diff --git a/changelog b/changelog index f70de7f..c57088b 100644 --- a/changelog +++ b/changelog @@ -1,4 +1,7 @@ -20120110 tpd src/axiom-website/patches.html 20130110.01.tpd.patch +20130122 tpd src/axiom-website/patches.html 20130122.01.tpd.patch +20130122 tpd src/input/Makefile trigtests added +20130122 tpd src/input/trigtests.input added +20130110 tpd src/axiom-website/patches.html 20130110.01.tpd.patch 20120110 tpd books/bookvolbib add Koutschan 20120106 tpd src/axiom-website/patches.html 20130106.01.tpd.patch 20130106 tpd books/bookvolbib add Che86 diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 557209b..eaefa97 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -3945,5 +3945,9 @@ Makefile.pamphlet add mint stanza
src/axiom-website/documentation.html 20130105.01.tpd.patch src/input/cherry.input added +20130110.01.tpd.patch +books/bookvolbib add Koutschan +20130122.01.tpd.patch +src/input/trigtests.input added diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 49f9a1a..0b5ddde 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -400,7 +400,7 @@ REGRESSTESTS= ackermann.regress \ test.regress testpackage.regress \ testprob.regress textfile.regress torus.regress tuplebug.regress \ tpiezas001.regress \ - tpiezas002.regress \ + tpiezas002.regress trigtests.regress \ triglim.regress tsetcatvermeer.regress tutchap1.regress \ typetower.regress void.regress uniseg.regress \ unittest1.regress unittest2.regress unittest3.regress unittest4.regress \ @@ -808,7 +808,7 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/tetra.input ${OUT}/textfile.input ${OUT}/tknot.input \ ${OUT}/tpiezas001.input \ ${OUT}/tpiezas002.input \ - ${OUT}/tree.input \ + ${OUT}/tree.input ${OUT}/trigtests.input \ ${OUT}/triglim.input ${OUT}/tschirn.input ${OUT}/tsetcatbutcher.input \ ${OUT}/tsetcatchemical.input ${OUT}/tsetcatvermeer.input \ ${OUT}/tuplebug.input \ @@ -1271,7 +1271,7 @@ DOCFILES= \ ${DOC}/testprob.input.dvi \ ${DOC}/tpiezas001.input.dvi \ ${DOC}/tpiezas002.input.dvi \ - ${DOC}/tree.input.dvi \ + ${DOC}/tree.input.dvi ${DOC}/trigtests.input.dvi \ ${DOC}/triglim.input.dvi ${DOC}/tschirn.input.dvi \ ${DOC}/tsetcatbutcher.input.dvi \ ${DOC}/tsetcatchemical.input.dvi \ diff --git a/src/input/trigtests.input.pamphlet b/src/input/trigtests.input.pamphlet new file mode 100644 index 0000000..da3cc78 --- /dev/null +++ b/src/input/trigtests.input.pamphlet @@ -0,0 +1,1102 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input trigtests.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f trigtests.output +)spool trigtests.output +)set message test on +)set message auto off +)clear all + +------------------------------------- +-- Definition of Hyperbolic Functions +------------------------------------- + +-- Hyperbolic sine of x, p26, 8.1 +--S 1 of 89 +t01:= sinh(x) - (exp(x)-exp(-x))/2 +--R +--R +--R x - x +--R 2sinh(x) - %e + %e +--R (1) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 1 + +-- Hyperbolic cosine of x, p26, 8.2 +--S 2 of 89 +t02:= cosh(x) - (exp(x)+exp(-x))/2 +--R +--R +--R x - x +--R - %e - %e + 2cosh(x) +--R (2) ------------------------ +--R 2 +--R Type: Expression(Integer) +--E 2 + +-- Hyperbolic tangent of x, p26, 8.3 +--S 3 of 89 +t03:= tanh(x) - (exp(x)-exp(-x))/(exp(x)+exp(-x)) +--R +--R +--R x - x x - x +--R (%e + %e )tanh(x) - %e + %e +--R (3) ---------------------------------- +--R x - x +--R %e + %e +--R Type: Expression(Integer) +--E 3 + +-- Hyperbolic cotangent of x, p26, 8.4 +--S 4 of 89 +t04:= coth(x) - (exp(x)+exp(-x))/(exp(x)-exp(-x)) +--R +--R +--R x - x +--R (coth(x) - 1)%e + (- coth(x) - 1)%e +--R (4) --------------------------------------- +--R x - x +--R %e - %e +--R Type: Expression(Integer) +--E 4 + +-- Hyperbolic secant of x, p26, 8.5 +--S 5 of 89 +t05:= sech(x) - 2/(exp(x)+exp(-x)) +--R +--R +--R x - x +--R (%e + %e )sech(x) - 2 +--R (5) ------------------------ +--R x - x +--R %e + %e +--R Type: Expression(Integer) +--E 5 + +-- Hyperbolic cosecant of x, p26, 8.6 +--S 6 of 89 +t06:= csch(x) - 2/(exp(x)-exp(-x)) +--R +--R +--R x - x +--R csch(x)%e - csch(x)%e - 2 +--R (6) ----------------------------- +--R x - x +--R %e - %e +--R Type: Expression(Integer) +--E 6 + +------------------------------------------- +-- Relationships among Hyperbolic Functions +------------------------------------------- + +-- Hyperbolic tangent of x, p26, 8.7 +--S 7 of 89 +t07:= tanh(x) - sinh(x)/cosh(x) +--R +--R +--R cosh(x)tanh(x) - sinh(x) +--R (7) ------------------------ +--R cosh(x) +--R Type: Expression(Integer) +--E 7 + +-- Hyperbolic cotangent of x, p26, 8.8 +--S 8 of 89 +t08:= coth(x) - 1/tanh(x) +--R +--R +--R coth(x)tanh(x) - 1 +--R (8) ------------------ +--R tanh(x) +--R Type: Expression(Integer) +--E 8 + +-- Hyperbolic cotangent of x, p26, 8.8 +--S 9 of 89 +t09:= coth(x) - cosh(x)/sinh(x) +--R +--R +--R coth(x)sinh(x) - cosh(x) +--R (9) ------------------------ +--R sinh(x) +--R Type: Expression(Integer) +--E 9 + +-- Hyperbolic secant of x, p26, 8.9 +--S 10 of 89 +t10:= sech(x) - 1/cosh(x) +--R +--R +--R cosh(x)sech(x) - 1 +--R (10) ------------------ +--R cosh(x) +--R Type: Expression(Integer) +--E 10 + +-- Hyperbolic cosecant of x, p26, 8.10 +--S 11 of 89 +t11:= csch(x) - 1/sinh(x) +--R +--R +--R csch(x)sinh(x) - 1 +--R (11) ------------------ +--R sinh(x) +--R Type: Expression(Integer) +--E 11 + +-- p26, 8.11 +--S 12 of 89 +t12:= cosh(x)^2-sinh(x)^2 - 1 +--R +--R +--R 2 2 +--R (12) - sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 12 + +-- p26, 8.12 +--S 13 of 89 +t13:= sech(x)^2+tanh(x)^2 - 1 +--R +--R +--R 2 2 +--R (13) tanh(x) + sech(x) - 1 +--R Type: Expression(Integer) +--E 13 + +-- p26, 8.13 +--S 14 of 89 +t14:= coth(x)^2-csch(x)^2 - 1 +--R +--R +--R 2 2 +--R (14) - csch(x) + coth(x) - 1 +--R Type: Expression(Integer) +--E 14 + +---------------------------------- +-- Functions of Negative Arguments +---------------------------------- + +-- p26, 8.14 +--S 15 of 89 +t15:= sinh(-x) - (-sinh(x)) +--R +--R +--R (15) 0 +--R Type: Expression(Integer) +--E 15 + +-- p26, 8.15 +--S 16 of 89 +t16:= cosh(-x) - cosh(x) +--R +--R +--R (16) 0 +--R Type: Expression(Integer) +--E 16 + +-- p26, 8.16 +--S 17 of 89 +t17:= tanh(-x) - (-tanh(x)) +--R +--R +--R (17) 0 +--R Type: Expression(Integer) +--E 17 + +-- p26, 8.17 +--S 18 of 89 +t18:= csch(-x) - (-csch(x)) +--R +--R +--R (18) 0 +--R Type: Expression(Integer) +--E 18 + +-- p26, 8.18 +--S 19 of 89 +t19:= sech(-x) - sech(x) +--R +--R +--R (19) 0 +--R Type: Expression(Integer) +--E 19 + +-- p26, 8.19 +--S 20 of 89 +t20:= coth(-x) - (-coth(x)) +--R +--R +--R (20) 0 +--R Type: Expression(Integer) +--E 20 + +-------------------- +-- Addition Formulas +-------------------- + +-- p27, 8.20 +--S 21 of 89 +t21:= sinh(x+y) - sinh(x)*cosh(y)+cosh(x)*sinh(y) +--R +--R +--R (21) sinh(y + x) + cosh(x)sinh(y) - cosh(y)sinh(x) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 89 +t22:= sinh(x-y) - sinh(x)*cosh(y)-cosh(x)*sinh(y) +--R +--R +--R (22) - cosh(x)sinh(y) - sinh(y - x) - cosh(y)sinh(x) +--R Type: Expression(Integer) +--E 22 + +-- p27, 8.21 +--S 23 of 89 +t23:= cosh(x+y) - cosh(x)*cosh(y)+sinh(x)*sinh(y) +--R +--R +--R (23) sinh(x)sinh(y) + cosh(y + x) - cosh(x)cosh(y) +--R Type: Expression(Integer) +--E 23 + +--S 24 of 89 +t24:= cosh(x-y) - cosh(x)*cosh(y)-sinh(x)*sinh(y) +--R +--R +--R (24) - sinh(x)sinh(y) - cosh(x)cosh(y) + cosh(y - x) +--R Type: Expression(Integer) +--E 24 + +-- p27, 8.22 +--S 25 of 89 +t25:= tanh(x+y) - (tanh(x)+tanh(y))/(1+tanh(x)*tanh(y)) +--R +--R +--R (tanh(x)tanh(y) + 1)tanh(y + x) - tanh(y) - tanh(x) +--R (25) --------------------------------------------------- +--R tanh(x)tanh(y) + 1 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 89 +t26:= tanh(x-y) - (tanh(x)-tanh(y))/(1-tanh(x)*tanh(y)) +--R +--R +--R (- tanh(x)tanh(y - x) - 1)tanh(y) + tanh(y - x) + tanh(x) +--R (26) --------------------------------------------------------- +--R tanh(x)tanh(y) - 1 +--R Type: Expression(Integer) +--E 26 + +-- p27, 8.23 +--S 27 of 89 +t27:= coth(x+y) - (coth(x)*coth(y)+1)/(coth(y)+coth(x)) +--R +--R +--R (coth(y) + coth(x))coth(y + x) - coth(x)coth(y) - 1 +--R (27) --------------------------------------------------- +--R coth(y) + coth(x) +--R Type: Expression(Integer) +--E 27 + +--S 28 of 89 +t28:= coth(x-y) - (coth(x)*coth(y)-1)/(coth(y)-coth(x)) +--R +--R +--R (- coth(y - x) - coth(x))coth(y) + coth(x)coth(y - x) + 1 +--R (28) --------------------------------------------------------- +--R coth(y) - coth(x) +--R Type: Expression(Integer) +--E 28 + +------------------------ +-- Double Angle Formulas +------------------------ + +-- p27, 8.24 +--S 29 of 89 +t29:= sinh(2*x) - 2*sinh(x)*cosh(x) +--R +--R +--R (29) sinh(2x) - 2cosh(x)sinh(x) +--R Type: Expression(Integer) +--E 29 + +-- p27, 8.25 +--S 30 of 89 +t30:= cosh(2*x) - cosh(x)^2+sinh(x)^2 +--R +--R +--R 2 2 +--R (30) sinh(x) + cosh(2x) - cosh(x) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 89 +t31:= cosh(2*x) - 2*cosh(x)^2-1 +--R +--R +--R 2 +--R (31) cosh(2x) - 2cosh(x) - 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 89 +t32:= cosh(2*x) - 1+2*sinh(x)^2 +--R +--R +--R 2 +--R (32) 2sinh(x) + cosh(2x) - 1 +--R Type: Expression(Integer) +--E 32 + +-- p27, 8.26 +--S 33 of 89 +t33:= tanh(2*x) - (2*tanh(x))/(1+tanh(x)^2) +--R +--R +--R 2 +--R (tanh(x) + 1)tanh(2x) - 2tanh(x) +--R (33) --------------------------------- +--R 2 +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 33 + +---------------------- +-- Half Angle Formulas +---------------------- + +-- p27, 8.27, assume x > 0 +--S 34 of 89 +t34:= sinh(x/2) - sqrt((cosh(x)-1)/2) +--R +--R +--R +-----------+ +-+ x +--R - \|cosh(x) - 1 + \|2 sinh(-) +--R 2 +--R (34) ------------------------------ +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 34 + +-- p27, 8.27, assume x < 0 +--S 35 of 89 +t35:= sinh(x/2) - (-sqrt((cosh(x)-1)/2)) +--R +--R +--R +-----------+ +-+ x +--R \|cosh(x) - 1 + \|2 sinh(-) +--R 2 +--R (35) ---------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 35 + +-- p27, 8.28 +--S 36 of 89 +t36:= cosh(x/2) - sqrt((cosh(x)+1)/2) +--R +--R +--R +-----------+ +-+ x +--R - \|cosh(x) + 1 + \|2 cosh(-) +--R 2 +--R (36) ------------------------------ +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 36 + +-- p27, 8.29, assume x > 0 +--S 37 of 89 +t37:= tanh(x/2) - sqrt((cosh(x)-1)/(cosh(x)+1)) +--R +--R +--R +-----------+ +--R |cosh(x) - 1 x +--R (37) - |----------- + tanh(-) +--R \|cosh(x) + 1 2 +--R Type: Expression(Integer) +--E 37 + +-- p27, 8.29, assume x < 0 +--S 38 of 89 +t38:= tanh(x/2) - (-sqrt((cosh(x)-1)/(cosh(x)+1))) +--R +--R +--R +-----------+ +--R |cosh(x) - 1 x +--R (38) |----------- + tanh(-) +--R \|cosh(x) + 1 2 +--R Type: Expression(Integer) +--E 38 + +-- p27, 8.29 +--S 39 of 89 +t39:= tanh(x/2) - sinh(x)/(cosh(x)+1) +--R +--R +--R x +--R (cosh(x) + 1)tanh(-) - sinh(x) +--R 2 +--R (39) ------------------------------ +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 39 + +-- p27, 8.29 +--S 40 of 89 +t40:= tanh(x/2) - (cosh(x)-1)/sinh(x) +--R +--R +--R x +--R sinh(x)tanh(-) - cosh(x) + 1 +--R 2 +--R (40) ---------------------------- +--R sinh(x) +--R Type: Expression(Integer) +--E 40 + +-------------------------- +-- Multiple Angle Formulas +-------------------------- + +-- p27, 8.30 +--S 41 of 89 +t41:= sinh(3*x) - 3*sinh(x)+4*sinh(x)^3 +--R +--R +--R 3 +--R (41) sinh(3x) + 4sinh(x) - 3sinh(x) +--R Type: Expression(Integer) +--E 41 + +-- p27, 8.31 +--S 42 of 89 +t42:= cosh(3*x) - 4*cosh(x)^3-3*cosh(x) +--R +--R +--R 3 +--R (42) cosh(3x) - 4cosh(x) - 3cosh(x) +--R Type: Expression(Integer) +--E 42 + +-- p27, 8.32 +--S 43 of 89 +t43:= tanh(3*x) - (3*tanh(x)+tanh(x)^3)/(1+3*tanh(x)^2) +--R +--R +--R 2 3 +--R (3tanh(x) + 1)tanh(3x) - tanh(x) - 3tanh(x) +--R (43) --------------------------------------------- +--R 2 +--R 3tanh(x) + 1 +--R Type: Expression(Integer) +--E 43 + +-- p27, 8.33 +--S 44 of 89 +t44:= sinh(4*x) - 8*sinh(x)^3*cosh(x)+4*sinh(x)*cosh(x) +--R +--R +--R 3 +--R (44) sinh(4x) - 8cosh(x)sinh(x) + 4cosh(x)sinh(x) +--R Type: Expression(Integer) +--E 44 + +-- p27, 8.34 +--S 45 of 89 +t45:= cosh(4*x) - 8*cosh(x)^4-8*cosh(x)^2+1 +--R +--R +--R 4 2 +--R (45) cosh(4x) - 8cosh(x) - 8cosh(x) + 1 +--R Type: Expression(Integer) +--E 45 + +-- p27, 8.35 +--S 46 of 89 +t46:= tanh(4*x) - (4*tanh(x)+4*tanh(x)^3)/(1+6*tanh(x)^2+tanh(x)^4) +--R +--R +--R 4 2 3 +--R (tanh(x) + 6tanh(x) + 1)tanh(4x) - 4tanh(x) - 4tanh(x) +--R (46) --------------------------------------------------------- +--R 4 2 +--R tanh(x) + 6tanh(x) + 1 +--R Type: Expression(Integer) +--E 46 + +--------------------------------- +-- Powers of Hyperbolic Functions +--------------------------------- + +-- p28, 8.36 +--S 47 of 89 +t47:= sinh(x)^2 - cosh(2*x)/2-1/2 +--R +--R +--R 2 +--R 2sinh(x) - cosh(2x) - 1 +--R (47) ------------------------ +--R 2 +--R Type: Expression(Integer) +--E 47 + +-- p28, 8.37 +--S 48 of 89 +t48:= cosh(x)^2 - cosh(2*x)/2+1/2 +--R +--R +--R 2 +--R - cosh(2x) + 2cosh(x) + 1 +--R (48) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 48 + +-- p28, 8.38 +--S 49 of 89 +t49:= sinh(x)^3 - sinh(3*x)/4-3*sinh(x)/4 +--R +--R +--R 3 +--R - sinh(3x) + 4sinh(x) - 3sinh(x) +--R (49) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 49 + +-- p28, 8.39 +--S 50 of 89 +t50:= cosh(x)^3 - cosh(3*x)/4+3*cosh(x)/4 +--R +--R +--R 3 +--R - cosh(3x) + 4cosh(x) + 3cosh(x) +--R (50) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 50 + +-- p28, 8.40 +--S 51 of 89 +t51:= sinh(x)^4 - 3/8-cosh(2*x)/2+cosh(4*x)/8 +--R +--R +--R 4 +--R 8sinh(x) + cosh(4x) - 4cosh(2x) - 3 +--R (51) ------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 51 + +-- p28, 8.41 +--S 52 of 89 +t52:= cosh(x)^4 - 3/8+cosh(2*x)/2+cosh(4*x)/8 +--R +--R +--R 4 +--R cosh(4x) + 4cosh(2x) + 8cosh(x) - 3 +--R (52) ------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 52 + +------------------------------------------------------- +--- Sum, Difference and Product of Hyperbolic Functions +------------------------------------------------------- + +-- p28, 8.42 +--S 53 of 89 +t53:= sinh(x)+sinh(y) - 2*sinh((x+y)/2)*cosh((x-y)/2) +--R +--R +--R y - x y + x +--R (53) sinh(y) - 2cosh(-----)sinh(-----) + sinh(x) +--R 2 2 +--R Type: Expression(Integer) +--E 53 + +-- p28, 8.43 +--S 54 of 89 +t54:= sinh(x)-sinh(y) - 2*cosh((x+y)/2)*sinh((x-y)/2) +--R +--R +--R y + x y - x +--R (54) - sinh(y) + 2cosh(-----)sinh(-----) + sinh(x) +--R 2 2 +--R Type: Expression(Integer) +--E 54 + +-- p28, 8.44 +--S 55 of 89 +t55:= cosh(x)+cosh(y) - 2*cosh((x+y)/2)*cosh((x-y)/2) +--R +--R +--R y - x y + x +--R (55) cosh(y) - 2cosh(-----)cosh(-----) + cosh(x) +--R 2 2 +--R Type: Expression(Integer) +--E 55 + +-- p28, 8.45 +--S 56 of 89 +t56:= cosh(x)-cosh(y) - 2*sinh((x+y)/2)*sinh((x-y)/2) +--R +--R +--R y - x y + x +--R (56) 2sinh(-----)sinh(-----) - cosh(y) + cosh(x) +--R 2 2 +--R Type: Expression(Integer) +--E 56 + +-- p28, 8.46 +--S 57 of 89 +t57:= sinh(x)*sinh(y) - (cosh(x+y)-cosh(x-y))/2 +--R +--R +--R 2sinh(x)sinh(y) - cosh(y + x) + cosh(y - x) +--R (57) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 57 + +-- p28, 8.47 +--S 58 of 89 +t58:= cosh(x)*cosh(y) - (cosh(x+y)+cosh(x-y))/2 +--R +--R +--R - cosh(y + x) + 2cosh(x)cosh(y) - cosh(y - x) +--R (58) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 58 + +-- p28, 8.48 +--S 59 of 89 +t59:= sinh(x)*cosh(y) - (sinh(x+y)+sinh(x-y))/2 +--R +--R +--R - sinh(y + x) + sinh(y - x) + 2cosh(y)sinh(x) +--R (59) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 59 + +-------------------------------------------------------- +-- Expression of Hyperbolic Functions in terms of others +-------------------------------------------------------- + +-- p28, table +--S 60 of 89 +t60:= sinh(x) - sqrt(cosh(x)-1) +--R +--R +--R +-----------+ +--R (60) - \|cosh(x) - 1 + sinh(x) +--R Type: Expression(Integer) +--E 60 + +--S 61 of 89 +t61:= sinh(x) - tanh(x)/sqrt(1-tanh(x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R sinh(x)\|- tanh(x) + 1 - tanh(x) +--R (61) ---------------------------------- +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 89 +t62:= sinh(x) - 1/sqrt(coth(x)^2-1) +--R +--R +--R +------------+ +--R | 2 +--R sinh(x)\|coth(x) - 1 - 1 +--R (62) -------------------------- +--R +------------+ +--R | 2 +--R \|coth(x) - 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 89 +t63:= sinh(x) - sqrt(1-sech(x)^2)/sech(x) +--R +--R +--R +--------------+ +--R | 2 +--R - \|- sech(x) + 1 + sech(x)sinh(x) +--R (63) ------------------------------------ +--R sech(x) +--R Type: Expression(Integer) +--E 63 + +--S 64 of 89 +t64:= sinh(x) - 1/csch(x) +--R +--R +--R csch(x)sinh(x) - 1 +--R (64) ------------------ +--R csch(x) +--R Type: Expression(Integer) +--E 64 + +--S 65 of 89 +t65:= cosh(x) - sqrt(1+sinh(x)^2) +--R +--R +--R +------------+ +--R | 2 +--R (65) - \|sinh(x) + 1 + cosh(x) +--R Type: Expression(Integer) +--E 65 + +--S 66 of 89 +t66:= cosh(x) - 1/sqrt(1-tanh(x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R cosh(x)\|- tanh(x) + 1 - 1 +--R (66) ---------------------------- +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 89 +t67:= cosh(x) - coth(x)/sqrt(coth(x)^2-1) +--R +--R +--R +------------+ +--R | 2 +--R cosh(x)\|coth(x) - 1 - coth(x) +--R (67) -------------------------------- +--R +------------+ +--R | 2 +--R \|coth(x) - 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 89 +t68:= cosh(x) - 1/sech(x) +--R +--R +--R cosh(x)sech(x) - 1 +--R (68) ------------------ +--R sech(x) +--R Type: Expression(Integer) +--E 68 + +--S 69 of 89 +t69:= cosh(x) - sqrt(1+csch(x)^2)/csch(x) +--R +--R +--R +------------+ +--R | 2 +--R - \|csch(x) + 1 + cosh(x)csch(x) +--R (69) ---------------------------------- +--R csch(x) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 89 +t70:= tanh(x) - sinh(x)/sqrt(1+sinh(x)^2) +--R +--R +--R +------------+ +--R | 2 +--R tanh(x)\|sinh(x) + 1 - sinh(x) +--R (70) -------------------------------- +--R +------------+ +--R | 2 +--R \|sinh(x) + 1 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 89 +t71:= tanh(x) - sqrt(cosh(x)^2-1)/cosh(x) +--R +--R +--R +------------+ +--R | 2 +--R - \|cosh(x) - 1 + cosh(x)tanh(x) +--R (71) ---------------------------------- +--R cosh(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 89 +t72:= tanh(x) - 1/coth(x) +--R +--R +--R coth(x)tanh(x) - 1 +--R (72) ------------------ +--R coth(x) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 89 +t73:= tanh(x) - sqrt(1-sech(x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (73) - \|- sech(x) + 1 + tanh(x) +--R Type: Expression(Integer) +--E 73 + +--S 74 of 89 +t74:= tanh(x) - 1/sqrt(1+csch(x)^2) +--R +--R +--R +------------+ +--R | 2 +--R tanh(x)\|csch(x) + 1 - 1 +--R (74) -------------------------- +--R +------------+ +--R | 2 +--R \|csch(x) + 1 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 89 +t75:= coth(x) - sqrt(sinh(x)^2+1)/sinh(x) +--R +--R +--R +------------+ +--R | 2 +--R - \|sinh(x) + 1 + coth(x)sinh(x) +--R (75) ---------------------------------- +--R sinh(x) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 89 +t76:= coth(x) - cosh(x)/sqrt(cosh(x)^2-1) +--R +--R +--R +------------+ +--R | 2 +--R coth(x)\|cosh(x) - 1 - cosh(x) +--R (76) -------------------------------- +--R +------------+ +--R | 2 +--R \|cosh(x) - 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 89 +t77:= coth(x) - 1/tanh(x) +--R +--R +--R coth(x)tanh(x) - 