>>= )clear all ---S 106 +--S 106 of 188 r:Record(a: INT) := [1] --R --R @@ -1413,7 +1413,7 @@ Fast generation of POLY FLOAT graphics code <<*>>= )clear all ---S 107 +--S 107 of 188 p: POLY FLOAT := (x-1)**30 --R --R @@ -1448,7 +1448,7 @@ Case broken in interpreter. fixed by SCM in early 1991 <<*>>= )clear all ---S 108 +--S 108 of 188 sayBranch x == _ if x case INT then output "Integer Branch" _ else if x case STRING then output "String Branch" _ @@ -1458,13 +1458,13 @@ sayBranch x == _ --R Type: Void --E 108 ---S 109 +--S 109 of 188 x:Union(INT,STRING,FLOAT) --R --R Type: Void --E 109 ---S 110 +--S 110 of 188 x:=3 --R --R @@ -1472,7 +1472,7 @@ x:=3 --R Type: Union(Integer,...) --E 110 ---S 111 +--S 111 of 188 sayBranch(x) --R --R @@ -1486,7 +1486,7 @@ Bug in evaluateType. fixed by SCM in May 1991 <<*>>= )clear all ---S 112 +--S 112 of 188 RFI := FRAC POLY INT --R --R @@ -1494,7 +1494,7 @@ RFI := FRAC POLY INT --R Type: Domain --E 112 ---S 113 +--S 113 of 188 g:DMP([x,y], RFI) := a**2*x**2/b**2 - c**2*y**2/d**2 --R --R @@ -1506,7 +1506,7 @@ g:DMP([x,y], RFI) := a**2*x**2/b**2 - c**2*y**2/d**2 --R Type: DistributedMultivariatePolynomial([x,y],Fraction Polynomial Integer) --E 113 ---S 114 +--S 114 of 188 factor g --R --R @@ -1523,7 +1523,7 @@ Bug in resolveTTSpecial. Fixed by SCM 6/2/91 <<*>>= )clear all ---S 115 +--S 115 of 188 f(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+v --R --R Function declaration f : (DoubleFloat,DoubleFloat) -> DoubleFloat @@ -1531,7 +1531,7 @@ f(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+v --R Type: Void --E 115 ---S 116 +--S 116 of 188 g(u:DoubleFloat, v:DoubleFloat):DoubleFloat == sin(u+v) --R --R Function declaration g : (DoubleFloat,DoubleFloat) -> DoubleFloat @@ -1539,7 +1539,7 @@ g(u:DoubleFloat, v:DoubleFloat):DoubleFloat == sin(u+v) --R Type: Void --E 116 ---S 117 +--S 117 of 188 h(u:DoubleFloat, v:DoubleFloat):DoubleFloat == u+cos(v) --R --R Function declaration h : (DoubleFloat,DoubleFloat) -> DoubleFloat @@ -1556,7 +1556,7 @@ Check for package calling from categories. fixed by SCM 6/4/91 )set mes test off ---S 118 +--S 118 of 188 (1+1)$Ring --R --R @@ -1571,7 +1571,7 @@ UnivariateSeries coercions. Fixed by SCM 6/20/91 <<*>>= )clear all ---S 119 +--S 119 of 188 s := series(sin(a*x), x=0) --R --R @@ -1582,7 +1582,7 @@ s := series(sin(a*x), x=0) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 119 ---S 120 +--S 120 of 188 s - a*x --R --R @@ -1597,7 +1597,7 @@ s - a*x --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 120 ---S 121 +--S 121 of 188 s - sin(a*x) --R --R @@ -1611,7 +1611,7 @@ Complex \& AlgebraicNumber coercions. fixed by SCM 6/91 <<*>>= )clear all ---S 122 +--S 122 of 188 sin %i --R --R @@ -1619,7 +1619,7 @@ sin %i --R Type: Expression Complex Integer --E 122 ---S 123 +--S 123 of 188 sin sqrt 2 --R --R @@ -1628,7 +1628,7 @@ sin sqrt 2 --R Type: Expression Integer --E 123 ---S 124 +--S 124 of 188 %i*sqrt(2) --R --R @@ -1637,7 +1637,7 @@ sin sqrt 2 --R Type: Expression Complex Integer --E 124 ---S 125 +--S 125 of 188 sin(%i*sqrt 