Groebner basis computation with symbolic constants

jooyous
13 ●1 ●1 ●4

Hello! If I have a system of polynomials in $CC[x, y, z]$ or any other field, is there a way to create constants that are in that field in a way that makes Groebner basis computation still work? For example, if I want to compute the Groebner basis for the ideal generated by

y^2 + z - c1
x*y^2 - c2 - 2

Is there a way to indicate that the $c1$ and $c2$ are in $CC$ or whatever field I'm in? I've figured out how to get them to not be indeterminates (over the symbolic ring),

Ideal (y^2 + z - c1, x*y^2 - c2 - 2) of Multivariate Polynomial Ring in x, y, z over Symbolic Ring

but then the polynomials containing them don't have division.

AttributeError: 'MPolynomialRing_polydict_with_category' object has no attribute 'monomial_divides'

Thank you!

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sage: R.<c1,c2> = PolynomialRing(QQ) sage: F = R.fraction_field() sage: S.<x,y,z> = PolynomialRing(F) sage: I = ideal(y^2 + z - c1, x*y^2 - c2 - 2) sage: I.groebner_basis() [y^2 + z - c1, x*z + (-c1)*x + c2 + 2]

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