1 +--R (77) ------------------ +--R tanh(x) +--R Type: Expression(Integer) +--E 77 + +--S 78 of 89 +t78:= coth(x) - 1/sqrt(1-sech(x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R coth(x)\|- sech(x) + 1 - 1 +--R (78) ---------------------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 78 + +--S 79 of 89 +t79:= coth(x) - sqrt(1+csch(x)^2) +--R +--R +--R +------------+ +--R | 2 +--R (79) - \|csch(x) + 1 + coth(x) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 89 +t80:= sech(x) - 1/sqrt(1+sinh(x)^2) +--R +--R +--R +------------+ +--R | 2 +--R sech(x)\|sinh(x) + 1 - 1 +--R (80) -------------------------- +--R +------------+ +--R | 2 +--R \|sinh(x) + 1 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 89 +t81:= sech(x) - 1/cosh(x) +--R +--R +--R cosh(x)sech(x) - 1 +--R (81) ------------------ +--R cosh(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 89 +t82:= sech(x) - sqrt(1-tanh(x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (82) - \|- tanh(x) + 1 + sech(x) +--R Type: Expression(Integer) +--E 82 + +--S 83 of 89 +t83:= sech(x) - sqrt(coth(x)^2-1)/coth(x) +--R +--R +--R +------------+ +--R | 2 +--R - \|coth(x) - 1 + coth(x)sech(x) +--R (83) ---------------------------------- +--R coth(x) +--R Type: Expression(Integer) +--E 83 + +--S 84 of 89 +t84:= sech(x) - csch(x)/sqrt(1+csch(x)^2) +--R +--R +--R +------------+ +--R | 2 +--R sech(x)\|csch(x) + 1 - csch(x) +--R (84) -------------------------------- +--R +------------+ +--R | 2 +--R \|csch(x) + 1 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 89 +t85:= csch(x) - 1/sinh(x) +--R +--R +--R csch(x)sinh(x) - 1 +--R (85) ------------------ +--R sinh(x) +--R Type: Expression(Integer) +--E 85 + +--S 86 of 89 +t86:= csch(x) - 1/sqrt(cosh(x)^2-1) +--R +--R +--R +------------+ +--R | 2 +--R csch(x)\|cosh(x) - 1 - 1 +--R (86) -------------------------- +--R +------------+ +--R | 2 +--R \|cosh(x) - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 89 +t87:= csch(x) - sqrt(1-tanh(x)^2)/tanh(x) +--R +--R +--R +--------------+ +--R | 2 +--R - \|- tanh(x) + 1 + csch(x)tanh(x) +--R (87) ------------------------------------ +--R tanh(x) +--R Type: Expression(Integer) +--E 87 + +--S 88 of 89 +t88:= csch(x) - sqrt(coth(x)^2-1) +--R +--R +--R +------------+ +--R | 2 +--R (88) - \|coth(x) - 1 + csch(x) +--R Type: Expression(Integer) +--E 88 + +--S 89 of 89 +t89:= csch(x) - sech(x)/sqrt(1-sech(x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R csch(x)\|- sech(x) + 1 - sech(x) +--R (89) ---------------------------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 89 + +-- +-- +-- sec(x)-1/cos(x) +-- csc(x)-1/sin(x) +-- cot(x)-1/tan(x) +-- +-- asin(x)-atan(x/sqrt(1-xx)) +-- acos(x)-(%pi/2-asin(x)) +-- asec(x)-atan(sqrt(x*x-1))+(sign(x)-1)*%pi/2 +-- acos(x)-atan(1/(sqrt(x*x-1))+(sign(x)-1)*%pi/2 +-- acot(x)+atan(x)+%pi/2 +-- +-- asinh(x)-log(x+sqrt(xx+1)) +-- acosh(x)-log(x+sqrt(xx-1)) +-- atanh(x)-log((1+x)/(1-x))/2 +-- +-- asech(x)-log((sqrt(1-xx)-1)/x) +-- acosh(x)-log(1+sign(x)*sqrt(1+x*x))/x +-- acoth(x)-log((x+1)/(x-1))/2 +-- +-- log(x)=log(x)/log(10) +-- pi-4*atan(1) +-- +-- sin(14885392687.0) -- should be 1.671 x 10^10 maybe use MPFR? +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + +