## How to expand an equation with complex terms...

Hello everyone,

I need to expand this:

>abs(u+v)^2+abs(u-v)^2

so I have as a final expressioin

>|u|^2+|v|^2=1

This is the property that has to be true so the probability is one.

>assume(u::complex, v::complex);  does not work and the simple commande

>expand() neither.  Any idea?

## How to solve matrix equation (Lyapunov Equation)?...

Let us assume we have a square matrix \$A\$ with known entries. We know the system is asymptotically stable by inspection of the eigenvalues, hence we know that the Lyapunov equation

A^TP+PA=-Id

will have a symmetric matrix P as a solution with Id being the identity matrix. How can I obtain the entries of the P matrix? I have tried the following code but was not able to solve for the entires of the P matrix.

I would be happy if someone could share a solution to this problem.

gc();
restart:

with(LinearAlgebra):

A := <<a__11|a__12>,<a__21|a__22>>;
P := <<p__11|p__12>,<p__12|p__22>>;
Id := <<1|0>,<0|1>>;
eqn := Transpose(A).P+P.A = -Id;

## ImageTools having a problem with workbook...

I am having a problem with image tools read a file from workbook.

In one document i get

Error, (in ImageTools:-Read) unable to open database file

In another document I cant save the file.

## How to suppress outputlines while varying input in...

Please find my error in the doc which produces outputlines always. Is there any otherway (other than view -  show contents and uncheck output which hides all other outputs as well in a programm) by commands, which can suppress these output lines.

Also is there any other way of giving continuously varying inputs (and visible in RotaryGauge ) like sin wave form (0 to 8 to 0 in a period) ?

 (1)

?

## Error: type 'sizeType' does not exist...

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.

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

Thanks.

## StringTools remove "*" asterisk...

I would like to remove asterisk * from a string....

such as...

a:=2*x-5:

withoutstar:=StringTools[Remove](*,convert(a,string));

Any ideas would be appreciated???

## How to tackle with complicated linear systems of e...

Dear All,

I am trying to formulate and solve a linear system of equations to determine the 15 unknowns (link to the script below.) The funcion solve does not seem to return a vlaue due to the lengthy and complex nature of the equations neither do linsolve or LinearSolve. I am wondering whether there exists an argument of another trick that can be employed in order to tackle with such complicated systems. Any help or hint is highly appreciated and desirable.

Thank you,

Bests

Federiko script: SolveLinearSystem.mw

## order of terms in series (algeqtoseries)...

I have a functional equation in 2 variables, and I want to write its solution(s) as (Puiseux) power series. When the order is relatively big, the output appears not in the increasing order of powers. For example, I execute

map(allvalues, algeqtoseries(P, t, u, 60, true))

and get as one of the solutions

O(t^(65/3)) + 13*t^9*(1/3) + 2*t^5*(1/3) + 115*t^15 + 37*t^13 + 5*t^7*(1/3) + 37*t^11*(1/3) + (1/3)*t^3 + 11836*t^21*(1/3) + 1193*t^19 + 1100*t^17*(1/3) [...]

What should I do in order to get the series with terms appearing in the increasing order of powers of t?

Thanks!

## Multiplying Matrices--editing initial ...

Maple will multiply two matrices for me perfectly.

However, when I change the value in one of the cells and try to re-evaluate the product, Maple starts giving me the sum of something in all of my cells.

Are you simply not allowed to ever change the initial values you set for a matrix?  This doesn't seem to make sense to me.

I have attached a screen shot to show an example with a random matrix.

## Strange result for sum of binomials...

Dear Maple users,

I recently had to deal with the following sum :

sum(binomial(k+i,k),i=0..infinity)

for an arbitrary positive value of k. This sum obviously seems to diverge but Maple gives me 0 as a result for it. It looks very strange to me, but it might be the same sort of result as the sum of all the positive integers is -1/12. I am wondering whether the result Maple gives me is correct, and if yes, where does it come from ?

Any idea ?

Thanks a lot!

## how do i work with implicit 2-d Plots?...

for example i have this equation: y=x+c , y and x are variable, but c is constant. i want to plot implicitly with respect to y and x, but the result has no line or something and just two axes. what can i do?

## Convert multiple deg to rad and assign each to spe...

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

## or or `or` or Or or OrProp...

is(k::OrProp(even, odd)) assuming k::integer;
false

is(k::Or(posint, nonposint)) assuming k::integer; # a synonym for OrProp
false

is(`or`(k::posint, k::negint, k = 0)) assuming k::integer;
false

Not including the infix or because that would fail for k=0 for different reasons.

## how to solve rational exponent differential equati...

Hey, friends, I have a differential equation to confuse me too much!  The question is shown in the below:

ODEs:

y''(x)-0.00003019*y(x)^0.337=0  ,       0<x<2945

BCs:

y(0)=0,    y'(2945)=0.0116

I want to have the numerical solution, I used to plot y(x) and y'(x) , but errors shows me "jacobian is singular at left endpoint, use midpoint method instead."  Thank you for you any help in advance!!!

Can you give me the code to figure it out in Maple?  Thank you so so so so much!

## Question on eliminate...

1.

eliminate({-a+x+y+z, -b+x*y+y*z+x*z, -c+x*y*z, -P+x^4+y^4+z^4}, {x, y, z});
[{x = (sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2+a*b*c-c^2)/(2*b*c),
y = -(sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2-a*b*c+c^2)/(2*b*c),
z = c/b}, {-a^4+4*a^2*b-4*a*c-2*b^2+P}],
[{x = -(sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2-a*b*c+c^2)/(2*b*c),
y = (sqrt(c^2*(a^2*b^2-2*a*b*c-4*b^3+c^2)/b^4)*b^2+a*b*c-c^2)/(2*b*c),
z = c/b}, {-a^4+4*a^2*b-4*a*c-2*b^2+P}]

The expression for P is fine, but how are x and y square roots and z=c/b??

2.

eliminate({y*z, x+y-z}, z);
[{z = 0}, {x + y}]

Is this supposed to happen? I was expecting y*(x+y):

Groebner:-Basis({y*z, x+y-z}, lexdeg([z], [x, y]));
[x*y + y^2, z - x - y]

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