diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index 818fdb9..0f98a25 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -3596,34 +3596,44 @@ AntiSymm(R:Ring, lVar:List Symbol): Exports == Implementation where Term ==> Record(k:EAB,c:R) Exports == Join(LALG(R), RetractableTo(R)) with + leadingCoefficient : % -> R ++ leadingCoefficient(p) returns the leading ++ coefficient of antisymmetric polynomial p. + leadingBasisTerm : % -> % ++ leadingBasisTerm(p) returns the leading ++ basis term of antisymmetric polynomial p. + reductum : % -> % ++ reductum(p), where p is an antisymmetric polynomial, ++ returns p minus the leading ++ term of p if p has at least two terms, and 0 otherwise. + coefficient : (%,%) -> R ++ coefficient(p,u) returns the coefficient of ++ the term in p containing the basis term u if such ++ a term exists, and 0 otherwise. ++ Error: if the second argument u is not a basis element. + generator : NNI -> % ++ generator(n) returns the nth multiplicative generator, ++ a basis term. + exp : L I -> % ++ exp([i1,...in]) returns \spad{u_1\^{i_1} ... u_n\^{i_n}} + homogeneous? : % -> Boolean ++ homogeneous?(p) tests if all of the terms of ++ p have the same degree. + retractable? : % -> Boolean ++ retractable?(p) tests if p is a 0-form, ++ i.e., if degree(p) = 0. + degree : % -> NNI ++ degree(p) returns the homogeneous degree of p. + map : (R -> R, %) -> % ++ map(f,p) changes each coefficient of p by the ++ application of f. @@ -4536,6 +4546,7 @@ latex a )lisp (bye) \end{chunk} + \begin{chunk}{ArrayStack.help} ==================================================================== ArrayStack examples @@ -4765,6 +4776,480 @@ o )show Heap o )show BagAggregate \end{chunk} + +\begin{chunk}{arrayStack.help} +==================================================================== +arrayStack from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + arrayStack + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + arrayStack: List S -> % + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + arrayStack([x,y,...,z]) creates an array stack with first (top) + element x, second element y,...,and last element z. + +ARGUMENTS +========= + + An element from List(SetCategory) + +RETURN VALUE +============ + + An element of ArrayStack(S:SetCategory) + +EXAMPLES +======== + + c:ArrayStack INT:= arrayStack [1,2,3,4,5] + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op arrayStack + +\end{chunk} + +\begin{chunk}{pop!.help} +==================================================================== +pop! from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + pop! + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + pop! : % -> S + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + pop! destructively modifies its argument and returns the + first item of the argument + +ARGUMENTS +========= + + An element from ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + An element of ArrayStack(S:SetCategory) + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + pop! a + a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op pop! + +\end{chunk} + +\begin{chunk}{extract!.help} +==================================================================== +extract! from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + extract! + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + extract! : % -> S + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + extract! destructively modifies its argument and returns the + first item of the argument + +ARGUMENTS +========= + + An element from ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + An element of ArrayStack(S:SetCategory) + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + extract! a + a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op extract! + +\end{chunk} + +\begin{chunk}{push!.help} +==================================================================== +push! from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + push! + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + push! : (S,%) -> S + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + push! destructively modifies its argument and returns a new + list with the element add to the front of the list + +ARGUMENTS +========= + + The first argument is an element of S:SetCategory + + The second argument is an element of ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + An element of S:SetCategory + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + push! a + a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op push! + +\end{chunk} + +\begin{chunk}{insert!.help} +==================================================================== +insert! from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + insert! + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + insert! : (S,%) -> S + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + insert! destructively modifies its argument and returns a new + list with the element add to the front of the list + +ARGUMENTS +========= + + The first argument is an element of S:SetCategory + + The second argument is an element of ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + An element of S:SetCategory + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + insert! a + a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op insert! + +\end{chunk} + +\begin{chunk}{inspect.help} +==================================================================== +inspect from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + inspect + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + inspect : % -> S + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + inspect returns the first item of the list without modifing the list + +ARGUMENTS +========= + + The argument is an element of ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + An element of the list + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + inspect a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op inspect + +\end{chunk} + +\begin{chunk}{top.help} +==================================================================== +top from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + top + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + top : % -> S + + where S is the argument of the constructor + ArrayStack(S:SetCategory) + +DESCRIPTION +=========== + + top returns the first item of the list without modifing the list + +ARGUMENTS +========= + + The argument is an element of ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + An element of the list + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + top a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op top + +\end{chunk} + +\begin{chunk}{depth.help} +==================================================================== +depth from ArrayStack (ASTACK) +==================================================================== + +NAME +==== + + depth + +DOMAIN +====== + + ArrayStack (ASTACK) + +SYNOPSYS +======== + + depth : % -> NonNegativeInteger + +DESCRIPTION +=========== + + depth returns the number of elements + +ARGUMENTS +========= + + The argument is an element of ArrayStack(S:SetCategory) + +RETURN VALUE +============ + + The number of elements in the list + +EXAMPLES +======== + + a:ArrayStack INT:= arrayStack [1,2,3,4,5] + depth a + +NOTES +===== + +REFERENCES +========== + +SEE ALSO +======== + +o )show ArrayStack +o )d op depth + +\end{chunk} + \pagehead{ArrayStack}{ASTACK} \pagepic{ps/v103arraystack.ps}{ASTACK}{1.00} {\bf See}\\ @@ -4819,144 +5304,190 @@ o )show BagAggregate --% Dequeue and Heap data types ArrayStack(S:SetCategory): StackAggregate(S) with + arrayStack: List S -> % ++ arrayStack([x,y,...,z]) creates an array stack with first (top) ++ element x, second element y,...,and last element z. ++ - ++E c:ArrayStack INT:= arrayStack [1,2,3,4,5] + ++X c:ArrayStack INT:= arrayStack [1,2,3,4,5] -- Inherited Signatures repeated for examples documentation pop_! : % -> S + ++ pop! destructively modifies its argument and returns the + ++ first item of the argument ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X pop! a ++X a + extract_! : % -> S + ++ extract! destructively modifies its argument and returns the + ++ first item of the argument ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X extract! a ++X a + push_! : (S,%) -> S + ++ push! destructively modifies its argument and returns a new + ++ list with the element add to the front of the list ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X push!