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I have a rather large multivatiate polynomial "Dtest"  I need to divie it by a cubic poly "DGm" using rem and quo. Both are determinants multiplied out,  both given below. Have spent the past 2 nights trying to sort, collect, expand, equate coefficients plex groebner etc. Am trying to collect up all the powers of c₃ but cant anything to work. even expand doesn't fully expand "Dtest". If I set c₁ and c₂ to 1 things are...

I wrote the following MAPLE code

restart; N := 2

alias(epsilon = e, eta = t)

eq1 := 5*(diff(F(t), `$`(t, 3)))+(1+3*e)*F(t)*(diff(F(t), `$`(t, 2)))-(2+e)*(diff(F(t), t))^2 = 0

F := proc (t) options operator, arrow; sum('F[i](t)*e^i', 'i' = 0 .. N) end proc

deqn := simplify(collect(eq1, e), {e^(N+1) = 0})

MAPLE says

Error, (in sum) too many levels of recursion

How do I get this error corrected?

How may I program the following with Maple?

(1) Define the function:

H(p) := p * c1 + p^2 * c2 + p^3 * c3  + ......

(2) Now construct the following expression:

(1-p) [ v''' + 1 ]  = H(p) [ v''' - 25 * v' + 1]

Here, v is some funciton of x.

(3) Now assume: v = u0 + u1 * p + u2 * p^2 + ...

and substitute this into the expression defined at the point (2).

Hi there,

I got an output

and would like to bring it in the form

.

How do I do that? :)

In fact I don't even manage to collect the factor of 3*beta^2 as follows

Why does collect only work sometimes?

I will show with a simple example.  I can do this

a := 5*x^2-4*x+3;
       
                             a := 5 x²  - 4 x + 3
h := exp(x)*a+exp(x);
            ...

From this expression I want to extract only terms with the variable x.

F := (1/2/Pi+Q*cos(k*x))^2*(1/2/Pi+Q*cos(k*y))/(1+beta^2*(1/2/Pi+Q*cos(k*x))^2);

I don't want to manually write it out rather extract the terms programmaticallly. I want to be left with

(1/2/Pi+Q*cos(k*x))^2 / (1+beta^2*(1/2/Pi+Q*cos(k*x))^2)

I have tried the collect fucntion but that did not seem to do it. Any suggestions...