## Powers of Complex Numbers...

What is the command to yield the expansion of Z^N in terms of x and y.

Z complex = x+iy,

N integer >1

e.g. Z^2 = x^2 - y^2 + 2.i.x.y

## Help me with determinant calculation of a matrix...

could you just delete the post !!!!!!!!!!!!!!!!!!!!!!!!!!!x!xxxx!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

## solving in maple for to variables divided ...

Is it possible to solve an expression like in the picture below?:
I´ve tried to figure it out at maplesoft.com but I could not find anything that worked...

I´ve also attached the equation as a file.

 > restart
 >
 >

## which package is better...

Can you please explain which optimization package is better from your experience

1 maple

2 matlab

3. mathematica

4. gams studio

5. gurobi

or any other

## How do I evaluate this Integral in Maple?...

Int1 := int(exp(-z*(R^2*k^2 - b^2*z)/(R*b))/(z*HeunB(0, k^2*R^2/(b*sqrt(R*b)), R^3*k^4/(4*b^3), 0, -sqrt(R*b)*z/R)^2), z = R .. r);

into cylindrical coords with z axis simetry and radius r;

where R, k, b are constants >0;

And HeunB is Maple funtion

I apreciate the exact calculus but maybe an aproximation is ok but or a plot.

## plot points and vectors ...

Dear all

If we travel in straight lines in R^3. We begin at the point A=(1, 2, 3)
in the direction of the vector (1, 2, 2) and we end at the final point (10, 11, 12).

We made a single 90-degree turn.

Can we sketch a figure and we show the position where we take the turn?

Thanks

## solve linear system of dimension n...

Dear all

I hope to solve a linear system AX=bk where A is a nxn matrix and X is a nx1 vector and b is a vector from the canonical basis of R^n ( for example in R^3 : b1=[ 1 0 0], b2 =[ 0 1 0] and b3=[ 0 0 1]

GramMat.mw

Thanks

## Can Maple compute two-dimensional Fourier transfor...

I am reading a paper which has some useful two-dimensional Fourier transforms in the appendix: for example,

Fourier transform of 1/r = (1/k)*e^(-kz),

where r = sqrt(x^2 + y^2 + z^2) and k =  sqrt(k_1^2 + k_2^2).

My guess is that the author has computed these by taking contour integrals in the upper half-plane and I would like to compute some of these myself but I have many of them to compute and was wondering if it could be done with Maple instead.

For example, could I use Maple to verify that the above 2D Fourier transform is correct and that the inverse 2D Fourier transform takes you back to the original (or almost takes you back).  After that I would then like to feed in the functions which I have to get Fourer and inverse Fourier transforms.

## How do I split an equation and save the right hand...

This may be a total newbie question, but is there a way to split an equation and save the right hand side? For example, have a look on what happens without split:

numer(L = 2/3);
"Error, invalid input: numer expects its 1st argument, x, to be of type {list, set, algebraic}, but received L = 2/3"

I thought that "convert"-function might be able to do this, but for example this does not work:

convert(L = 2/3, algebraic)

"Error, invalid input: `convert/algebraic` expects its 1st argument, pr, to be of type procedure, but received L = 2/3"

Please understand that this is a simplified example. The real problem looks like

sol := solve({eq1, eq2,eq3, res}, {L, x1, x2, x3})

The point here is how to convert the sol[1], which is L = numerator/denumerator into --> numerator/denumerator

Taking a copy of the equation works, but this is only an intermediate result, so if the split does not work automatically, Maple cannot compute the problem to the end without human intervention, and since this problem takes a long time to solve, it would be nice if I could just leave Maple to finish the task by itself.

## How would I compute the series expansion of cos(x)...

How would I compute the series expansion of cos(x)^n at the point x=0?