(9,a) ++X a + insert_! : (S,%) -> % + ++ insert! destructively modifies its argument and returns a new + ++ list with the element add to the front of the list ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X insert!(8,a) ++X a + inspect : % -> S + ++ inspect returns the first item of the list without modifing the list ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X inspect a + top : % -> S + ++ top returns the first item of the list without modifing the list ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X top a + depth : % -> NonNegativeInteger + ++ depth returns the number of elements ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X depth a + less? : (%,NonNegativeInteger) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X less?(a,9) + more? : (%,NonNegativeInteger) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X more?(a,9) + size? : (%,NonNegativeInteger) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X size?(a,5) + bag : List S -> % ++ ++X bag([1,2,3,4,5])$ArrayStack(INT) + empty? : % -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X empty? a + empty : () -> % ++ ++X b:=empty()$(ArrayStack INT) + sample : () -> % ++ ++X sample()$ArrayStack(INT) + copy : % -> % ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X copy a + eq? : (%,%) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X b:=copy a ++X eq?(a,b) + map : ((S -> S),%) -> % ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X map(x+->x+10,a) ++X a + if $ has shallowlyMutable then + map! : ((S -> S),%) -> % ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X map!(x+->x+10,a) ++X a + if S has SetCategory then + latex : % -> String ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X latex a + hash : % -> SingleInteger ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X hash a + coerce : % -> OutputForm ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X coerce a + "=": (%,%) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X b:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X (a=b)@Boolean + "~=" : (%,%) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X b:=copy a ++X (a~=b) + if % has finiteAggregate then + every? : ((S -> Boolean),%) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X every?(x+->(x=4),a) + any? : ((S -> Boolean),%) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X any?(x+->(x=4),a) + count : ((S -> Boolean),%) -> NonNegativeInteger ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X count(x+->(x>2),a) + _# : % -> NonNegativeInteger ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X #a + parts : % -> List S ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X parts a + members : % -> List S ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X members a + if % has finiteAggregate and S has SetCategory then + member? : (S,%) -> Boolean ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] ++X member?(3,a) + count : (S,%) -> NonNegativeInteger ++ ++X a:ArrayStack INT:= arrayStack [1,2,3,4,5] @@ -27820,7 +28351,8 @@ Dequeue(S:SetCategory): DequeueAggregate S with )set message test on )set message auto off )clear all ---S 1 of 100 + +--S 1 of 148 coefRing := Integer --R --R @@ -27828,7 +28360,7 @@ coefRing := Integer --R Type: Domain --E 1 ---S 2 of 100 +--S 2 of 148 lv : List Symbol := [x,y,z] --R --R @@ -27836,7 +28368,7 @@ lv : List Symbol := [x,y,z] --R Type: List(Symbol) --E 2 ---S 3 of 100 +--S 3 of 148 der := DERHAM(coefRing,lv) --R --R @@ -27844,7 +28376,7 @@ der := DERHAM(coefRing,lv) --R Type: Domain --E 3 ---S 4 of 100 +--S 4 of 148 R := Expression coefRing --R --R @@ -27852,7 +28384,7 @@ R := Expression coefRing --R Type: Domain --E 4 ---S 5 of 100 +--S 5 of 148 f : R := x**2*y*z-5*x**3*y**2*z**5 --R --R @@ -27861,7 +28393,7 @@ f : R := x**2*y*z-5*x**3*y**2*z**5 --R Type: Expression(Integer) --E 5 ---S 6 of 100 +--S 6 of 148 g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --R --R @@ -27870,7 +28402,7 @@ g : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 --R Type: Expression(Integer) --E 6 ---S 7 of 100 +--S 7 of 148 h : R :=x*y*z-2*x**3*y*z**2 --R --R @@ -27879,7 +28411,7 @@ h : R :=x*y*z-2*x**3*y*z**2 --R Type: Expression(Integer) --E 7 ---S 8 of 100 +--S 8 of 148 dx : der := generator(1) --R --R @@ -27887,7 +28419,7 @@ dx : der := generator(1) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 8 ---S 9 of 100 +--S 9 of 148 dy : der := generator(2) --R --R @@ -27895,7 +28427,7 @@ dy : der := generator(2) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 9 ---S 10 of 100 +--S 10 of 148 dz : der := generator(3) --R --R @@ -27903,7 +28435,7 @@ dz : der := generator(3) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 10 ---S 11 of 100 +--S 11 of 148 [dx,dy,dz] := [generator(i)$der for i in 1..3] --R --R @@ -27911,7 +28443,7 @@ dz : der := generator(3) --R Type: List(DeRhamComplex(Integer,[x,y,z])) --E 11 ---S 12 of 100 +--S 12 of 148 alpha : der := f*dx + g*dy + h*dz --R --R @@ -27924,7 +28456,7 @@ alpha : der := f*dx + g*dy + h*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 12 ---S 13 of 100 +--S 13 of 148 beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy --R --R @@ -27932,8 +28464,8 @@ beta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy --R Type: DeRhamComplex(Integer,[x,y,z]) --E 13 ---S 14 of 100 -exteriorDifferential alpha +--S 14 of 148 +m1:=exteriorDifferential alpha --R --R --R (14) @@ -27948,15 +28480,15 @@ exteriorDifferential alpha --R Type: DeRhamComplex(Integer,[x,y,z]) --E 14 ---S 15 of 100 -exteriorDifferential % +--S 15 of 148 +exteriorDifferential m1 --R --R --R (15) 0 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 15 ---S 16 of 100 +--S 16 of 148 gamma := alpha * beta --R --R @@ -27969,7 +28501,7 @@ gamma := alpha * beta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 16 ---S 17 of 100 +--S 17 of 148 exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - _ alpha * exteriorDifferential(beta)) --R @@ -27978,7 +28510,7 @@ exteriorDifferential(gamma) - (exteriorDifferential(alpha)*beta - _ --R Type: DeRhamComplex(Integer,[x,y,z]) --E 17 ---S 18 of 100 +--S 18 of 148 a : BOP := operator('a) --R --R @@ -27986,7 +28518,7 @@ a : BOP := operator('a) --R Type: BasicOperator --E 18 ---S 19 of 100 +--S 19 of 148 b : BOP := operator('b) --R --R @@ -27994,7 +28526,7 @@ b : BOP := operator('b) --R Type: BasicOperator --E 19 ---S 20 of 100 +--S 20 of 148 c : BOP := operator('c) --R --R @@ -28002,7 +28534,7 @@ c : BOP := operator('c) --R Type: BasicOperator --E 20 ---S 21 of 100 +--S 21 of 148 sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz --R --R @@ -28010,7 +28542,7 @@ sigma := a(x,y,z) * dx + b(x,y,z) * dy + c(x,y,z) * dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 21 ---S 22 of 100 +--S 22 of 148 theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz --R --R @@ -28018,7 +28550,7 @@ theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 22 ---S 23 of 100 +--S 23 of 148 totalDifferential(a(x,y,z))$der --R --R @@ -28027,7 +28559,7 @@ totalDifferential(a(x,y,z))$der --R Type: DeRhamComplex(Integer,[x,y,z]) --E 23 ---S 24 of 100 +--S 24 of 148 exteriorDifferential sigma --R --R @@ -28040,7 +28572,7 @@ exteriorDifferential sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 24 ---S 25 of 100 +--S 25 of 148 exteriorDifferential theta --R --R @@ -28049,7 +28581,7 @@ exteriorDifferential theta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 25 ---S 26 of 100 +--S 26 of 148 one : der := 1 --R --R @@ -28057,7 +28589,7 @@ one : der := 1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 26 ---S 27 of 100 +--S 27 of 148 g1 : der := a([x,t,y,u,v,z,e]) * one --R --R @@ -28065,7 +28597,7 @@ g1 : der := a([x,t,y,u,v,z,e]) * one --R Type: DeRhamComplex(Integer,[x,y,z]) --E 