Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

The procedure "ContractIndices" seems to produce wrong results. This is proved by the following source code, comparing the result of this procedure and a simple direct calculation:

with(DifferentialGeometry):with(Tensor):with(Tools):

DGsetup([x,y],P);
m:=nops(DGinfo("FrameBaseVectors"));
g:=evalDG(1/y^2*dx &t dx+1/y^2*dy &t dy);
CS:=Christoffel(g,"SecondKind");
R0:=CurvatureTensor(CS);
RFc:=ContractIndices(R0,g,[[1,1]]); # Maple Version 2015

# Out of the Help Page: ?Tensor[ContractIndices]
# Form the tensor product T ⊗ S and contract 
# the 1st index of T against the 1st index of S. 
# ContractIndices(T, S, [[1, 1]]);

# Only for comparison: g:= 
# _DG([["tensor", P, [["cov_bas", "cov_bas"], []]], [[
# [1, 1], 1/y^2], 
# [[2, 2], 1/y^2]]]);

# g in table form with all indices, including the zeros: 
g1t:=
table([(1, 1) = 1/y^2, (2, 1) = 0, (1, 2) = 0, (2, 2) = 1/y^2]);

# Only fpr comparison:
# R0:=
# _DG([["tensor", P, [["con_bas", "cov_bas", "cov_bas", "cov_bas"], 
# []]], 
# [
# [[1, 2, 1, 2], -1/y^2], 
# [[1, 2, 2, 1], 1/y^2], 
# [[2, 1, 1, 2], 1/y^2], 
# [[2, 1, 2, 1], -1/y^2]]
# ]);

# R0 in table form with all indices, including the zeros:
R01t:=
table([
(2, 1, 1, 2) = 1/y^2, 
(2, 1, 1, 1) = 0, 
(2, 2, 2, 1) = 0, 
(2, 1, 2, 1) = -1/y^2, 
(1, 1, 1, 2) = 0, 
(1, 2, 2, 2) = 0, 
(1, 2, 2, 1) = 1/y^2, 
(2, 1, 2, 2) = 0, 
(2, 2, 1, 2) = 0, 
(2, 2, 2, 2) = 0, 
(1, 1, 2, 1) = 0, 
(1, 2, 1, 2) = -1/y^2, 
(2, 2, 1, 1) = 0, 
(1, 1, 2, 2) = 0, 
(1, 1, 1, 1) = 0, 
(1, 2, 1, 1) = 0
]);

# Only fpr comparison:
# RFc := 
# _DG([["tensor", P, [["cov_bas", "cov_bas", "cov_bas", "cov_bas"], 
# []]], 
# [
# [[1, 1, 2, 2], 1/y^4], 
# [[1, 2, 1, 2], -1/y^4], 
# [[2, 1, 2, 1], -1/y^4], 
# [[2, 2, 1, 1], 1/y^4]]
# ]);

# RFc in table form with all indices, including the zeros:
RFc1t:=
table(
[(2, 1, 1, 2) = 0, 
(2, 1, 1, 1) = 0, 
(2, 2, 2, 1) = 0, 
(2, 1, 2, 1) = -1/y^4, 
(1, 1, 1, 2) = 0, 
(1, 2, 2, 2) = 0, 
(1, 2, 2, 1) = 0, 
(2, 1, 2, 2) = 0, 
(2, 2, 1, 2) = 0, 
(2, 2, 2, 2) = 0, 
(1, 1, 2, 1) = 0, 
(1, 2, 1, 2) = -1/y^4, 
(2, 2, 1, 1) = 1/y^4, 
(1, 1, 2, 2) = 1/y^4, 
(1, 1, 1, 1) = 0, 
(1, 2, 1, 1) = 0
]);

TestContr:=proc()
    description "Simple contraction";
    local i,j,k,l;
    global RR;
    for i from 1 to m do
        for j from 1 to m do
            for k from 1 to m do
                for l from 1 to m do
                    RR[i,j,k,l]:=add(R01t[r,j,k,l]*g1t[i,r],r=1..m)
                od;
            od;
        od;
    od;
    print(`OK`)
end;

TestContr();

