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/weighted univariate polynomialshttps://ask.sagemath.org/question/47628/weighted-univariate-polynomials/I have a polynomial algebra in n variables k[x_1,...,x_n]. I know how assign different degrees to each of the generators as in
sage: P = PolynomialRing(QQ, 'x,y,z', order = TermOrder('wdegrevlex', (2,3,4)))
sage: P.inject_variables()
Defining x, y, z
sage: z.degree()
sage:
4
However if I want to do this with only one variable this does not work
sage: P = PolynomialRing(QQ, 'x', order = TermOrder('wdegrevlex', (2)))
sage: P.inject_variables()
Defining x
sage: x.degree()
1
I wander if I can do this in an uniform way cause I need to use a class that takes an arbitrary number of variables.
heluaniTue, 27 Aug 2019 20:55:48 +0200https://ask.sagemath.org/question/47628/Polynomials over number fieldshttps://ask.sagemath.org/question/38381/polynomials-over-number-fields/Below I define a polynomial ring K[s,t]. My goal is to compute the minors of a large matrix with entries in this ring.
var('x')
# K.<t> = NumberField(x^2-2)
K.<s,t> = NumberField([x^2-2,x^2-5])
R.<p0,p1,p2,p3,p4,p5> = K[]
M = Mat(R,10,10).random_element()
mins = M.minors(2)
This code works fine, but if I replace the last line with
mins = M.minors(7)
it fails with the error message
TypeError: no conversion to a Singular ring defined
Is it possible to avoid this error?coreyharrisMon, 24 Jul 2017 18:09:25 +0200https://ask.sagemath.org/question/38381/