I need to create a vector from a symbolic polynomial function,but when i use sym2poly command, matlab tells me it is not a polynomial, how should i do?

f1=(497*c1^2 + 497*c2^2 + 497*c3^2 + 11*(c3 + c1*c2)*(c2 - c1*c3)*(c1^2 + c2^2 + c3^2 + 1) + 497)^2/(103684*(c1^2 + c2^2 + c3^2 + 1)^2) + (136*c1^2 + 136*c2^2 + 136*c3^2 + (11*(c2 - c1*c3)*(c1^2 - c2^2 - c3^2 + 1)*(c1^2 + c2^2 + c3^2 + 1))/2 + 136)^2/(103684*(c1^2 + c2^2 + c3^2 + 1)^2) - 1;

sym2poly(f1)

Error using sym/sym2poly (line 30)

Not a polynomial

why matlab tells me this?

Answer 1

[Star Strider]

One option is to use the coeffs function —

syms c1 c2 c3 
sympref('AbbreviateOutput',false);
f1=(497*c1^2 + 497*c2^2 + 497*c3^2 + 11*(c3 + c1*c2)*(c2 - c1*c3)*(c1^2 + c2^2 + c3^2 + 1) + 497)^2/(103684*(c1^2 + c2^2 + c3^2 + 1)^2) + (136*c1^2 + 136*c2^2 + 136*c3^2 + (11*(c2 - c1*c3)*(c1^2 - c2^2 - c3^2 + 1)*(c1^2 + c2^2 + c3^2 + 1))/2 + 136)^2/(103684*(c1^2 + c2^2 + c3^2 + 1)^2) - 1

f1 = 

f1 = simplify(f1, 500)

f1 = 

[f1n, f1d] = numden(f1)

f1n = 

f1d = 

414736

[f1n_cfs, f1n_trms] = coeffs(f1n)                               % Numerator Coefficients & Terms

f1n_cfs = 

f1n_trms = 

[f1n_cfs_all, trms_all] = coeffs(f1, 'All')

f1n_cfs_all(:,:,1) = 

f1n_cfs_all(:,:,2) = 

f1n_cfs_all(:,:,3) = 

f1n_cfs_all(:,:,4) = 

f1n_cfs_all(:,:,5) = 

f1n_cfs_all(:,:,6) = 

f1n_cfs_all(:,:,7) = 

trms_all(:,:,1) = 

trms_all(:,:,2) = 

trms_all(:,:,3) = 

trms_all(:,:,4) = 

trms_all(:,:,5) = 

trms_all(:,:,6) = 

trms_all(:,:,7) = 

That is as completely and thoroughly as it is possible to decompose this polynomial expression.

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[sebastiano della gatta]

thank you for the answer but I don't want to completely decompose the polynomial, I just need the vector of this function because then I have to apply the grobner bases to arrive at my solution.

[Star Strider]

As always, my pleasure!

The first coeffs call then:

[f1n_cfs, f1n_trms] = coeffs(f1n)

is likely as close as it is possible to get. MATLAB inteprets ‘polynomial’ as a univariate polynomial, the reason the sym2poly call fails.

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Answer 2

[sebastiano della gatta]

thank you. I have the last question. Can i compute groebner basis from f1? (The first function that I put in the first question).

[Star Strider]

I honestly have no idea. I had to look up Gröbner basis to understand the context. (I have hard of them, however never used them and barely understand them.)

I suggest posting the Gröbner basis question as a separate, new Question, linking to this one as a reference. It is likely someone here (other than me) will be able to provide an appropriate reply.

(I just addressed the single issue posed in the original Question here.)

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[sebastiano della gatta]

thanks for all.

[Star Strider]

As always, my pleasure!

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