27 ---S 28 of 100 +--S 28 of 148 h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one --R --R @@ -28073,7 +28605,7 @@ h1 : der := a([x,y,x,t,x,z,y,r,u,x]) * one --R Type: DeRhamComplex(Integer,[x,y,z]) --E 28 ---S 29 of 100 +--S 29 of 148 exteriorDifferential g1 --R --R @@ -28082,7 +28614,7 @@ exteriorDifferential g1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 29 ---S 30 of 100 +--S 30 of 148 exteriorDifferential h1 --R --R @@ -28103,7 +28635,7 @@ exteriorDifferential h1 --R Type: DeRhamComplex(Integer,[x,y,z]) --E 30 ---S 31 of 100 +--S 31 of 148 coefficient(gamma, dx*dy) --R --R @@ -28112,7 +28644,7 @@ coefficient(gamma, dx*dy) --R Type: Expression(Integer) --E 31 ---S 32 of 100 +--S 32 of 148 coefficient(gamma, one) --R --R @@ -28120,7 +28652,7 @@ coefficient(gamma, one) --R Type: Expression(Integer) --E 32 ---S 33 of 100 +--S 33 of 148 coefficient(g1,one) --R --R @@ -28128,7 +28660,7 @@ coefficient(g1,one) --R Type: Expression(Integer) --E 33 ---S 34 of 100 +--S 34 of 148 gamma := alpha * beta --R --R @@ -28141,7 +28673,7 @@ gamma := alpha * beta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 34 ---S 35 of 100 +--S 35 of 148 t1:=generator(1)$der --R --R @@ -28149,7 +28681,7 @@ t1:=generator(1)$der --R Type: DeRhamComplex(Integer,[x,y,z]) --E 35 ---S 36 of 100 +--S 36 of 148 degree(t1) --R --R @@ -28158,9 +28690,8 @@ degree(t1) --E 36 )clear all - ---S 37 of 100 +--S 37 of 148 X:=DERHAM(Integer,[x,y,z]) --R --R @@ -28168,7 +28699,7 @@ X:=DERHAM(Integer,[x,y,z]) --R Type: Domain --E 37 ---S 38 of 100 +--S 38 of 148 [dx,dy,dz]:=[generator(i)$X for i in 1..3] --R --R @@ -28176,7 +28707,7 @@ X:=DERHAM(Integer,[x,y,z]) --R Type: List(DeRhamComplex(Integer,[x,y,z])) --E 38 ---S 39 of 100 +--S 39 of 148 f:BOP:=operator('f) --R --R @@ -28184,7 +28715,7 @@ f:BOP:=operator('f) --R Type: BasicOperator --E 39 ---S 40 of 100 +--S 40 of 148 g:BOP:=operator('g) --R --R @@ -28192,7 +28723,7 @@ g:BOP:=operator('g) --R Type: BasicOperator --E 40 ---S 41 of 100 +--S 41 of 148 h:BOP:=operator('h) --R --R @@ -28200,7 +28731,7 @@ h:BOP:=operator('h) --R Type: BasicOperator --E 41 ---S 42 of 100 +--S 42 of 148 a:BOP:=operator('a) --R --R @@ -28208,7 +28739,7 @@ a:BOP:=operator('a) --R Type: BasicOperator --E 42 ---S 43 of 100 +--S 43 of 148 b:BOP:=operator('b) --R --R @@ -28216,7 +28747,7 @@ b:BOP:=operator('b) --R Type: BasicOperator --E 43 ---S 44 of 100 +--S 44 of 148 c:BOP:=operator('c) --R --R @@ -28224,7 +28755,7 @@ c:BOP:=operator('c) --R Type: BasicOperator --E 44 ---S 45 of 100 +--S 45 of 148 sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz --R --R @@ -28232,7 +28763,7 @@ sigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 45 ---S 46 of 100 +--S 46 of 148 theta:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz --R --R @@ -28240,13 +28771,13 @@ theta:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 46 ---S 47 of 100 +--S 47 of 148 d ==> exteriorDifferential --R --R Type: Void --E 47 ---S 48 of 100 +--S 48 of 148 leadingCoefficient sigma --R --R @@ -28254,7 +28785,7 @@ leadingCoefficient sigma --R Type: Expression(Integer) --E 48 ---S 49 of 100 +--S 49 of 148 leadingBasisTerm sigma --R --R @@ -28262,7 +28793,7 @@ leadingBasisTerm sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 49 ---S 50 of 100 +--S 50 of 148 reductum sigma --R --R @@ -28270,7 +28801,7 @@ reductum sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 50 ---S 51 of 100 +--S 51 of 148 coefficient(sigma,dz) --R --R @@ -28278,7 +28809,7 @@ coefficient(sigma,dz) --R Type: Expression(Integer) --E 51 ---S 52 of 100 +--S 52 of 148 homogeneous? sigma --R --R @@ -28286,7 +28817,7 @@ homogeneous? sigma --R Type: Boolean --E 52 ---S 53 of 100 +--S 53 of 148 homogeneous? (sigma+theta) --R --R @@ -28294,7 +28825,7 @@ homogeneous? (sigma+theta) --R Type: Boolean --E 53 ---S 54 of 100 +--S 54 of 148 retractable? sigma --R --R @@ -28302,7 +28833,7 @@ retractable? sigma --R Type: Boolean --E 54 ---S 55 of 100 +--S 55 of 148 retractable? (1::X) --R --R @@ -28310,7 +28841,7 @@ retractable? (1::X) --R Type: Boolean --E 55 ---S 56 of 100 +--S 56 of 148 [degree x for x in [sigma,theta,1::X]] --R --R @@ -28318,7 +28849,7 @@ retractable? (1::X) --R Type: List(NonNegativeInteger) --E 56 ---S 57 of 100 +--S 57 of 148 R:=Expression(Integer) --R --R @@ -28326,19 +28857,19 @@ R:=Expression(Integer) --R Type: Domain --E 57 ---S 58 of 100 +--S 58 of 148 T:R->R --R --R Type: Void --E 58 ---S 59 of 100 +--S 59 of 148 T(x)==x^2 --R --R Type: Void --E 59 ---S 60 of 100 +--S 60 of 148 map(T,sigma) --R --R Compiling function T with type Expression(Integer) -> Expression( @@ -28349,7 +28880,7 @@ map(T,sigma) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 60 ---S 61 of 100 +--S 61 of 148 exteriorDifferential sigma --R --R @@ -28362,7 +28893,7 @@ exteriorDifferential sigma --R Type: DeRhamComplex(Integer,[x,y,z]) --E 61 ---S 62 of 100 +--S 62 of 148 d theta --R --R @@ -28371,7 +28902,7 @@ d theta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 62 ---S 63 of 100 +--S 63 of 148 F:=operator 'F --R --R @@ -28379,7 +28910,7 @@ F:=operator 'F --R Type: BasicOperator --E 63 ---S 64 of 100 +--S 64 of 148 nullForm:=F(x,y,z)*(1::X) --R --R @@ -28387,7 +28918,7 @@ nullForm:=F(x,y,z)*(1::X) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 64 ---S 65 of 100 +--S 65 of 148 d nullForm --R --R @@ -28396,7 +28927,7 @@ d nullForm --R Type: DeRhamComplex(Integer,[x,y,z]) --E 65 ---S 66 of 100 +--S 66 of 148 totalDifferential(x^2+y^2+sin(x)*z^2)$X --R --R @@ -28405,7 +28936,7 @@ totalDifferential(x^2+y^2+sin(x)*z^2)$X --R Type: DeRhamComplex(Integer,[x,y,z]) --E 66 ---S 67 of 100 +--S 67 of 148 d(d sigma) --R --R @@ -28420,7 +28951,7 @@ d(d sigma) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 67 ---S 68 of 100 +--S 68 of 148 d(d theta) --R --R @@ -28428,7 +28959,7 @@ d(d theta) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 68 ---S 69 of 100 +--S 69 of 148 sigma*theta --R --R @@ -28436,7 +28967,7 @@ sigma*theta --R Type: DeRhamComplex(Integer,[x,y,z]) --E 69 ---S 70 of 100 +--S 70 of 148 dx*dy+dy*dx --R --R @@ -28444,7 +28975,7 @@ dx*dy+dy*dx --R Type: DeRhamComplex(Integer,[x,y,z]) --E 70 ---S 71 of 100 +--S 71 of 148 sigma+dz --R --R @@ -28452,7 +28983,7 @@ sigma+dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 71 ---S 72 of 100 +--S 72 of 148 theta-(2/3)*sigma+%pi*dx --R --R @@ -28465,7 +28996,7 @@ theta-(2/3)*sigma+%pi*dx --R Type: DeRhamComplex(Integer,[x,y,z]) --E 72 ---S 73 of 100 +--S 73 of 148 G:=diagonalMatrix([1,1,1]) --R --R @@ -28477,7 +29008,7 @@ G:=diagonalMatrix([1,1,1]) --R Type: Matrix(Integer) --E 73 ---S 74 of 100 +--S 74 of 148 dot(sigma,sigma,G) --R --R @@ -28486,7 +29017,7 @@ dot(sigma,sigma,G) --R Type: Expression(Integer) --E 74 ---S 75 of 100 +--S 75 of 148 hodgeStar(sigma,G) --R --R @@ -28494,7 +29025,7 @@ hodgeStar(sigma,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 75 ---S 76 of 100 +--S 76 of 148 A:=dot(sigma,sigma,G)*sqrt(abs(determinant(G))) --R --R @@ -28503,7 +29034,7 @@ A:=dot(sigma,sigma,G)*sqrt(abs(determinant(G))) --R Type: Expression(Integer) --E 76 ---S 77 of 100 +--S 77 of 148 B:=sigma*hodgeStar(sigma,G) --R --R @@ -28512,7 +29043,7 @@ B:=sigma*hodgeStar(sigma,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 77 ---S 78 of 100 +--S 78 of 148 test(A*dx*dy*dz=B) --R --R @@ -28520,7 +29051,7 @@ test(A*dx*dy*dz=B) --R Type: Boolean --E 78 ---S 79 of 100 +--S 79 of 148 hodgeStar(dx,G) --R --R @@ -28528,7 +29059,7 @@ hodgeStar(dx,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 79 ---S 80 of 100 +--S 80 of 148 hodgeStar(dy,G) --R --R @@ -28536,7 +29067,7 @@ hodgeStar(dy,G) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 80 ---S 81 of 100 +--S 81 of 148 d hodgeStar(d nullForm,G) --- = Laplace(F) ? --R --R @@ -28545,7 +29076,7 @@ d hodgeStar(d nullForm,G) --- = Laplace(F) ? --R Type: DeRhamComplex(Integer,[x,y,z]) --E 81 ---S 82 of 100 +--S 82 of 148 H:=diagonalMatrix([1+x^2,z^2+exp(-y^2),1/z^2]) --R --R @@ -28563,7 +29094,7 @@ H:=diagonalMatrix([1+x^2,z^2+exp(-y^2),1/z^2]) --R Type: Matrix(Expression(Integer)) --E 82 ---S 83 of 100 +--S 83 of 148 hodgeStar(dy,H) --R --R @@ -28581,7 +29112,7 @@ hodgeStar(dy,H) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 83 ---S 84 of 100 +--S 84 of 148 hodgeStar(sigma,H) --R --R @@ -28619,7 +29150,7 @@ hodgeStar(sigma,H) --R Type: DeRhamComplex(Integer,[x,y,z]) --E 84 ---S 85 of 100 +--S 85 of 148 VolH:=sqrt(abs(determinant(H)))*dx*dy*dz --R --R @@ -28633,7 +29164,7 @@ VolH:=sqrt(abs(determinant(H)))*dx*dy*dz --R Type: DeRhamComplex(Integer,[x,y,z]) --E 85 ---S 86 of 100 +--S 86 of 148 AA:=dot(sigma,sigma,H)*VolH --R --R @@ -28661,7 +29192,7 @@ AA:=dot(sigma,sigma,H)*VolH --R Type: DeRhamComplex(Integer,[x,y,z]) --E 86 ---S 87 of 100 +--S 87 of 148 BB:=sigma*hodgeStar(sigma,H) --R --R @@ -28687,126 +29218,596 @@ BB:=sigma*hodgeStar(sigma,H) --R * --R dx dy dz --R Type: DeRhamComplex(Integer,[x,y,z]) ---E 87 +--E 87 + +--S 88 of 148 +test(AA=BB) +--R +--R +--R (52) true +--R Type: Boolean +--E 88 + +--S 89 of 148 +M:=DERHAM(Integer,[t,x,y,z]) +--R +--R +--R (53) DeRhamComplex(Integer,[t,x,y,z]) +--R Type: Domain +--E 89 + +--S 90 of 148 +[dt,dx,dy,dz]:=[generator(i)$M for i in 1..4] +--R +--R +--R (54) [dt,dx,dy,dz] +--R Type: List(DeRhamComplex(Integer,[t,x,y,z])) +--E 90 + +--S 91 of 148 +L:=diagonalMatrix([1,-1,-1,-1]) +--R +--R +--R +1 0 0 0 + +--R | | +--R |0 - 1 0 0 | +--R (55) | | +--R |0 0 - 1 0 | +--R | | +--R +0 0 0 - 1+ +--R Type: Matrix(Integer) +--E 91 + +--S 92 of 148 +hodgeStar(dt,L) +--R +--R +--R (56) dx dy dz +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 92 + +--S 93 of 148 +hodgeStar(dx,L) +--R +--R +--R (57) dt dy dz +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 93 + +--S 94 of 148 +hodgeStar(dy,L) +--R +--R +--R (58) - dt dx dz +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 94 + +--S 95 of 148 +hodgeStar(dz,L) +--R +--R +--R (59) dt dx dy +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 95 + +--S 96 of 148 +hodgeStar(dt*dz,L) +--R +--R +--R (60) - dx dy +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 96 + +--S 97 of 148 +P:=a(t,x,y,z)*(dx+dy+dz-dt) +--R +--R +--R (61) a(t,x,y,z)dz + a(t,x,y,z)dy + a(t,x,y,z)dx - a(t,x,y,z)dt +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 97 + +--S 98 of 148 +dot(P,P,L) +--R +--R +--R 2 +--R (62) - 2a(t,x,y,z) +--R Type: Expression(Integer) +--E 98 + +--S 99 of 148 +P*P +--R +--R +--R (63) 0 +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 99 + +--S 100 of 148 +d P +--R +--R +--R (64) +--R (- a (t,x,y,z) + a (t,x,y,z))dy dz + (- a (t,x,y,z) + a (t,x,y,z))dx dz +--R ,4 ,3 ,4 ,2 +--R + +--R (- a (t,x,y,z) + a (t,x,y,z))dx dy + (a (t,x,y,z) + a (t,x,y,z))dt dz +--R ,3 ,2 ,4 ,1 +--R + +--R (a (t,x,y,z) + a (t,x,y,z))dt dy + (a (t,x,y,z) + a (t,x,y,z))dt dx +--R ,3 ,1 ,2 ,1 +--R Type: DeRhamComplex(Integer,[t,x,y,z]) +--E 100 + +)clear all + +--S 101 of 148 +coefRing := Integer +--R +--R +--R (1) Integer +--R Type: Domain +--E 101 + +--S 102 of 148 +R3 : List Symbol := [x,y,z] +--R +--R +--R (2) [x,y,z] +--R Type: List(Symbol) +--E 102 + +--S 103 of 148 +X := DERHAM(coefRing,R3) +--R +--R +--R (3) DeRhamComplex(Integer,[x,y,z]) +--R Type: Domain +--E 103 + +--S 104 of 148 +[dx,dy,dz] := [generator(i)$X for i in 1..3] +--R +--R +--R (4) [dx,dy,dz] +--R Type: List(DeRhamComplex(Integer,[x,y,z])) +--E 104 + +--S 105 of 148 +f : BOP := operator('f) +--R +--R +--R (5) f +--R Type: BasicOperator +--E 105 + +--S 106 of 148 +g : BOP := operator('g) +--R +--R +--R (6) g +--R Type: BasicOperator +--E 106 + +--S 107 of 148 +h : BOP := operator('h) +--R +--R +--R (7) h +--R Type: BasicOperator +--E 107 + +--S 108 of 148 +a : BOP := operator('a) +--R +--R +--R (8) a +--R Type: BasicOperator +--E 108 + +--S 109 of 148 +b : BOP := operator('b) +--R +--R +--R (9) b +--R Type: BasicOperator +--E 109 + +--S 110 of 148 +c : BOP := operator('c) +--R +--R +--R (10) c +--R Type: BasicOperator +--E 110 + +--S 111 of 148 +U : BOP := operator('U) +--R +--R +--R (11) U +--R Type: BasicOperator +--E 111 + +--S 112 of 148 +V : BOP := operator('V) +--R +--R +--R (12) V +--R Type: BasicOperator +--E 112 + +--S 113 of 148 +W : BOP := operator('W) +--R +--R +--R (13) W +--R Type: BasicOperator +--E 113 + +--S 114 of 148 +v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] +--R +--R +--R (14) [U(x,y,z),V(x,y,z),W(x,y,z)] +--R Type: Vector(Expression(Integer)) +--E 114 + +--S 115 of 148 +sigma := f(x,y,z) * dx + g(x,y,z) * dy + h(x,y,z) * dz +--R +--R +--R (15) h(x,y,z)dz + g(x,y,z)dy + f(x,y,z)dx +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 115 + +--S 116 of 148 +theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz +--R +--R +--R (16) c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 116 + +--S 117 of 148 +d ==> exteriorDifferential +--R +--R Type: Void +--E 117 + +--S 118 of 148 +G := diagonalMatrix([1,1,1]) +--R +--R +--R +1 0 0+ +--R | | +--R (18) |0 1 0| +--R | | +--R +0 0 1+ +--R Type: Matrix(Integer) +--E 118 + +--S 119 of 148 +interiorProduct(v,sigma,G) +--R +--R +--R (19) W(x,y,z)h(x,y,z) + V(x,y,z)g(x,y,z) + U(x,y,z)f(x,y,z) +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 119 + +--S 120 of 148 +interiorProduct(v,theta,G) +--R +--R +--R (20) +--R (W(x,y,z)b(x,y,z) + V(x,y,z)a(x,y,z))dx +--R + +--R (W(x,y,z)c(x,y,z) - U(x,y,z)a(x,y,z))dy +--R + +--R (- V(x,y,z)c(x,y,z) - U(x,y,z)b(x,y,z))dz +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 120 + +--S 121 of 148 +t1 := d interiorProduct(v,dz*dy*dz,G) +--R +--R +--R (21) 0 +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 121 + +--S 122 of 148 +hodgeStar(t1,G) -- should be div(v) +--R +--R +--R (22) 0 +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 122 + +--S 123 of 148 +eta := lieDerivative(v,theta,G) +--R +--R +--R (23) +--R - W(x,y,z)c (x,y,z) - V(x,y,z)c (x,y,z) - U(x,y,z)b (x,y,z) +--R ,3 ,2 ,2 +--R + +--R U(x,y,z)a (x,y,z) - c(x,y,z)W (x,y,z) - c(x,y,z)V (x,y,z) +--R ,3 ,3 ,2 +--R + +--R a(x,y,z)U (x,y,z) - b(x,y,z)U (x,y,z) +--R ,3 ,2 +--R * +--R dy dz +--R + +--R - V(x,y,z)c (x,y,z) - W(x,y,z)b (x,y,z) - U(x,y,z)b (x,y,z) +--R ,1 ,3 ,1 +--R + +--R - V(x,y,z)a (x,y,z) - b(x,y,z)W (x,y,z) - a(x,y,z)V (x,y,z) +--R ,3 ,3 ,3 +--R + +--R - c(x,y,z)V (x,y,z) - b(x,y,z)U (x,y,z) +--R ,1 ,1 +--R * +--R dx dz +--R + +--R 2W(x,y,z)c (x,y,z) - 2W(x,y,z)b (x,y,z) + W(x,y,z)a (x,y,z) +--R ,1 ,2 ,3 +--R + +--R - V(x,y,z)a (x,y,z) - U(x,y,z)a (x,y,z) - b(x,y,z)W (x,y,z) +--R ,2 ,1 ,2 +--R + +--R c(x,y,z)W (x,y,z) - a(x,y,z)V (x,y,z) - a(x,y,z)U (x,y,z) +--R ,1 ,2 ,1 +--R * +--R dx dy +--R + +--R (- V(x,y,z)c (x,y,z) + V(x,y,z)b (x,y,z) - V(x,y,z)a (x,y,z))dx dz +--R ,1 ,2 ,3 +--R + +--R (U(x,y,z)c (x,y,z) - U(x,y,z)b (x,y,z) + U(x,y,z)a (x,y,z))dy dz +--R ,1 ,2 ,3 +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 123 + +--S 124 of 148 +proj(dx+dy*dz+dx*dy*dz,2) +--R +--R +--R (24) dy dz +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 124 ---S 88 of 100 -test(AA=BB) +--S 125 of 148 +proj(sigma+theta,1) --R --R ---R (52) true ---R Type: Boolean ---E 88 +--R (25) h(x,y,z)dz + g(x,y,z)dy + f(x,y,z)dx +--R Type: DeRhamComplex(Integer,[x,y,z]) +--E 125 ---S 89 of 100 -M:=DERHAM(Integer,[t,x,y,z]) +--S 126 of 148 +dim(sigma) --R --R ---R (53) DeRhamComplex(Integer,[t,x,y,z]) +--R (26) 3 +--R Type: PositiveInteger +--E 126 + +--S 127 of 148 +degree(sigma) +--R +--R +--R (27) 1 +--R Type: PositiveInteger +--E 127 + +-- Laplace Operator for $S^2:\delta F := \star d \star dF$ +)clear all + +--S 128 of 148 +coefRing := Integer +--R +--R +--R (1) Integer --R Type: Domain ---E 89 +--E 128 ---S 90 of 100 -[dt,dx,dy,dz]:=[generator(i)$M for i in 1..4] +--S 129 of 148 +S2 : List Symbol := [r,theta] --R --R ---R (54) [dt,dx,dy,dz] ---R Type: List(DeRhamComplex(Integer,[t,x,y,z])) ---E 90 +--R (2) [r,theta] +--R Type: List(Symbol) +--E 129 ---S 91 of 100 -L:=diagonalMatrix([1,-1,-1,-1]) +--S 130 of 148 +Y := DERHAM(coefRing,S2) --R --R ---R +1 0 0 0 + ---R | | ---R |0 - 1 0 0 | ---R (55) | | ---R |0 0 - 1 0 | ---R | | ---R +0 0 0 - 1+ ---R Type: Matrix(Integer) ---E 91 +--R (3) DeRhamComplex(Integer,[r,theta]) +--R Type: Domain +--E 130 ---S 92 of 100 -hodgeStar(dt,L) +--S 131 of 148 +g := diagonalMatrix([1,r^2]) --R --R ---R (56) - dx dy dz ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 92 +--R +1 0 + +--R (4) | | +--R | 2| +--R +0 r + +--R Type: Matrix(Polynomial(Integer)) +--E 131 ---S 93 of 100 -hodgeStar(dx,L) +--S 132 of 148 +F := operator 'F --R --R ---R (57) - dt dy dz ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 93 +--R (5) F +--R Type: BasicOperator +--E 132 ---S 94 of 100 -hodgeStar(dy,L) +--S 133 of 148 +d ==> exteriorDifferential +--R +--R Type: Void +--E 133 + +--S 134 of 148 +[dr,dtheta] := [generator(i)$Y for i in 1..2] --R --R ---R (58) dt dx dz ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 94 +--R (7) [dr,dtheta] +--R Type: List(DeRhamComplex(Integer,[r,theta])) +--E 134 ---S 95 of 100 -hodgeStar(dz,L) +--S 135 of 148 +F0 := F(r,theta)*1::Y --R --R ---R (59) - dt dx dy ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 95 +--R (8) F(r,theta) +--R Type: DeRhamComplex(Integer,[r,theta]) +--E 135 ---S 96 of 100 -hodgeStar(dt*dz,L) +--S 136 of 148 +F1 := d F0 --R --R ---R (60) - dx dy ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 96 +--R (9) F (r,theta)dtheta + F (r,theta)dr +--R ,2 ,1 +--R Type: DeRhamComplex(Integer,[r,theta]) +--E 136 ---S 97 of 100 -P:=a(t,x,y,z)*(dx+dy+dz-dt) +--S 137 of 148 +F2 := hodgeStar(F1,g) --R --R ---R (61) a(t,x,y,z)dz + a(t,x,y,z)dy + a(t,x,y,z)dx - a(t,x,y,z)dt ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 97 +--R +-------+ +--R | 2 +--R \|abs(r ) F (r,theta) +-------+ +--R ,2 | 2 +--R (10) - ---------------------- dr + \|abs(r ) F (r,theta)dtheta +--R 2 ,1 +--R r +--R Type: DeRhamComplex(Integer,[r,theta]) +--E 137 ---S 98 of 100 -dot(P,P,L) +--S 138 of 148 +F3 := d F2 --R --R ---R 2 ---R (62) - 2a(t,x,y,z) +--R (11) +--R 2 2 2 2 +--R abs(r )F (r,theta) + r abs(r )F (r,theta) + r abs(r )F (r,theta) +--R ,2,2 ,1,1 ,1 +--R ----------------------------------------------------------------------- dr +--R +-------+ +--R 2 | 2 +--R r \|abs(r ) +--R * +--R dtheta +--R Type: DeRhamComplex(Integer,[r,theta]) +--E 138 + +--S 139 of 148 +LaplaceF := hodgeStar(F3,g) +--R +--R +--R (12) +--R 2 2 2 2 +--R abs(r )F (r,theta) + r abs(r )F (r,theta) + r abs(r )F (r,theta) +--R ,2,2 ,1,1 ,1 +--R ----------------------------------------------------------------------- +--R 4 +--R r +--R Type: DeRhamComplex(Integer,[r,theta]) +--E 139 + +--S 140 of 148 +LapF := LaplaceF::Expression(Integer) +--R +--R +--R (13) +--R 2 2 2 2 +--R abs(r )F (r,theta) + r abs(r )F (r,theta) + r abs(r )F (r,theta) +--R ,2,2 ,1,1 ,1 +--R ----------------------------------------------------------------------- +--R 4 +--R r --R Type: Expression(Integer) ---E 98 +--E 140 ---S 99 of 100 -P*P +--S 141 of 148 +subst(LapF,abs(r^2)=r^2) --R --R ---R (63) 0 ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 99 +--R 2 +--R F (r,theta) + r F (r,theta) + rF (r,theta) +--R ,2,2 ,1,1 ,1 +--R (14) ------------------------------------------------- +--R 2 +--R r +--R Type: Expression(Integer) +--E 141 ---S 100 of 100 -d P +-- Internal representation + +--S 142 of 148 +R := Expression(Integer) --R --R ---R (64) ---R (- a (t,x,y,z) + a (t,x,y,z))dy dz + (- a (t,x,y,z) + a (t,x,y,z))dx dz ---R ,4 ,3 ,4 ,2 ---R + ---R (- a (t,x,y,z) + a (t,x,y,z))dx dy + (a (t,x,y,z) + a (t,x,y,z))dt dz ---R ,3 ,2 ,4 ,1 ---R + ---R (a (t,x,y,z) + a (t,x,y,z))dt dy + (a (t,x,y,z) + a (t,x,y,z))dt dx ---R ,3 ,1 ,2 ,1 ---R Type: DeRhamComplex(Integer,[t,x,y,z]) ---E 100 +--R (15) Expression(Integer) +--R Type: Domain +--E 142 + +--S 143 of 148 +Y := DERHAM(coefRing,S2) +--R +--R +--R (16) DeRhamComplex(Integer,[r,theta]) +--R Type: Domain +--E 143 + +--S 144 of 148 +terms : Y -> List Record(k : EAB, c : R) +--R +--R Type: Void +--E 144 + +--S 145 of 148 +terms(a) == a pretend List Record(k : EAB, c : R) +--R +--R Type: Void +--E 145 + +--S 146 of 148 +terms(dr) +--R +--R Compiling function terms with type DeRhamComplex(Integer,[r,theta]) +--R -> List(Record(k: ExtAlgBasis,c: Expression(Integer))) +--R +--R (19) [[k= [1,0],c= 1]] +--R Type: List(Record(k: ExtAlgBasis,c: Expression(Integer))) +--E 146 + +--S 147 of 148 +terms(dtheta) +--R +--R +--R (20) [[k= [0,1],c= 1]] +--R Type: List(Record(k: ExtAlgBasis,c: Expression(Integer))) +--E 147 + +--S 148 of 148 +terms(F1) +--R +--R +--R (21) [[k= [0,1],c= F (r,theta)],[k= [1,0],c= F (r,theta)]] +--R ,2 ,1 +--R Type: List(Record(k: ExtAlgBasis,c: Expression(Integer))) +--E 148 + )spool )lisp (bye) @@ -29057,6 +30058,268 @@ consists of the eight forms: 1, dx, dy, dz, dx*dy, dx*dz, dy*dz, and dx*dy*dz. a(x,t,y,u,v,z,e) Type: Expression Integer +Further examples are: + +coefRing := Integer + + Integer + +R3 : List Symbol := [x,y,z] + + [x,y,z] + +X := DERHAM(coefRing,R3) + + DeRhamComplex(Integer,[x,y,z]) + +[dx,dy,dz] := [generator(i)$X for i in 1..3] + + [dx,dy,dz] + +f : BOP := operator('f) + + f + +g : BOP := operator('g) + + g + +h : BOP := operator('h) + + h + +a : BOP := operator('a) + + a + +b : BOP := operator('b) + + b + +c : BOP := operator('c) + + c + +U : BOP := operator('U) + + U + +V : BOP := operator('V) + + V + +W : BOP := operator('W) + + W + +v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] + + [U(x,y,z),V(x,y,z),W(x,y,z)] + +sigma := f(x,y,z) * dx + g(x,y,z) * dy + h(x,y,z) * dz + + h(x,y,z)dz + g(x,y,z)dy + f(x,y,z)dx + +theta := a(x,y,z) * dx * dy + b(x,y,z) * dx * dz + c(x,y,z) * dy * dz + + c(x,y,z)dy dz + b(x,y,z)dx dz + a(x,y,z)dx dy + +d ==> exteriorDifferential + +G := diagonalMatrix([1,1,1]) + + +1 0 0+ + | | + |0 1 0| + | | + +0 0 1+ + +interiorProduct(v,sigma,G) + + W(x,y,z)h(x,y,z) + V(x,y,z)g(x,y,z) + U(x,y,z)f(x,y,z) + +interiorProduct(v,theta,G) + + (W(x,y,z)b(x,y,z) + V(x,y,z)a(x,y,z))dx + + + (W(x,y,z)c(x,y,z) - U(x,y,z)a(x,y,z))dy + + + (- V(x,y,z)c(x,y,z) - U(x,y,z)b(x,y,z))dz + +t1 := d interiorProduct(v,dz*dy*dz,G) + + 0 + +hodgeStar(t1,G) -- should be div(v) + + 0 + +eta := lieDerivative(v,theta,G) + + - W(x,y,z)c (x,y,z) - V(x,y,z)c (x,y,z) - U(x,y,z)b (x,y,z) + ,3 ,2 ,2 + + + U(x,y,z)a (x,y,z) - c(x,y,z)W (x,y,z) - c(x,y,z)V (x,y,z) + ,3 ,3 ,2 + + + a(x,y,z)U (x,y,z) - b(x,y,z)U (x,y,z) + ,3 ,2 + * + dy dz + + + - V(x,y,z)c (x,y,z) - W(x,y,z)b (x,y,z) - U(x,y,z)b (x,y,z) + ,1 ,3 ,1 + + + - V(x,y,z)a (x,y,z) - b(x,y,z)W (x,y,z) - a(x,y,z)V (x,y,z) + ,3 ,3 ,3 + + + - c(x,y,z)V (x,y,z) - b(x,y,z)U (x,y,z) + ,1 ,1 + * + dx dz + + + 2W(x,y,z)c (x,y,z) - 2W(x,y,z)b (x,y,z) + W(x,y,z)a (x,y,z) + ,1 ,2 ,3 + + + - V(x,y,z)a (x,y,z) - U(x,y,z)a (x,y,z) - b(x,y,z)W (x,y,z) + ,2 ,1 ,2 + + + c(x,y,z)W (x,y,z) - a(x,y,z)V (x,y,z) - a(x,y,z)U (x,y,z) + ,1 ,2 ,1 + * + dx dy + + + (- V(x,y,z)c (x,y,z) + V(x,y,z)b (x,y,z) - V(x,y,z)a (x,y,z))dx dz + ,1 ,2 ,3 + + + (U(x,y,z)c (x,y,z) - U(x,y,z)b (x,y,z) + U(x,y,z)a (x,y,z))dy dz + ,1 ,2 ,3 + +proj(dx+dy*dz+dx*dy*dz,2) + + dy dz + +proj(sigma+theta,1) + + h(x,y,z)dz + g(x,y,z)dy + f(x,y,z)dx + +dim(sigma) + + 3 + +degree(sigma) + + 1 + +S2 : List Symbol := [r,theta] + + [r,theta] + +Y := DERHAM(coefRing,S2) + + DeRhamComplex(Integer,[r,theta]) + +g := diagonalMatrix([1,r^2]) + + +1 0 + + | | + | 2| + +0 r + + +F := operator 'F + + F + +d ==> exteriorDifferential + +[dr,dtheta] := [generator(i)$Y for i in 1..2] + + [dr,dtheta] + +F0 := F(r,theta)*1::Y + + F(r,theta) + +F1 := d F0 + + F (r,theta)dtheta + F (r,theta)dr + ,2 ,1 + +F2 := hodgeStar(F1,g) + + +-------+ + | 2 + \|abs(r ) F (r,theta) +-------+ + ,2 | 2 + (10) - ---------------------- dr + \|abs(r ) F (r,theta)dtheta + 2 ,1 + r + +F3 := d F2 + + 2 2 2 2 + abs(r )F (r,theta) + r abs(r )F (r,theta) + r abs(r )F (r,theta) + ,2,2 ,1,1 ,1 + ----------------------------------------------------------------------- dr + +-------+ + 2 | 2 + r \|abs(r ) + * + dtheta + +LaplaceF := hodgeStar(F3,g) + + 2 2 2 2 + abs(r )F (r,theta) + r abs(r )F (r,theta) + r abs(r )F (r,theta) + ,2,2 ,1,1 ,1 + ----------------------------------------------------------------------- + 4 + r + +LapF := LaplaceF::Expression(Integer) + + 2 2 2 2 + abs(r )F (r,theta) + r abs(r )F (r,theta) + r abs(r )F (r,theta) + ,2,2 ,1,1 ,1 + ----------------------------------------------------------------------- + 