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.Sun, 25 Mar 2012 08:53:55 +0200Find specific linear combination in multivariate polynomial ringhttps://ask.sagemath.org/question/8827/find-specific-linear-combination-in-multivariate-polynomial-ring/Assume that I have given a sequence of polynomials $f_1,\dotsc,f_s$ in a multivariate polynomial ring (over $\mathbb{Z}$, if that matters) and want to decide whether a given polynomial $g$ can be written as $g = \lambda_1 f_1 + \dotsc + \lambda_s f_s$. Then in Sage I just let
I = Ideal([f_1,...,f_s])
and test with
g in I
If this returns True, how can I get Sage to display some possible $\lambda_1,\dotsc,\lambda_s$?
As for my specific problem, I have already tried it by hand, but this is hard: My polynomial ring has $15$ indeterminates and there are $s = 250$ polynomials.Martin BrandenburgSun, 25 Mar 2012 08:53:55 +0200https://ask.sagemath.org/question/8827/Ideal Radicals Question?https://ask.sagemath.org/question/7990/ideal-radicals-question/
Hello experts,
Given that there is a commutative ring R and 2 ideals I and J, also given that I is included in J
I need to prove
1) radical of I is in radical of J
2) radical of radical of ideal I = radical of ideal I.
Please give me a detailed answer, I need it urgently!!!!
Thanks in advance!SteveSat, 12 Mar 2011 10:07:19 +0100https://ask.sagemath.org/question/7990/