# Result of this:
# RR:=
# table(
# [(2, 1, 1, 2) = 1/y^4, 
# (2, 1, 1, 1) = 0, 
# (2, 2, 2, 1) = 0, 
# (2, 1, 2, 1) = -1/y^4, 
# (1, 1, 1, 2) = 0, 
# (1, 2, 2, 2) = 0, 
# (1, 2, 2, 1) = 1/y^4, 
# (2, 1, 2, 2) = 0, 
# (2, 2, 1, 2) = 0, 
# (2, 2, 2, 2) = 0, 
# (1, 1, 2, 1) = 0, 
# (1, 2, 1, 2) = -1/y^4, 
# (2, 2, 1, 1) = 0, 
# (1, 1, 2, 2) = 0, 
# (1, 1, 1, 1) = 0, 
# (1, 2, 1, 1) = 0
# ]);

Testeq:=proc()
    local i,j,k,l;
    # global
    for i from 1 to m do
        for j from 1 to m do
            for k from 1 to m do
                for l from 1 to m do
    if not (RFc1t[i,j,k,l] = RR[i,j,k,l]) then 
     print([i,j,k,l]) fi;
                od;
            od;
        od;
    od;
end;

Testeq();
# Result of this:
#                          [1, 1, 2, 2]
#                          [1, 2, 2, 1]
#                          [2, 1, 1, 2]
#                          [2, 2, 1, 1]

# No equality for these indices!

I am trying to implement an example from page 106 in the book Essential Maple 7 in hope that I can understand a problem related to the "solve" function. The example is:

restart;
f[1] := c*x[1]^2*x[2]+9*x[1]^2+2*x[1]*x[2]+5*x[1]+x[2]-3;

f[2] := 2*x[1]^3*x[2]+6*x[1]^3-2*x[1]^2-x[1]*x[2]-3*x[1]-x[2]+3;

f[3] := x[1]^3*x[2]+3*x[1]^3+x[1]^2*x[2]+2*x[1]^2;

with(Groebner)

infolevel[primpart]:=5

gb:=gbasis([f[1],f[2],f[3]],tdeg(x[1],x[2])):

According to the book, I should receive an output that tell me what "content" has been removed. This will tell me what values of the parameter c have special solutions.

If I enter this in my version of Maple 2015 with no changes, I receive no output. This is not so surprising since the example was written for Maple 7. So I changed infolevel[primpart] to infolevel[all]. With this change, I receive some information, but it is rather general and not what I want.

Does anyone know if there is some other way to do this example in Maple 2015?

Thanks for your help.

Hello dear!

I want to find the vector field of a vector field my approch is below:

with(VectorCalculus);
SetCoordinates(cartesian[x, y, z]);
V := VectorField(<(u(x, y, z), v(x, y, z), w(x, y, z))>);
Gradient(V);

I want answer as bellow:

Matrix(3, 3, {(1, 1) = Diff(u, x), (1, 2) = Diff(u, y), (1, 3) = Diff(u, z), (2, 1) = Diff(v, x), (2, 2) = Diff(v, y), (2, 3) = Diff(v, z), (3, 1) = Diff(w, x), (3, 2) = Diff(w, y), (3, 3) = Diff(w, z)});

Please help me to fix this problem. I am waiting the quick answer.

THANKS in advance

How to find the range of poset?

i would like to search the range of range is equal to the range of domain after solve system.

it may not exactly equal but around 80% of elements in range belong to the range of domain

if it is not factorisation domain,

how to generate ideal with function in maple?

How to get the number of parameters of an operator/procedure? Like this.

How do I move a circle around a sphere?

See attached:  WA61_circle_sphere_post.mw

Circle shares surface area of sphere, how can circle be moved independently around sphere?

I would like to retain the patchwork of the sphere to resemble latitude/longitude lines.

Thanks in advance

Les

Hello,

For example, let's say we have the following function

 

Now if we want to calculate the value of a function we have to

subs([x1=10,x2=20],eval(hf));

My question is the following: How to substitute values for x1 and x2 using values from vector? something like that

x:=[10,20];

subs([x],eval(hf));

 

Best,

Rariusz

 

I have a problem that seems rather simple in theory, yet if implemented in maple there arise problems. I want to solve systems of linear equations that involve roots of unity.

This problem arises when trying to find explicit equations of multivariate polynomials of fixed degree through given points (together with conditions on the derivatives of the curve at these points). In the following case, the points are dented by P[i] and I'm looking for the explicit equation of the degree 9 polynomial through these points. Actually, I know there is a two parameter family of such polynomials, so the solution will be of dimension two.

