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How to calculate the coefficients of a non-polynomial?

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Usman Saleem 2021-1-7

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评论： Usman Saleem 2021-1-13

在 MATLAB Online 中打开

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

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Cris LaPierre 2021-1-8

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What is B?

Usman Saleem 2021-1-8

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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 2021-1-8

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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 2021-1-11

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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 2021-1-11

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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 2021-1-11

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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 2021-1-11

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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 2021-1-11

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Although I will try what you mentioned earlier

J. Alex Lee 2021-1-11

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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 2021-1-12