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Extract coefficients of polynomials

asked 2016-04-14 05:59:50 +0200

sophia gravatar image

updated 2016-04-14 14:54:30 +0200

kcrisman gravatar image

I have the following code:

_.<k> = PolynomialRing(ZZ)
f = k^3+2*k^2+1
g = k^3 + a*k^2 + 1

the coefficients of f that i get are perfect:

[1, 2, 1]

the coefficients of g should be [1,a,1], but instead i get:

 [[k^3 + 1, 0], [k^2, 1]]

I've tried the solution suggested here:

but it doesn't always produce the coefficients in a logical order.

As always, any help figuring out how to get the correct coefficients of g would be greatly appreciated.

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answered 2016-04-14 08:41:55 +0200

nbruin gravatar image

One solution is to force g into the univariate polynomial ring with respect to which you want to take coefficients:

sage: ZZ['a']['k'](g).coefficients()
[1, a, 1]

By mixing var('a') and _.<k> you're creating an element that has a rather complicated representation. You're better off either sticking entirely with var('a,k') or with defining the appropriate polynomial ring explicitly.

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that works, thank you!

sophia gravatar imagesophia ( 2016-04-14 17:15:34 +0200 )edit

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Asked: 2016-04-14 05:59:50 +0200

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Last updated: Apr 14 '16