## Solving matrix equations (e.g. an algebraic Riccat...

Hello everyone,

I'm trying to solve a largeish matrix equation of the form A*X + Transpose(A*X) = B for X, where A and B are known matrices.  I know there must be some clever way to get Maple to automatically unpack this equation into the equations for the components and then solve them symbolically, but I haven't had much success.  Could someone more skilled point the way?

Thanks.

## Simplistic ln problem...

Hello,

Using Maple, I integrated and expression and got ln(e) in the answer.  How can I eliminate this?

Thanks

## complicated integration...

i have this integration:

int(q*exp((1-b)^2* qz^2/lambda )/((1+b^2*q^2+b^2*qz^2)*(q^2+qz^2)),qz=-infinity..infinity) then w.r.t      q  from (0......infinity)

## sequence and separate out individual numbers from ...

I want to take two numbers, for example 37665432 and 59374696 (later extrapolate to 3 or 4 etc... sets of numbers) and take each individual number alternately and put them into a list.

Here's what I have

a:=37665432;

b:=59374696;

c:=convert(a,base,10);

d:=convert(b,base,10);

e:=ListTools:-Reverse(c);

f:=ListTools:-Reverse(d);

So now I have the numbers all in a list and I want to select each one alternately into another list.

g:=seq(e[i],f[i],i=1..8);

## How can I suppress simplify factoring out -1?...

I am going to simplify the following formula:

sqrt(a^2*p*(1-p)*(N-n)/(n^2*(N-1)))

I wrote simplify(sqrt(a^2*p*(1-p)*(N-n)/(n^2*(N-1))),symbolic), the output was:

## Simplification...

Hi,

I have a series solution to a differential equation. The recurrence relation is such that knowing the first four coefficients is sufficient to determine all the other coefficients. Now I want to represent this solution in terms of f(x)*c0+g(x)*c1+h(x)*c2+k(x)*c3 where f,g,h,k are all polynomials in x. I tried searching for commands related to simplify, but I was unable to solve my problem.

p.s : i am not aware if this has already been discussed so please bear with me

## integrating with lots of parameters...

Hello,

I am having trouble with posing an integration for the following function, wrt z.

u:= sin (theta)  * ((s^2 + z^2)/2 +h*z)

I want to be able to change the values of h, s, and theta.

I would like to integrate u, wrt z, from s to h.

I have tried the basics, such as....

int(u, z)   and

int(u, z=s..h)

I get the integrand symbol and a general setup but I am not posing it clearly enough to get Maple to perform the integration.

## PDE problem, that puzzles me ......

```Based on some older Math group thread my problem is the following (0 < t):

F:= (x,t) -> Int(exp(-t*eta^2+x*eta)/(1+exp(eta)),eta = -infinity .. infinity);

satisfies 0 = 'diff(F(x,t),t) + diff(F(x,t),x\$2)' and for that PDE Maple gives

pdsolve(PDE, f(x,t),build): combine(%):
subs(_c[1]=c,_C1=c1,_C2=c2,_C3=c3,%): rhs(%);
S:=unapply(%, x,t);

S := (x, t) -> c3*c1*exp(c^(1/2)*x-c*t)+c3*c2*exp(-c^(1/2)*x-c*t)

by separation of variables.

I am interested in t=1/2 ( to get (F(x,1/2) ) and for that define

```

## How to include a Maple procedure file?...

I have a procedure that I use frequently. I tried to include this procedure in other Maple sessions so that I can reuse that procudure. I tried the command \$include but received the following error message:

\$include "c:/myworks/myplot.wm"

Error, unexpected string

where myplot.wm is a file that contains a procedure which I want use repeatedly.  What is wrong there?

Thanks.

## Not willing to compute...

assume(u::real)

assume(v>0)

assume(lambda>0)

Im( u+i v / u+i v+lambda )   is ok.

Im( (u+i v / u+i v+lambda)^2 )   is ok.

Im( (u+i v / u+i v+lambda)^3 )   is ok.

Im( (u+i v / u+i v+lambda)^4 )   is not ok.

Maple gives back the input.

What is the problem with my input?

Sandor

## solving ODE system with boundary conditions...

Hi,

I need some help.  I have a system of ODE's subject to a system of Boundary Conditions.  I can't figure out the sequence of commands to get MAPLE to generate a solution.

ODE System:

SYS1 := {diff((C[10])(z), `\$`(z, 2)) = (BR[1]+BR[2])*(C[10])(z)-BR[3]-(BR[4]+BR[5])*C[50], diff((C[51])(z), `\$`(z, 2)) = Ped*u[0]*C[50*x]-BR[5]*(C[10])(z)+BR[3]*C[50]}

Boundary Conditions:  I am going to be evaluating from z=s to z=h

BC1 := {(C[10])(h) = 1, diff((C[10])(s), s) = 0, diff((C[51])(h), h) = 0, diff((C[51])(s), s) = Da[1]*(C[50]-J3)}

## Procedure/Module description...

I write a lot of maple code that my advisor uses, and I'm wanting to make it easier for him to use with as little extra work on my side as possible. Most recently I've started using modules to hold the procedures that go together. For example, I may have something like this

Resultants := module()
description "This uses various methods to find resultants.":
export UResultant, MacaulayResultant:

MacaulayResultant := proc(F,vars)
-- description and code
end proc:

## Help! Is this right?...

I am running the student version of maple, the one for hundred, and my final question is wondering if we could solve second order de as in a spring mass system.

The problem reads,  a mass weighing 32 lb stretches a spring 2 ft. The mass is initially relesed from a point 1 foot above equilibrium position with an upward velocity of 2 ft/s

## Sum simplification...

I would like to simplify (automatically...) a sum containing constant terms, as in the trivial one:

Sum((A*x[i]+B)^2, i = 1 .. n) = A^2*(sum(x[i]^2, i = 1 .. n))+2*A*B*(sum(x[i], i = 1 .. n))+n*B^2

I can reach this result easily enough by:

- Using the "student" package

- Then expressing the sum underits inert form (Sum(...))

- Expanding it

- Taking its value.

Now the "student" package is "deprecated".... How can I do this without it?