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.Fri, 28 Jan 2022 17:06:38 +0100reduce() for fraction field elementshttps://ask.sagemath.org/question/60856/reduce-for-fraction-field-elements/I am having an issue with the `reduce()` method for `FractionFieldElement`.
In a Jupyter notebook I executed the following code
sage: S = FractionField(QQ['t'])
sage: S.inject_variables()
sage: R = PolynomialRing(FractionField(QQ['t']),'x',3)
sage: R.inject_variables()
sage: (((x0^2-x1^2)/(x0-x1)).reduce())
but this returned an object with `NoneType`, rather than
a fraction field element or ring element. What am I doing wrong?AShahFri, 28 Jan 2022 17:06:38 +0100https://ask.sagemath.org/question/60856/Quotient of Polynomial rings reduction not workinghttps://ask.sagemath.org/question/27068/quotient-of-polynomial-rings-reduction-not-working/<code>
<br>R.<x>=PolynomialRing(QQ)
<br>R.ideal(x^4).reduce(x^8+1)
<br>R.<x>=PolynomialRing(ZZ)
<br>R.ideal(x^4).reduce(x^8+1)
1
x^8 + 1
</code>
Why am I not getting the result 1 in both cases?WizqTue, 09 Jun 2015 15:44:26 +0200https://ask.sagemath.org/question/27068/Reducing a Set of Polynomial Equations to Minimal Variables and Equationshttps://ask.sagemath.org/question/10187/reducing-a-set-of-polynomial-equations-to-minimal-variables-and-equations/I have a list of polynomial equations equal to zero, lets call it
> equations = [f1 == 0, f2 == 0, ..., fn ==0]
I know that each polynomial $f_{i}$ is a function of $n^2$ variables where $n$ is determined by input from the user. Is there any way that I can reduce this system of polynomial equations in Python (or with a Sage package) to a minimal number of polynomials and variables?
I tried looking up Grobner basis (http://www.sagemath.org/doc/constructions/polynomials.html#grobner-bases) but it does not seem to be working for what I want as it doesn't check out correctly with the analytical math I have been doing. Thanks!Samuel ReidMon, 03 Jun 2013 19:23:57 +0200https://ask.sagemath.org/question/10187/