4 + r + +subst(LapF,abs(r^2)=r^2) + + 2 + F (r,theta) + r F (r,theta) + rF (r,theta) + ,2,2 ,1,1 ,1 + ------------------------------------------------- + 2 + r + +R := Expression(Integer) + + Expression(Integer) + +Y := DERHAM(coefRing,S2) + + DeRhamComplex(Integer,[r,theta]) + +terms : Y -> List Record(k : EAB, c : R) + +terms(a) == a pretend List Record(k : EAB, c : R) + +terms(dr) + + [[k= [1,0],c= 1]] + +terms(dtheta) + + [[k= [0,1],c= 1]] + +terms(F1) + + [[k= [0,1],c= F (r,theta)],[k= [1,0],c= F (r,theta)]] + ,2 ,1 + + See Also: o )help Operator o )show DeRhamComplex @@ -29842,6 +31105,13 @@ RETURN VALUE EXAMPLES ======== + der := DeRhamComplex(Integer,[x,y,z]) + f:BOP:=operator('f) + g:BOP:=operator('g) + h:BOP:=operator('h) + sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz + dim sigma + NOTES ===== @@ -30042,6 +31312,12 @@ RETURN VALUE EXAMPLES ======== + coefRing := Integer + R3 : List Symbol := [x,y,z] + X := DERHAM(coefRing,R3) + [dx,dy,dz] := [generator(i)$X for i in 1..3] + proj(dx+dy*dz+dx*dy*dz,2) + NOTES ===== @@ -30106,6 +31382,26 @@ RETURN VALUE EXAMPLES ======== + coefRing := Integer + R3 : List Symbol := [x,y,z] + X := DERHAM(coefRing,R3) + [dx,dy,dz] := [generator(i)$X for i in 1..3] + f : BOP := operator('f) + g : BOP := operator('g) + h : BOP := operator('h) + a : BOP := operator('a) + b : BOP := operator('b) + c : BOP := operator('c) + U : BOP := operator('U) + V : BOP := operator('V) + W : BOP := operator('W) + v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] + sigma := f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz + theta := a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz + G := diagonalMatrix([1,1,1]) + interiorProduct(v,sigma,G) + interiorProduct(v,theta,G) + NOTES ===== @@ -30170,6 +31466,21 @@ RETURN VALUE EXAMPLES ======== + coefRing := Integer + R3 : List Symbol := [x,y,z] + X := DERHAM(coefRing,R3) + [dx,dy,dz] := [generator(i)$X for i in 1..3] + a : BOP := operator('a) + b : BOP := operator('b) + c : BOP := operator('c) + U : BOP := operator('U) + V : BOP := operator('V) + W : BOP := operator('W) + v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] + theta := a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz + G := diagonalMatrix([1,1,1]) + eta := lieDerivative(v,theta,G) + NOTES ===== @@ -30254,6 +31565,7 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where O ==> OutputForm R ==> Expression(CoefRing) SMR ==> SquareMatrix(#listIndVar,R) + REABR ==> Record(k : EAB, c : R) Export == Join(LALG(R), RetractableTo(R)) with @@ -30399,6 +31711,13 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where dim : % -> NNI ++ dimension of the underlying space ++ that is, dim ExtAlg = 2^dim + ++ + ++X der := DeRhamComplex(Integer,[x,y,z]) + ++X f:BOP:=operator('f) + ++X g:BOP:=operator('g) + ++X h:BOP:=operator('h) + ++X sigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz + ++X dim sigma hodgeStar : (%,SMR) -> % ++ computes the Hodge dual of the differential form with respect @@ -30425,14 +31744,55 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where proj : (%,NNI) -> % ++ projection to homogeneous terms of degree p + ++ + ++X coefRing := Integer + ++X R3 : List Symbol := [x,y,z] + ++X D := DERHAM(coefRing,R3) + ++X [dx,dy,dz] := [generator(i)$D for i in 1..3] + ++X proj(dx+dy*dz+dx*dy*dz,2) interiorProduct : (Vector(R),%,SMR) -> % ++ calculates the interior product i_X(a) of the vector field X ++ with the differential form a (w.r.t. metric g) + ++ + ++X coefRing := Integer + ++X R3 : List Symbol := [x,y,z] + ++X D := DERHAM(coefRing,R3) + ++X [dx,dy,dz] := [generator(i)$D for i in 1..3] + ++X f : BOP := operator('f) + ++X g : BOP := operator('g) + ++X h : BOP := operator('h) + ++X a : BOP := operator('a) + ++X b : BOP := operator('b) + ++X c : BOP := operator('c) + ++X U : BOP := operator('U) + ++X V : BOP := operator('V) + ++X W : BOP := operator('W) + ++X v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] + ++X sigma := f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz + ++X theta := a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz + ++X G := diagonalMatrix([1,1,1]) + ++X interiorProduct(v,sigma,G) + ++X interiorProduct(v,theta,G) lieDerivative : (Vector(R),%,SMR) -> % ++ calculates the Lie derivative L_X(a) of the differential ++ form a with respect to the vector field X (w.r.t. metric g) + ++ + ++X coefRing := Integer + ++X R3 : List Symbol := [x,y,z] + ++X D := DERHAM(coefRing,R3) + ++X [dx,dy,dz] := [generator(i)$D for i in 1..3] + ++X a : BOP := operator('a) + ++X b : BOP := operator('b) + ++X c : BOP := operator('c) + ++X U : BOP := operator('U) + ++X V : BOP := operator('V) + ++X W : BOP := operator('W) + ++X v := vector[U(x,y,z),V(x,y,z),W(x,y,z)] + ++X theta := a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz + ++X G := diagonalMatrix([1,1,1]) + ++X eta := lieDerivative(v,theta,G) Implement == ASY add Rep := ASY @@ -30471,10 +31831,10 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where -- it is the case that there are at least two terms in a a pretend List Record(k: EAB, c: R) - err1:="CoefRing has no IntegralDomain" - err2:="Not Implemented" + err1:="CoefRing has not IntegralDomain" + err2:="Metric tensor is not symmetric" err3:="Degenerate metric" - err4:="Index out of range" + err4:="Index out of range" -- coord space dimension dim(f) == dim @@ -30498,17 +31858,17 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where reduce("*",[1/g(j,j) for j in idx]::List(R))*r.c*s.c -- compute dot of singleton terms, general symmetric g --- dot2(r:REABR, s:REABR, g:SMR):R == --- not CoefRing has IntegralDomain => error(err1) --- pr := pos(r.k,1) -- list positions of 1 in r --- ps := pos(s.k,1) -- list positions of 1 in s --- test(#p1 ^= #ps) => 0::R -- not same degree => 0 --- pr = [] => r.c * s.c -- empty pr,ps => product of coefs --- G := inverse(g)::SMR -- compute the inverse of the metric g --- test(#pr = 1) => G(pr.1,ps.1)::R * r.c * s.c -- only one element --- M:Matrix(R) -- the minor --- M := matrix([[G(pr.i,ps.j])::R for j in 1..#ps] for i in 1..#pr]) --- determinant(M)::R * r.c * s.c + dot2(r:REABR, s:REABR, g:SMR):R == + not CoefRing has IntegralDomain => error(err1) + pr := pos(r.k,1) -- list positions of 1 in r + ps := pos(s.k,1) -- list positions of 1 in s + test(#pr ^= #ps) => 0::R -- not same degree => 0 + pr = [] => r.c * s.c -- empty pr,ps => product of coefs + G := inverse(g)::SMR -- compute the inverse of the metric g + test(#pr = 1) => G(pr.1,ps.1)::R * r.c * s.c -- only one element + M:Matrix(R) -- the minor + M := matrix([[G(pr.i,ps.j)::R for j in 1..#ps] for i in 1..#pr]) + determinant(M)::R * r.c * s.c -- export dot(x,y,g) == @@ -30516,11 +31876,10 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where tx:=terms(x) ty:=terms(y) tx = [] or ty = [] => 0::R --- if diagonal? g then -- better performance --- reduce("+",[dot2(tx.j,ty.j,g) for j in 1..#tx]) --- else --- reduce("+",[dot1(tx.j,ty.j,g) for j in 1..#tx]) - reduce("+",[dot1(tx.j,ty.j,g) for j in 1..#tx]) + if diagonal? g then -- better performance + reduce("+",[dot2(tx.j,ty.j,g) for j in 1..#tx]) + else + reduce("+",[dot1(tx.j,ty.j,g) for j in 1..