2) --R --R @@ -1646,7 +1646,7 @@ sin(%i*sqrt 2) --R Type: Expression Complex Integer --E 125 ---S 126 +--S 126 of 188 %i * sin(x) --R --R @@ -1654,7 +1654,7 @@ sin(%i*sqrt 2) --R Type: Expression Complex Integer --E 126 ---S 127 +--S 127 of 188 sin(x/sqrt(2)) --R --R @@ -1672,7 +1672,7 @@ Bug in resolve. fixed by SCM 8/12/91 )set msg test off ---S 128 +--S 128 of 188 primaryDecomp xx --R --R There are 1 exposed and 0 unexposed library operations named @@ -1699,14 +1699,14 @@ Functions with ADEFs were broken. fixed by SCM 8/9/91 <<*>>= )clear all ---S 129 +--S 129 of 188 f l == reduce((x,y) +-> l.1 + x + y, l) --R --R Type: Void --E 129 ---S 130 +--S 130 of 188 f [10,2,53] --R --R Compiling function f with type List PositiveInteger -> @@ -1716,14 +1716,14 @@ f [10,2,53] --R Type: PositiveInteger --E 130 ---S 131 +--S 131 of 188 g l == (x:INT):INT +-> l.x --R --R Type: Void --E 131 ---S 132 +--S 132 of 188 w := g [23,1,341,12] ; --R --R Compiling function g with type List PositiveInteger -> (Integer -> @@ -1732,7 +1732,7 @@ w := g [23,1,341,12] ; --R Type: (Integer -> Integer) --E 132 ---S 133 +--S 133 of 188 w(1) + w(3) --R --R @@ -1740,7 +1740,7 @@ w(1) + w(3) --R Type: PositiveInteger --E 133 ---S 134 +--S 134 of 188 w(-1) --R --R @@ -1757,7 +1757,7 @@ Coerces RN to PF and POLY to EXPR. fixed by SCM 8/9/91 <<*>>= )clear all ---S 135 +--S 135 of 188 a := 2/3 --R --R @@ -1769,7 +1769,7 @@ a := 2/3 )set mes test off ---S 136 +--S 136 of 188 a::PF 3 --R --R @@ -1778,7 +1778,7 @@ a::PF 3 )set mes test on ---S 137 +--S 137 of 188 b := x+1 --R --R @@ -1786,7 +1786,7 @@ b := x+1 --R Type: Polynomial Integer --E 137 ---S 138 +--S 138 of 188 b:: EXPR FLOAT --R --R @@ -1799,7 +1799,7 @@ Minivector use in coercion functions. <<*>>= )clear all ---S 139 +--S 139 of 188 symbol(s:Symbol,i:Integer):Symbol == st0:String:= convert(i) st0:= concat(string(s),st0) @@ -1810,13 +1810,13 @@ symbol(s:Symbol,i:Integer):Symbol == --R Type: Void --E 139 ---S 140 +--S 140 of 188 f(a,b) == symbol(a,b) --R --R Type: Void --E 140 ---S 141 +--S 141 of 188 f('abc,3) --R --R Compiling function symbol with type (Symbol,Integer) -> Symbol @@ -1832,7 +1832,7 @@ Coercing undeclared maps to Mapping types. fixed by SCM 9/3/91 <<*>>= )clear all ---S 142 +--S 142 of 188 f := operator 'f --R --R @@ -1840,7 +1840,7 @@ f := operator 'f --R Type: BasicOperator --E 412 ---S 143 +--S 143 of 188 y := f(x) --R --R @@ -1848,13 +1848,13 @@ y := f(x) --R Type: Expression Integer --E 143 ---S 144 +--S 144 of 188 foo(u) == sin(u) --R --R Type: Void --E 144 ---S 145 +--S 145 of 188 eval(y, 'f, foo) --R --R There are 2 exposed and 6 unexposed library operations named sin @@ -1876,7 +1876,7 @@ Package calling constants. fixed by SCM 9/3/91 <<*>>= )clear all ---S 146 +--S 146 of 188 init()$(PF 3) --R --R @@ -1896,7 +1896,7 @@ DP bug. Don't know where this came from, but its fixed. DP makes problems: <<*>>= )clear all ---S 147 +--S 147 of 188 dmp := DMP([u1,u2,u3],Fraction INT) --R --R @@ -1904,7 +1904,7 @@ dmp := DMP([u1,u2,u3],Fraction INT) --R Type: Domain --E 147 ---S 148 +--S 148 of 188 p : dmp := 2*u1**4*u2*u3 --R --R @@ -1913,7 +1913,7 @@ p : dmp := 2*u1**4*u2*u3 --R Type: DistributedMultivariatePolynomial([u1,u2,u3],Fraction Integer) --E 148 ---S 149 +--S 149 of 188 e1 := degree p --R --R @@ -1921,7 +1921,7 @@ e1 := degree p --R Type: DirectProduct(3,NonNegativeInteger) --E 149 ---S 150 +--S 150 of 188 e2 : DirectProduct(3,NonNegativeInteger) := e1 --R --R @@ -1929,7 +1929,7 @@ e2 : DirectProduct(3,NonNegativeInteger) := e1 --R Type: DirectProduct(3,NonNegativeInteger) --E 150 ---S 151 +--S 151 of 188 sup(e1,e1) --R --R @@ -1941,7 +1941,7 @@ sup(e1,e1) If you give to many infos to the Interpreter it has problems. <<*>>= ---S 152 +--S 152 of 188 sup(e1,e1)$DirectProduct(3,NonNegativeInteger) --R --R @@ -1951,7 +1951,7 @@ sup(e1,e1)$DirectProduct(3,NonNegativeInteger) )clear all ---S 153 +--S 153 of 188 sum:=0 --R --R @@ -1959,7 +1959,7 @@ sum:=0 --R Type: NonNegativeInteger --E 153 ---S 154 +--S 154 of 188 m:=matrix [[1,2],[3,4]] --R --R @@ -1969,7 +1969,7 @@ m:=matrix [[1,2],[3,4]] --R Type: Matrix Integer --E 154 ---S 155 +--S 155 of 188 lastcol:=ncols(m) --R --R @@ -1977,7 +1977,7 @@ lastcol:=ncols(m) --R Type: PositiveInteger --E 155 ---S 156 +--S 156 of 188 for r in 1..nrows(m) repeat -- interpreter having a value for "row" would cause it to hide -- the system function @@ -1988,7 +1988,7 @@ for r in 1..nrows(m) repeat --R Type: Void --E 156 ---S 157 +--S 157 of 188 sum --R --R @@ -2002,14 +2002,14 @@ fixed by SCM <<*>>= )clear all ---S 158 +--S 158 of 188 splitPoly(f,var) == map(g +-> multivariate(g,var),monomials univariate(f,var)) --R --R Type: Void --E 158 ---S 159 +--S 159 of 188 g:=sin(x)+cos(x) --R --R @@ -2017,7 +2017,7 @@ g:=sin(x)+cos(x) --R Type: Expression Integer --E 159 ---S 160 +--S 160 of 188 k:=kernels(g).1 --R --R @@ -2027,7 +2027,7 @@ k:=kernels(g).1 )set mes test off ---S 161 +--S 161 of 188 splitPoly([g],k) -- this is an incorrect call --R --R There are 4 exposed and 1 unexposed library operations named @@ -2064,7 +2064,7 @@ splitPoly([g],k) -- this is an incorrect call )set mes test on ---S 162 +--S 162 of 188 splitPoly(numer g,k) -- this is a correct call --R --R Compiling function splitPoly with type (SparseMultivariatePolynomial @@ -2081,7 +2081,7 @@ Scoping of lambda variables. fixed by SCM in March, 1992 <<*>>= )clear all ---S 163 +--S 163 of 188 f x == g := (y:DoubleFloat):DoubleFloat +-> y+x output(y+1) @@ -2090,7 +2090,7 @@ f x == --R Type: Void --E 163 ---S 164 +--S 164 of 188 f 3 --R --R Compiling function f with type PositiveInteger -> DoubleFloat @@ -2107,13 +2107,13 @@ fixed by SCM in March, 1992 <<*>>= )clear all ---S 165 +--S 165 of 188 f x == 1/factorial(x) --R --R Type: Void --E 165 ---S 166 +--S 166 of 188 series(f, x=0) --R --R Compiling function f with type Integer -> Expression Integer @@ -2134,43 +2134,43 @@ Rule dependencies with dependencies on the operator position. <<*>>= )clear all ---S 167 +--S 167 of 188 node_a == i1+i2+i3-i5+i6=0 --R --R Type: Void --E 167 ---S 168 +--S 168 of 188 node_b == -i2-i3+i4-i6=0 --R --R Type: Void --E 168 ---S 169 +--S 169 of 188 i1 == va/r1 --R --R Type: Void --E 169 ---S 170 +--S 170 of 188 i2 == (va-vb)/r2 --R --R Type: Void --E 170 ---S 171 +--S 171 of 188 i3 == (va-vb)/r3 --R --R Type: Void --E 171 ---S 172 +--S 172 of 188 i4 == vb/r4 --R --R Type: Void --E 172 ---S 173 +--S 173 of 188 node_a --R --R Compiling body of rule i1 to compute value of type Fraction @@ -2188,7 +2188,7 @@ node_a --R Type: Equation Fraction Polynomial Integer --E 173 ---S 174 +--S 174 of 188 node_b --R --R Compiling body of rule i4 to compute value of type Fraction @@ -2202,25 +2202,25 @@ node_b --R Type: Equation Fraction Polynomial Integer --E 174 ---S 175 +--S 175 of 188 ans == solve([node_a,node_b],[va,vb]) -- (*) --R --R Type: Void --E 175 ---S 176 +--S 176 of 188 x1 == rhs(ans.1.1) --R --R Type: Void --E 176 ---S 177 +--S 177 of 188 x2 == rhs(ans.1.2) --R --R Type: Void --E 177 ---S 178 +--S 178 of 188 x1 -- (**) --R --R Compiling body of rule ans to compute value of type List List @@ -2234,7 +2234,7 @@ x1 -- (**) --R Type: Fraction Polynomial Integer --E 178 ---S 179 +--S 179 of 188 r1 == 2 -- (***) --R --R Compiled code for i1 has been cleared. @@ -2244,7 +2244,7 @@ r1 == 2 -- (***) --R Type: Void --E 179 ---S 180 +--S 180 of 188 x1 -- (****) --R --R Compiling body of rule r1 to compute value of type PositiveInteger @@ -2269,7 +2269,7 @@ fixed in March 1992 by SCM and RSS <<*>>= )clear all ---S 181 +--S 181 of 188 "asd" "sdfsdf" "dfgdfg" --R --R @@ -2283,7 +2283,7 @@ fixed by SCM <<*>>= )clear all ---S 182 +--S 182 of 188 s := 3.4 --R --R @@ -2291,7 +2291,7 @@ s := 3.4 --R Type: Float --E 182 ---S 183 +--S 183 of 188 while s > 1.0 repeat (s := 1/2; print s) --R --R 1 @@ -2300,7 +2300,7 @@ while s > 1.0 repeat (s := 1/2; print s) --R Type: Void --E 183 ---S 184 +--S 184 of 188 s --R --R @@ -2312,7 +2312,7 @@ s )clear all ---S 185 +--S 185 of 188 f x == free s s := x @@ -2322,7 +2322,7 @@ f x == --R Type: Void --E 185 ---S 186 +--S 186 of 188 f(3.4) --R --R Compiling function f with type Float -> Float @@ -2338,7 +2338,7 @@ Returns in sequences. fixed by SCM <<*>>= )clear all ---S 187 +--S 187 of 188 t x == if x = 1 then (1; return [x]) return [2] @@ -2346,7 +2346,7 @@ t x == --R Type: Void --E 187 ---S 188 +--S 188 of 188 t 1 --R --R Compiling function t with type PositiveInteger -> List diff --git a/src/input/tutchap1.input.pamphlet b/src/input/tutchap1.input.pamphlet index d0c41f9..7ad8065 100644 --- a/src/input/tutchap1.input.pamphlet +++ b/src/input/tutchap1.input.pamphlet @@ -152,7 +152,7 @@ c : PositiveInteger := 3 )clear properties c i ---S 16 of 19 +--S 16 of 19 %%(1) --R --R diff --git a/src/input/void.input.pamphlet b/src/input/void.input.pamphlet index 928c5a6..dc1dc55 100644 --- a/src/input/void.input.pamphlet +++ b/src/input/void.input.pamphlet @@ -26,7 +26,7 @@ a : Integer )set message void on ---S 2 of 4 +--S 2 of 4 b : Fraction Integer --R --R @@ -36,7 +36,7 @@ b : Fraction Integer )set message void off ---S 3 of 4 +--S 3 of 4 3::Void --R --R Type: Void