Sorry for the rather crude implementation.

with(Groebner): with(algcurves): with(LinearAlgebra):

t := exp((1/9)*(2*Pi*I)):
s := exp((1/3)*(2*Pi*I)):
a_1 := -1*t:
a_2 := -s*t:
a_3 := -s^2*t:
P[1] := a_1, 0, 1: P[2] := a_2, 0, 1: P[3] := a_3, 0, 1:
P[4] := 1, t*a_1, 0: P[5] := 1, t*a_2, 0: P[6] := 1, t*a_3, 0:
P[7] := 0, 1, a_1: P[8] := 0, 1, a_2: P[9] := 0, 1, a_3:

G := 0: var1 := 0:
for n from 0 to 9 do
G := G+add(c[k, n-k]*x^k*y^(n-k), k = 0 .. n):
for k from 0 to n do var1 := var1, c[k, n-k]:
end do: 
end do:
F := Homogenize(G, z):
Fx := diff(F, x):
Fy := diff(F, y):
Fz := diff(F, z):
Fxx := diff(F, x, x):
Fxy := diff(F, x, y):
Fyx := Fxy:
Fyy := diff(F, y, y):
Fxz := diff(F, x, z):
Fzx := Fxz:
Fzz := diff(F, z, z):
Fyz := diff(F, y, z):
Fzy := diff(F, z, y):

f := unapply(F, [x, y, z]): fx := unapply(Fx, [x, y, z]): fy := unapply(Fy, [x, y, z]): fz := unapply(Fz, [x, y, z]): fxx := unapply(Fxx, [x, y, z]): fxy := unapply(Fxy, [x, y, z]): fyx := unapply(Fyx, [x, y, z]): fyy := unapply(Fyy, [x, y, z]): fxz := unapply(Fxz, [x, y, z]): fzx := unapply(Fzx, [x, y, z]): fzz := unapply(Fzz, [x, y, z]): fyz := unapply(Fyz, [x, y, z]): fzy := unapply(Fzy, [x, y, z]):

sys := [f(P[1]) = 0, fx(P[1]) = 0, fy(P[1]) = 0, fz(P[1]) = 0, fxy(P[1]) = 0, fxz(P[1]) = 0, fxx(P[1]) = 0, fyy(P[1]) = 0, fzz(P[1]) = 0, fyz(P[1]) = 0, f(P[2]) = 0, fx(P[2]) = 0, fy(P[2]) = 0, fz(P[2]) = 0, fxy(P[2]) = 0, fxz(P[2]) = 0, fxx(P[2]) = 0, fyy(P[2]) = 0, fzz(P[2]) = 0, fyz(P[2]) = 0, f(P[3]) = 0, fx(P[3]) = 0, fy(P[3]) = 0, fz(P[3]) = 0, fxy(P[3]) = 0, fxz(P[3]) = 0, fxx(P[3]) = 0, fyy(P[3]) = 0, fzz(P[3]) = 0, fyz(P[3]) = 0, f(P[4]) = 0, fx(P[4]) = 0, fy(P[4]) = 0, fz(P[4]) = 0, fxy(P[4]) = 0, fxz(P[4]) = 0, fxx(P[4]) = 0, fyy(P[4]) = 0, fzz(P[4]) = 0, fyz(P[4]) = 0, f(P[5]) = 0, fx(P[5]) = 0, fy(P[5]) = 0, fz(P[5]) = 0, fxy(P[5]) = 0, fxz(P[5]) = 0, fxx(P[5]) = 0, fyy(P[5]) = 0, fzz(P[5]) = 0, fyz(P[5]) = 0, f(P[6]) = 0, fx(P[6]) = 0, fy(P[6]) = 0, fz(P[6]) = 0, fxy(P[6]) = 0, fxz(P[6]) = 0, fxx(P[6]) = 0, fyy(P[6]) = 0, fzz(P[6]) = 0, fyz(P[6]) = 0, f(P[7]) = 0, fx(P[7]) = 0, fy(P[7]) = 0, fz(P[7]) = 0, fxy(P[7]) = 0, fxz(P[7]) = 0, fxx(P[7]) = 0, fyy(P[7]) = 0, fzz(P[7]) = 0, fyz(P[7]) = 0, f(P[8]) = 0, fx(P[8]) = 0, fy(P[8]) = 0, fz(P[8]) = 0, fxy(P[8]) = 0, fxz(P[8]) = 0, fxx(P[8]) = 0, fyy(P[8]) = 0, fzz(P[8]) = 0, fyz(P[8]) = 0, f(P[9]) = 0, fx(P[9]) = 0, fy(P[9]) = 0, fz(P[9]) = 0, fxy(P[9]) = 0, fxz(P[9]) = 0, fxx(P[9]) = 0, fyy(P[9]) = 0, fzz(P[9]) = 0, fyz(P[9]) = 0]:
var := [c[0, 0], c[0, 1], c[1, 0], c[0, 2], c[1, 1], c[2, 0], c[0, 3], c[1, 2], c[2, 1], c[3, 0], c[0, 4], c[1, 3], c[2, 2], c[3, 1], c[4, 0], c[0, 5], c[1, 4], c[2, 3], c[3, 2], c[4, 1], c[5, 0], c[0, 6], c[1, 5], c[2, 4], c[3, 3], c[4, 2], c[5, 1], c[6, 0], c[0, 7], c[1, 6], c[2, 5], c[3, 4], c[4, 3], c[5, 2], c[6, 1], c[7, 0], c[0, 8], c[1, 7], c[2, 6], c[3, 5], c[4, 4], c[5, 3], c[6, 2], c[7, 1], c[8, 0], c[0, 9], c[1, 8], c[2, 7], c[3, 6], c[4, 5], c[5, 4], c[6, 3], c[7, 2], c[8, 1], c[9, 0]]:
A, b := GenerateMatrix(sys, var):

