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Translating a list of polynomials using sage

asked 2020-12-27 19:11:04 +0100

klaaa gravatar image

updated 2020-12-27 20:45:06 +0100

Juanjo gravatar image

I have a list of polynomials in Sage as follows:

W=[P.coxeter_polynomial() for P in posets(n)]

Now I want to have the list of all such polynomials as polynomials in R.<x> = PolynomialRing(ComplexField(100)) .

My question is: Is there an easy way to translate the above list W so that Sage views every polynomial in that list as a polynomial in R.<x> = PolynomialRing(ComplexField(100))?

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Side remark : sage: P.is_cyclotomic_product() is useful to recognize polynomials with all their roots on the unit circle.

FrédéricC gravatar imageFrédéricC ( 2020-12-27 20:52:44 +0100 )edit

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answered 2020-12-27 20:44:17 +0100

Juanjo gravatar image

updated 2020-12-27 23:53:16 +0100

slelievre gravatar image

Yes, there is.

This can be done either as post-treatment after you have already built the list of polynomials, or at the time of building the list.

If you already have the list W defined as in the question, you can write:

C = ComplexField(100)
W = [w.change_ring(C) for w in W]

Or you could regenerate the list to directly get polynomials in the desired ring:

n = 5
C = ComplexField(100)
W = [P.coxeter_polynomial().change_ring(C) for P in posets(n)]


n = 5
R.<x> = PolynomialRing(ComplexField(100))
W = [R(P.coxeter_polynomial()) for P in posets(n)]
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Asked: 2020-12-27 19:11:04 +0100

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Last updated: Dec 27 '20