## Trying to icombine; is too...

 > combine(2^n*4, icombine);
 (1)
 > combine(2^n*4);
 (2)
 > combine(2^n/4, icombine); # BUG
 > combine(2^n/4);
 (3)
 > combine(2^n/2^m, icombine); # BUG
 > combine(2^n*2^(-m), icombine);
 (4)
 > combine(2^n/2^m);
 (5)
 > is(2^n/4 = 2^(n-2)); # ???
 (6)
 >

## Command-line Maple doesn't evaluate certain functi...

Hi everyone, I'm having issues using Maple through the command line (I have reasons to be avoiding the GUI, namely I am trying to use Maple in a development environment that integrates other programs, e.g. Mathematica into the mix. This forces me to only be able to access Maple via the command line).

Here is my issue: for some functions, like diff(), which differentiates functions, Maple evaluates the function on the input:

```> f:=x+2;
f := x + 2

> g := diff(f, x);
g := 1```

For other functions though, such as SPolynomial() (from the Ore_algebra library), command-line Maple is lazy and just spits back the input:

```> with(Ore_algebra)

> A:=diff_algebra([D1, x1], [D2, x2]);
A := diff_algebra([D1, x1], [D2, x2])

> T:=MonomialOrder(A, grlex(D1, D2));
T := MonomialOrder(diff_algebra([D1, x1], [D2, x2]), grlex(D1, D2))

> L1:=D1;
L1 := D1

> L2:=D2;
L2 := D2

> L:=SPolynomial(L1, L2, T);
L := SPolynomial(D1, D2, MonomialOrder(diff_algebra([D1, x1], [D2, x2]), grlex(D1, D2)))```

Let me know if you get the same error as well! The correct output (outputted by the worksheet version of Maple) should be:

`L := 0`

## How to change tickmarks in sparsematrixplot?...

Hi,

Let's take the last example (Maple 2019) given in help[sparsematrixplot] (representation of the adjacency matrix of a graph).
Vertices of this graph are labelled 1, 2, ...20.
Suppose I change these names as a, b, ...t.
I would like the tickmarks of the sparsematrixplot output match the names of the vertices of the graph, and not the integers 1, 2, ..20

I tried this:
S := [\$1..20] =~ StringTools:-Char~(96 +~  [\$1..20]);
plots:-sparsematrixplot(..., tickmarks=[S, S])

But the only the tickmars of the columns are changed, not those of the rows.

Is it possible to change the names of the tickmarks ?

## step by step solutions...

How  to get step by step solutions in dsolve?

## How can I make the Maple show the solution? (ODE)...

Hello,

Please, what is going wrong that it is not graphing the ODE system solution?

eqs := seq(eq[i], i = 1 .. 6*n);
cis := seq(ci[i], i = 1 .. 6*n);
sol := dsolve([eqs, cis], numeric, stiff = true, output = listprocedure);
for i to n do
graf1[i] := odeplot(sol, [t, x[i](t)], 0 .. 5, color = black);
end do;
for i from 11 to 2*n do
graf2[i] := odeplot(sol, [t, x[i](t)], 0 .. 5, color = blue);
end do;
for i from 21 to 3*n do
graf3[i] := odeplot(sol, [t, x[i](t)], 0 .. 5, color = green);
end do;
for i from 31 to 4*n do
graf4[i] := odeplot(sol, [t, x[i](t)], 0 .. 5, color = red);
end do;
for i from 41 to 5*n do
graf5[i] := odeplot(sol, [t, x[i](t)], 0 .. 5, color = pink);
end do;
for i from 51 to 6*n do
graf6[i] := odeplot(sol, [t, x[i](t)], 0 .. 5, color = orange);
end do;

display(seq(graf1[i], i = 1 .. n));
display(seq(graf2[i], i = 11 .. 2*n));
display(seq(graf3[i], i = 21 .. 3*n));
display(seq(graf4[i], i = 31 .. 4*n));
display(seq(graf5[i], i = 41 .. 5*n));
display(seq(graf6[i], i = 51 .. 6*n));

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