ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 02 Sep 2020 23:41:22 +0200Rewriting linear combination of Groebner basis in terms of original termshttps://ask.sagemath.org/question/53267/rewriting-linear-combination-of-groebner-basis-in-terms-of-original-terms/ Let assume I have an ideal given by
x,y,z = QQ['x,y,z'].gens()
I = ideal(f1,f2,f3)
B = I.groebner_basis()
where f1,f2,f3 are just polynomials in variables x,y,z. Let's say B=(g1,g2).
Let's assume I happen to take a polynomial,h, that is in my ideal I. Then doing polynomial division, I can write
h=h1*g1+h2*g2
Basically I can write h as a linear combination of the elements in my Groebner basis. Is there a function that converts a linear combination in terms of Groebner to linear combination of terms in my ideal I? i.e.I can write
h=q1*f1+q2*f2+q3*f3
whatupmattWed, 02 Sep 2020 23:41:22 +0200https://ask.sagemath.org/question/53267/Groebner basis computation with symbolic constantshttps://ask.sagemath.org/question/26748/groebner-basis-computation-with-symbolic-constants/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!jooyousWed, 06 May 2015 21:56:22 +0200https://ask.sagemath.org/question/26748/