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.Mon, 19 Apr 2021 22:33:39 +0200Quotient of polynomial ring over integers not workinghttps://ask.sagemath.org/question/56734/quotient-of-polynomial-ring-over-integers-not-working/I have a problem. I want Sage to calculate in $\mathbb Z[x]/\langle4,2x,x^2\rangle$ but none of the relations are being calculated/recognized properly:
sage: R.<x> = ZZ[]
sage: I = R.ideal(4,2*x,x^2)
sage: S.<a> = R.quotient(I)
sage: a^2 # the output should be 0
a^2
sage: 2*a # the output should be 0
2*a
sage: S(2)+S(2) # the output should be 0
4
When I introduce a superfluous variable $y$ and consider $\mathbb Z[x,y]/\langle4,2x,x^2,y\rangle$ instead, which is practically the same ring (i.e. isomorphic), then it seems to work:
sage: R.<x,y> = ZZ[]
sage: I = R.ideal(4,2*x,x^2,y)
sage: S.<a,b> = R.quotient(I)
sage: a^2
0
sage: 2*a
0
sage: S(2)+S(2)
0
But now look at this:
sage: S(2)+S(3) # the output should be 1
5
How can I solve this problem?ThrashMon, 19 Apr 2021 22:33:39 +0200https://ask.sagemath.org/question/56734/