ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 18 Apr 2017 04:34:27 -0500How to compute syzygy module of an ideal in a quotient ring?https://ask.sagemath.org/question/37320/how-to-compute-syzygy-module-of-an-ideal-in-a-quotient-ring/I am trying to compute the syzygy module of an ideal generated by two polynomials `<p,q>` modulo `I`, where `I` is another ideal. This means to compute a generating set `[(p1,q1),...,(ps,qs)]` of the module `{(g,h): gp+hq is in I}`. I know that in Sage, we can use singular command to compute syzygy module:
R.<x,y> = PolynomialRing(QQ, order='lex')
f=2*x^2+y
g=y
h=2*f+g
I=ideal(f,g,h)
M = I.syzygy_module();M
[ -2 -1 1]
[ -y 2*x^2 + y 0]
But this does not work with modulo `I`:
R.<x,y> = PolynomialRing(QQ, order='lex')
S.<a,b>=R.quo(x^2+y^2)
I=ideal(a^2,b^2);I
M = I.syzygy_module();M
Ideal (-b^2, b^2) of Quotient of Multivariate Polynomial Ring in x, y over Rational Field by the ideal (x^2 + y^2)
Error in lines 4-4
Traceback (most recent call last):
Is there a way to do that?KittyLTue, 18 Apr 2017 04:34:27 -0500https://ask.sagemath.org/question/37320/