How to calculate the coefficients of a non-polynomial?

I want to subtitute this expansion in an equation and want to equate the coefficients of powers of ϵ, so that i can solve them afterwards. But due to negative power of ϵ, the built-in function 'coeffs' does not work cause as an input it needs a polynomial.

syms E x0 x1 x2 y k

u1=[y x0 x1 x2];
UU=sum(subs(u1(1:4)).*subs(E^k,k,-1:2));

G=coeffs(collect(B(UU,E),E))

I get this error while doing so.

Error using symengine (line 59)
Expression is not a polynomial.

Error in sym/coeffs (line 38)
    cSym = mupadmex('symobj::coeffs',p.s, args{:});

Any one knows how to fix this?

Thanks

[Cris LaPierre]

What is B?

[Usman Saleem]

Sorry, I didn't mention B. Its a basic equation that needs to be solved, for example, B=@(x,E)E*x^3+x+2+E

[J. Alex Lee]

can you lay out the whole problem that you are trying to solve? is it ultimately a fitting problem where you have some list of values for epsilon and corresponding list of values for some other outcome, via some model that involves powers of epsilon and fitted coefficients y,x0,x1,x2?

[J. Alex Lee]

Is the ultimately objective to find the values of and y in the form of (2.64) for the problem (2.60)?

Is this a homework problem? If so, does it specify you must use Matlab? If so, does it specify for what aspect of the solution you must use Matlab?

[Usman Saleem]

It is not a homework problem and we don't have to find the value of y. I just wanted the coefficients of , 1, ϵ, in an array. The above screenshots are attached on your demand and the attached m-file is to illustrate my objective as a result of F.

[J. Alex Lee]

Well, your screenshots only served to confuse...it was not the actual problem you wanted to solve...

Anyway the way I see it, what you are asking for is not really well defined for non-polynomials...e.g., what if you wanted to include fractional powers? How do you decide how finely to divide?

If you only will have whole number powers, specifically for the example you have, you can multiply the whole expression by an extra factor of ϵ and then just remember you did that when you do whatever you need with the coefficients.

[Usman Saleem]

As built-in functions are basically function m-files so can we copy the code of coeffs and create a user defined function m-file with some other name. In there instead of polynomials we take expressions with negative powers as input. Is it possible?

[Usman Saleem]

Although I will try what you mentioned earlier

[J. Alex Lee]

i'd rather check if there are other functions related to collect() that can parse the result, i.e., split it into the various terms and their "coefficients".

[J. Alex Lee]

i guess for this specific example you should multiply through by , not just ϵ

[J. Alex Lee]

check out the function "children"

[Usman Saleem]

I will check out the function and thank you for your help.