Solving this with

simplify(LinearSolve(A, b))

Gives a rather nicely looking solution. But the calculation strongly depends on the form of s, t and the a_i.

For example if we instead define 

s:=t^3:

The computation takes much longer and the result doesn't take a particularly nice form. Similarly if we instead take

a_1 := -t: a_2 := -t^4: a_3 := -t^7:

the computation takes hours / days and the result looks rather ugly (huge coefficients). Yet both of these inputs are mathematically equivalent to the original one.

The thing is that I have similar systems of linear equations that I know must have solutions, but the solution vector that maple puts out has coefficients with thousands of digits (which after the above I suspect to be wrong). I know the systems are vastly overdetermined, but even removing all redundant equations does not solve the problen.

Is there a way to get the correct solutions with maple? Does anyone know whether a different program would handle this problem better?

Hello,

I am trying to do parallel computing by using task programming. In the attached file, I am having the following error:

Error, (in generate) type 'sizeType' does not exist.

The error comes out only when the size of the computation is large enough and so the Threads piece of my "generate" function is run.

Could you please help me to understand what is wrong?

Here is the link to my .mv file: 0927.mw

Thanks.

 

If I have 4 latitude and longitude coordinates in degree.  How can I convert all of them to radian and assign each to a specific variable inside a procedure?

>

> DBP(36.9,102.04,37.345,101.6104)
Error, invalid loop statement termination

attached: WA57dev.mw

Hi!
I'm very new to Maple, so I apologize ahead if this is a stupid question.

It seems that my "Determinant" function is not working properly, as shown in the picture.
I simply defined the matrix M and called for the determinant, as instructed by the help system in Maple.

 

 

Does anyone know what's happening?

Thank you very much.

is there an algorithm to search whether protocol exist for movement of balls in different boxes

for example

assume there are 5 boxes, each box has a variable number of number balls

ball number 1 move from box 1 to box 3 and box 5

then when discover ball number 8 in any box, ball number 1 will disappear

if input data are 5 list of numbers each row

1. [1,2,3],[5,7,12],[12,14,15],[1,5,7,9,15],[12,13,14]

2. [2,3],[5,7,12],[1,12,14,15],[1,5,7,9,15],[1,12,13,14]

....

etc

 

 

I would like to plot h over the real interval from 0 to 2*Pi, but

produces an empty plot...  How can I plot successfully?

If I enter the following I do not get the residue... how do I make the residue command work?

 

is it possible to express rational number into fraction in terms of power of 2

input

2.142857143

output

(2^3+2^2+2+1)/(1+2+2^2)

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