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Calculating Groebner base with constants

asked 2023-06-01 13:09:32 +0200

updated 2023-06-06 12:18:26 +0200

slelievre gravatar image

I want to see what the Groebner base of an ideal is, but the polynomials generating it have some constants inside. Is there any way to do that with Sage?

R.<x,y> = PolynomialRing(CC, 2, order='lex')
I = ideal(y^4*a, y^2*x - y*a - x, y - x*a)
B = I.groebner_basis()

This doesn't seem to work. a is the constant. Also, this example is just a dummy, I want to know in general how to have constant coefficient in polynomials.

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See especially " see more comments"

achrzesz gravatar imageachrzesz ( 2023-06-06 13:41:10 +0200 )edit

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answered 2023-06-06 15:04:05 +0200

Max Alekseyev gravatar image

updated 2023-06-06 15:05:14 +0200

Don't mix up polynomial variables with symbolic ones. Instead introduce your symbolic constants also as polynomial variables - like: R.<x,y,a> = PolynomialRing(QQ).

On a related note, polynomial machinery does not work over inexact fields like CC - use QQ, QQ[I], AA or QQbar instead. See this answer for more details.

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Asked: 2023-06-01 13:09:32 +0200

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Last updated: Jun 06