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Calculating Groebner base with constants

asked 2 years ago

updated 2 years ago

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?

var('a')
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()
B

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 https://ask.sagemath.org/question/666... especially " see more comments"

achrzesz gravatar imageachrzesz ( 2 years ago )

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answered 2 years ago

Max Alekseyev gravatar image

updated 2 years ago

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: 2 years ago

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Last updated: Jun 06 '23