#tx]) -- export hodgeStar(x,g) == @@ -30566,7 +31925,7 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where a+b coerce(a):O == - a = 0$Rep => 0$I::O + a = 0$Rep => 0$I::O ta := terms a null ta.rest => makeTerm(ta.first.c, ta.first.k) reduce(_+,[makeTerm(t.c,t.k) for t in ta])$L(O) diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index 4a66671..2b4f9c3 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -28,88 +28,88 @@ of effort. We would like to acknowledge and thank the following people: "Christian Aistleitner Richard Anderson George Andrews" "S.J. Atkins Henry Baker Martin Baker" "Stephen Balzac Yurij Baransky David R. Barton" -"Gerald Baumgartner Gilbert Baumslag Michael Becker" -"Nelson H. F. Beebe Jay Belanger David Bindel" -"Fred Blair Vladimir Bondarenko Mark Botch" -"Raoul Bourquin Alexandre Bouyer Karen Braman" -"Peter A. Broadbery Martin Brock Manuel Bronstein" -"Stephen Buchwald Florian Bundschuh Luanne Burns" -"William Burge Ralph Byers Quentin Carpent" -"Robert Caviness Bruce Char Ondrej Certik" -"Tzu-Yi Chen Cheekai Chin David V. Chudnovsky" -"Gregory V. Chudnovsky Mark Clements James Cloos" -"Jia Zhao Cong Josh Cohen Christophe Conil" -"Don Coppersmith George Corliss Robert Corless" -"Gary Cornell Meino Cramer Jeremy Du Croz" -"David Cyganski Nathaniel Daly Timothy Daly Sr." -"Timothy Daly Jr. James H. Davenport David Day" -"James Demmel Didier Deshommes Michael Dewar" -"Jack Dongarra Jean Della Dora Gabriel Dos Reis" -"Claire DiCrescendo Sam Dooley Lionel Ducos" -"Iain Duff Lee Duhem Martin Dunstan" -"Brian Dupee Dominique Duval Robert Edwards" -"Heow Eide-Goodman Lars Erickson Richard Fateman" -"Bertfried Fauser Stuart Feldman John Fletcher" -"Brian Ford Albrecht Fortenbacher George Frances" -"Constantine Frangos Timothy Freeman Korrinn Fu" -"Marc Gaetano Rudiger Gebauer Van de Geijn" -"Kathy Gerber Patricia Gianni Gustavo Goertkin" -"Samantha Goldrich Holger Gollan Teresa Gomez-Diaz" -"Laureano Gonzalez-Vega Stephen Gortler Johannes Grabmeier" -"Matt Grayson Klaus Ebbe Grue James Griesmer" -"Vladimir Grinberg Oswald Gschnitzer Ming Gu" -"Jocelyn Guidry Gaetan Hache Steve Hague" -"Satoshi Hamaguchi Sven Hammarling Mike Hansen" -"Richard Hanson Richard Harke Bill Hart" -"Vilya Harvey Martin Hassner Arthur S. 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Chudnovsky Mark Clements" +"James Cloos Jia Zhao Cong Josh Cohen" +"Christophe Conil Don Coppersmith George Corliss" +"Robert Corless Gary Cornell Meino Cramer" +"Jeremy Du Croz David Cyganski Nathaniel Daly" +"Timothy Daly Sr. Timothy Daly Jr. James H. Davenport" +"David Day James Demmel Didier Deshommes" +"Michael Dewar Jack Dongarra Jean Della Dora" +"Gabriel Dos Reis Claire DiCrescendo Sam Dooley" +"Lionel Ducos Iain Duff Lee Duhem" +"Martin Dunstan Brian Dupee Dominique Duval" +"Robert Edwards Heow Eide-Goodman Lars Erickson" +"Richard Fateman Bertfried Fauser Stuart Feldman" +"John Fletcher Brian Ford Albrecht Fortenbacher" +"George Frances Constantine Frangos Timothy Freeman" +"Korrinn Fu Marc Gaetano Rudiger Gebauer" +"Van de Geijn Kathy Gerber Patricia Gianni" +"Gustavo Goertkin Samantha Goldrich Holger Gollan" +"Teresa Gomez-Diaz Laureano Gonzalez-Vega Stephen Gortler" +"Johannes Grabmeier Matt Grayson Klaus Ebbe Grue" +"James Griesmer Vladimir Grinberg Oswald Gschnitzer" +"Ming Gu Jocelyn Guidry Gaetan Hache" +"Steve Hague Satoshi Hamaguchi Sven Hammarling" +"Mike Hansen Richard Hanson Richard Harke" +"Bill Hart Vilya Harvey Martin Hassner" +"Arthur S. Hathaway Dan Hatton Waldek Hebisch" +"Karl Hegbloom Ralf Hemmecke Henderson" +"Antoine Hersen Roger House Gernot Hueber" +"Pietro Iglio Alejandro Jakubi Richard Jenks" +"William Kahan Kyriakos Kalorkoti Kai Kaminski" +"Grant Keady Wilfrid Kendall Tony Kennedy" +"Ted Kosan Paul Kosinski Klaus Kusche" +"Bernhard Kutzler Tim Lahey Larry Lambe" +"Kaj Laurson George L. Legendre Franz Lehner" +"Frederic Lehobey Michel Levaud Howard Levy" +"Ren-Cang Li Rudiger Loos Michael Lucks" +"Richard Luczak Camm Maguire Francois Maltey" +"Alasdair McAndrew Bob McElrath Michael McGettrick" +"Edi Meier Ian Meikle David Mentre" +"Victor S. Miller Gerard Milmeister Mohammed Mobarak" +"H. Michael Moeller Michael Monagan Marc Moreno-Maza" +"Scott Morrison Joel Moses Mark Murray" +"William Naylor Patrice Naudin C. Andrew Neff" +"John Nelder Godfrey Nolan Arthur Norman" +"Jinzhong Niu Michael O'Connor Summat Oemrawsingh" +"Kostas Oikonomou Humberto Ortiz-Zuazaga Julian A. Padget" +"Bill Page David Parnas Susan Pelzel" +"Michel Petitot Didier Pinchon Ayal Pinkus" +"Frederick H. Pitts Jose Alfredo Portes Gregorio Quintana-Orti" +"Claude Quitte Arthur C. Ralfs Norman Ramsey" +"Anatoly Raportirenko Albert D. Rich Michael Richardson" +"Guilherme Reis Huan Ren Renaud Rioboo" +"Jean Rivlin Nicolas Robidoux Simon Robinson" +"Raymond Rogers Michael Rothstein Martin Rubey" +"Philip Santas Alfred Scheerhorn William Schelter" +"Gerhard Schneider Martin Schoenert Marshall Schor" +"Frithjof Schulze Fritz Schwarz Steven Segletes" +"V. Sima Nick Simicich William Sit" +"Elena Smirnova Jonathan Steinbach Fabio Stumbo" +"Christine Sundaresan Robert Sutor Moss E. Sweedler" +"Eugene Surowitz Max Tegmark T. Doug Telford" +"James Thatcher Balbir Thomas Mike Thomas" +"Dylan Thurston Steve Toleque Barry Trager" +"Themos T. Tsikas Gregory Vanuxem Bernhard Wall" +"Stephen Watt Jaap Weel Juergen Weiss" +"M. Weller Mark Wegman James Wen" +"Thorsten Werther Michael Wester R. Clint Whaley" +"James T. Wheeler John M. Wiley Berhard Will" +"Clifton J. Williamson Stephen Wilson Shmuel Winograd" +"Robert Wisbauer Sandra Wityak Waldemar Wiwianka" +"Knut Wolf Liu Xiaojun Clifford Yapp" +"David Yun Vadim Zhytnikov Richard Zippel" +"Evelyn Zoernack Bruno Zuercher Dan Zwillinger" )) diff --git a/buglist b/buglist index 324b888..cfd9d5e 100644 --- a/buglist +++ b/buglist @@ -1,6 +1,6 @@ ========================================================================= -bug 7261: +bug 7262: todo 336: wish 1012: meh 5: @@ -12,6 +12,12 @@ dup 50006: nonextend 60077: ========================================================================= +bug 7261: wrong integral (reported by Thomas Baruchel ) + +t1:=(16*x^14-125*x^10+150*x^6+375*x^2)/(256*x^16+480*x^12+1025*x^8+750*x^4+625) +integrate(t1,x) + +========================================================================= bug 7259: x:=taylor 'x diff --git a/changelog b/changelog index 6f61b2f..1f2bff6 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,10 @@ +20141122 txp src/axiom-website/patches.html 20141122.01.txp.patch +20141122 txp buglist add bug 7261: wrong integral +20141122 txp bookvol5 add Thomas Baruchel to credits +20141122 txp readme add Thomas Baruchel +20141122 txp Thomas Baruchel +20141121 kxp src/axiom-website/patches.html 20141121.01.kxp.patch +20141121 kxp books/bookvol10.3 more help information for DeRhamComplex 20141119 tpd src/axiom-website/patches.html 20141119.01.tpd.patch 20141119 tpd books/bookvol10.3 help files for DeRhamComplex 20141119 tpd books/bookvolbib fix Flan03 author list diff --git a/patch b/patch index 89cb94a..e46ff41 100644 --- a/patch +++ b/patch @@ -1,38 +1,6 @@ -books/bookvol10.3 help files for DeRhamComplex +buglist add bug 7261: wrong integral -The )help command now recognizes - )help DeRhamComplex -- the constructor name - )help DERHAM -- the abbreviation - )help leadingCoefficient - )help leadingBasisTerm - )help reductum - )help coefficient - )help generator - )help homogeneous? - )help retractable? - )help degree - )help map - )help totalDifferential - )help exteriorDifferential - )help dim - )help hodgeStar - )help dot - )help proj - )help interiorProduct - )help lieDerivative -all of which open in an edit window +bug 7261: wrong integral (reported by Thomas Baruchel -There are also usage example code for - )d op leadingCoefficient - )d op leadingBasisTerm - )d op reductum - )d op coefficient - )d op generator - )d op homogeneous? - )d op retractable? - )d op degree - )d op map - )d op totalDifferential - )d op exteriorDifferential - )d op hodgeStar - )d op dot +t1:=(16*x^14-125*x^10+150*x^6+375*x^2)/(256*x^16+480*x^12+1025*x^8+750*x^4+625) +integrate(t1,x) diff --git a/readme b/readme index 0bfd8b5..34cb2d3 100644 --- a/readme +++ b/readme @@ -182,7 +182,7 @@ Scratchpad and Axiom. If you contribute, add your name. The names are in alphabetical order as we make no attempt to quantify the relative merit of the contributions. -In src/interp/setq.lisp.pamphlet is a variable called credits +In books/bookvol5.pamphlet is a variable called credits which contains this list. Typing )credits at the axiom command prompt will prettyprint the list. @@ -192,88 +192,88 @@ at the axiom command prompt will prettyprint the list. "Christian Aistleitner Richard Anderson George Andrews" "S.J. Atkins Henry Baker Martin Baker" "Stephen Balzac Yurij Baransky David R. Barton" -"Gerald Baumgartner Gilbert Baumslag Michael Becker" -"Nelson H. F. Beebe Jay Belanger David Bindel" -"Fred Blair Vladimir Bondarenko Mark Botch" -"Raoul Bourquin Alexandre Bouyer Karen Braman" -"Peter A. Broadbery Martin Brock Manuel Bronstein" -"Stephen Buchwald Florian Bundschuh Luanne Burns" -"William Burge Ralph Byers Quentin Carpent" -"Robert Caviness Bruce Char Ondrej Certik" -"Tzu-Yi Chen Cheekai Chin David V. Chudnovsky" -"Gregory V. Chudnovsky Mark Clements James Cloos" -"Jia Zhao Cong Josh Cohen Christophe Conil" -"Don Coppersmith George Corliss Robert Corless" -"Gary Cornell Meino Cramer Jeremy Du Croz" -"David Cyganski Nathaniel Daly Timothy Daly Sr." -"Timothy Daly Jr. James H. Davenport David Day" -"James Demmel Didier Deshommes Michael Dewar" -"Jack Dongarra Jean Della Dora Gabriel Dos Reis" -"Claire DiCrescendo Sam Dooley Lionel Ducos" -"Iain Duff Lee Duhem Martin Dunstan" -"Brian Dupee Dominique Duval Robert Edwards" -"Heow Eide-Goodman Lars Erickson Richard Fateman" -"Bertfried Fauser Stuart Feldman John Fletcher" -"Brian Ford Albrecht Fortenbacher George Frances" -"Constantine Frangos Timothy Freeman Korrinn Fu" -"Marc Gaetano Rudiger Gebauer Van de Geijn" -"Kathy Gerber Patricia Gianni Gustavo Goertkin" -"Samantha Goldrich Holger Gollan Teresa Gomez-Diaz" -"Laureano Gonzalez-Vega Stephen Gortler Johannes Grabmeier" -"Matt Grayson Klaus Ebbe Grue James Griesmer" -"Vladimir Grinberg Oswald Gschnitzer Ming Gu" -"Jocelyn Guidry Gaetan Hache Steve Hague" -"Satoshi Hamaguchi Sven Hammarling Mike Hansen" -"Richard Hanson Richard Harke Bill Hart" -"Vilya Harvey Martin Hassner Arthur S. Hathaway" -"Dan Hatton Waldek Hebisch Karl Hegbloom" -"Ralf Hemmecke Henderson Antoine Hersen" -"Roger House Gernot Hueber Pietro Iglio" -"Alejandro Jakubi Richard Jenks William Kahan" -"Kyriakos Kalorkoti Kai Kaminski Grant Keady" -"Wilfrid Kendall Tony Kennedy Ted Kosan" -"Paul Kosinski Klaus Kusche Bernhard Kutzler" -"Tim Lahey Larry Lambe Kaj Laurson" -"George L. Legendre Franz Lehner Frederic Lehobey" -"Michel Levaud Howard Levy Ren-Cang Li" -"Rudiger Loos Michael Lucks Richard Luczak" -"Camm Maguire Francois Maltey Alasdair McAndrew" -"Bob McElrath Michael McGettrick Edi Meier" -"Ian Meikle David Mentre Victor S. Miller" -"Gerard Milmeister Mohammed Mobarak H. Michael Moeller" -"Michael Monagan Marc Moreno-Maza Scott Morrison" -"Joel Moses Mark Murray William Naylor" -"Patrice Naudin C. Andrew Neff John Nelder" -"Godfrey Nolan Arthur Norman Jinzhong Niu" -"Michael O'Connor Summat Oemrawsingh Kostas Oikonomou" -"Humberto Ortiz-Zuazaga Julian A. Padget Bill Page" -"David Parnas Susan Pelzel Michel Petitot" -"Didier Pinchon Ayal Pinkus Frederick H. Pitts" -"Jose Alfredo Portes Gregorio Quintana-Orti Claude Quitte" -"Arthur C. Ralfs Norman Ramsey Anatoly Raportirenko" -"Albert D. Rich Michael Richardson Guilherme Reis" -"Huan Ren Renaud Rioboo Jean Rivlin" -"Nicolas Robidoux Simon Robinson Raymond Rogers" -"Michael Rothstein Martin Rubey Philip Santas" -"Alfred Scheerhorn William Schelter Gerhard Schneider" -"Martin Schoenert Marshall Schor Frithjof Schulze" -"Fritz Schwarz Steven Segletes V. Sima" -"Nick Simicich William Sit Elena Smirnova" -"Jonathan Steinbach Fabio Stumbo Christine Sundaresan" -"Robert Sutor Moss E. Sweedler Eugene Surowitz" -"Max Tegmark T. Doug Telford James Thatcher" -"Balbir Thomas Mike Thomas Dylan Thurston" -"Steve Toleque Barry Trager Themos T. Tsikas" -"Gregory Vanuxem Bernhard Wall Stephen Watt" -"Jaap Weel Juergen Weiss M. Weller" -"Mark Wegman James Wen Thorsten Werther" -"Michael Wester R. Clint Whaley James T. Wheeler" -"John M. Wiley Berhard Will Clifton J. Williamson" -"Stephen Wilson Shmuel Winograd Robert Wisbauer" -"Sandra Wityak Waldemar Wiwianka Knut Wolf" -"Liu Xiaojun Clifford Yapp David Yun" -"Vadim Zhytnikov Richard Zippel Evelyn Zoernack" -"Bruno Zuercher Dan Zwillinger" +"Thomas Baruchel Gerald Baumgartner Gilbert Baumslag" +"Michael Becker Nelson H. F. Beebe Jay Belanger" +"David Bindel Fred Blair Vladimir Bondarenko" +"Mark Botch Raoul Bourquin Alexandre Bouyer" +"Karen Braman Peter A. Broadbery Martin Brock" +"Manuel Bronstein Stephen Buchwald Florian Bundschuh" +"Luanne Burns William Burge Ralph Byers" +"Quentin Carpent Robert Caviness Bruce Char" +"Ondrej Certik Tzu-Yi Chen Cheekai Chin" +"David V. Chudnovsky Gregory V. Chudnovsky Mark Clements" +"James Cloos Jia Zhao Cong Josh Cohen" +"Christophe Conil Don Coppersmith George Corliss" +"Robert Corless Gary Cornell Meino Cramer" +"Jeremy Du Croz David Cyganski Nathaniel Daly" +"Timothy Daly Sr. Timothy Daly Jr. James H. Davenport" +"David Day James Demmel Didier Deshommes" +"Michael Dewar Jack Dongarra Jean Della Dora" +"Gabriel Dos Reis Claire DiCrescendo Sam Dooley" +"Lionel Ducos Iain Duff Lee Duhem" +"Martin Dunstan Brian Dupee Dominique Duval" +"Robert Edwards Heow Eide-Goodman Lars Erickson" +"Richard Fateman Bertfried Fauser Stuart Feldman" +"John Fletcher Brian Ford Albrecht Fortenbacher" +"George Frances Constantine Frangos Timothy Freeman" +"Korrinn Fu Marc Gaetano Rudiger Gebauer" +"Van de Geijn Kathy Gerber Patricia Gianni" +"Gustavo Goertkin Samantha Goldrich Holger Gollan" +"Teresa Gomez-Diaz Laureano Gonzalez-Vega Stephen Gortler" +"Johannes Grabmeier Matt Grayson Klaus Ebbe Grue" +"James Griesmer Vladimir Grinberg Oswald Gschnitzer" +"Ming Gu Jocelyn Guidry Gaetan Hache" +"Steve Hague Satoshi Hamaguchi Sven Hammarling" +"Mike Hansen Richard Hanson Richard Harke" +"Bill Hart Vilya Harvey Martin Hassner" +"Arthur S. Hathaway Dan Hatton Waldek Hebisch" +"Karl Hegbloom Ralf Hemmecke Henderson" +"Antoine Hersen Roger House Gernot Hueber" +"Pietro Iglio Alejandro Jakubi Richard Jenks" +"William Kahan Kyriakos Kalorkoti Kai Kaminski" +"Grant Keady Wilfrid Kendall Tony Kennedy" +"Ted Kosan Paul Kosinski Klaus Kusche" +"Bernhard Kutzler Tim Lahey Larry Lambe" +"Kaj Laurson George L. Legendre Franz Lehner" +"Frederic Lehobey Michel Levaud Howard Levy" +"Ren-Cang Li Rudiger Loos Michael Lucks" +"Richard Luczak Camm Maguire Francois Maltey" +"Alasdair McAndrew Bob McElrath Michael McGettrick" +"Edi Meier Ian Meikle David Mentre" +"Victor S. Miller Gerard Milmeister Mohammed Mobarak" +"H. Michael Moeller Michael Monagan Marc Moreno-Maza" +"Scott Morrison Joel Moses Mark Murray" +"William Naylor Patrice Naudin C. Andrew Neff" +"John Nelder Godfrey Nolan Arthur Norman" +"Jinzhong Niu Michael O'Connor Summat Oemrawsingh" +"Kostas Oikonomou Humberto Ortiz-Zuazaga Julian A. Padget" +"Bill Page David Parnas Susan Pelzel" +"Michel Petitot Didier Pinchon Ayal Pinkus" +"Frederick H. Pitts Jose Alfredo Portes Gregorio Quintana-Orti" +"Claude Quitte Arthur C. Ralfs Norman Ramsey" +"Anatoly Raportirenko Albert D. Rich Michael Richardson" +"Guilherme Reis Huan Ren Renaud Rioboo" +"Jean Rivlin Nicolas Robidoux Simon Robinson" +"Raymond Rogers Michael Rothstein Martin Rubey" +"Philip Santas Alfred Scheerhorn William Schelter" +"Gerhard Schneider Martin Schoenert Marshall Schor" +"Frithjof Schulze Fritz Schwarz Steven Segletes" +"V. Sima Nick Simicich William Sit" +"Elena Smirnova Jonathan Steinbach Fabio Stumbo" +"Christine Sundaresan Robert Sutor Moss E. Sweedler" +"Eugene Surowitz Max Tegmark T. Doug Telford" +"James Thatcher Balbir Thomas Mike Thomas" +"Dylan Thurston Steve Toleque Barry Trager" +"Themos T. Tsikas Gregory Vanuxem Bernhard Wall" +"Stephen Watt Jaap Weel Juergen Weiss" +"M. Weller Mark Wegman James Wen" +"Thorsten Werther Michael Wester R. Clint Whaley" +"James T. Wheeler John M. Wiley Berhard Will" +"Clifton J. Williamson Stephen Wilson Shmuel Winograd" +"Robert Wisbauer Sandra Wityak Waldemar Wiwianka" +"Knut Wolf Liu Xiaojun Clifford Yapp" +"David Yun Vadim Zhytnikov Richard Zippel" +"Evelyn Zoernack Bruno Zuercher Dan Zwillinger" Pervasive Literate Programming diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 2d843fd..ae5e44e 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4712,6 +4712,10 @@ books/bookvol5 newHelpSpad2Cmd now recognizes )help abbreviations
books/bookvol10.3 help files for PermutationGroup
20141119.01.tpd.patch books/bookvol10.3 help files for DeRhamComplex
+20141121.01.kxp.patch +books/bookvol10.3 more help information for DeRhamComplex
+20141122.01.txp.patch +buglist add bug 7261: wrong integral