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, 25 Jan 2019 07:16:59 +0100codimension of an ideal or free submodulehttps://ask.sagemath.org/question/45174/codimension-of-an-ideal-or-free-submodule/Is there an option to calculate the codimension of an ideal Sage? For example, I have the following ideal
$I=(1+xy, x+y)$
in $\mathbb{Z}_{2}\left[x,y\right]$ which is a polynomial ring over the field $\mathbb{Z}_2$. How do I calculate the codimension for this simple example? I would like to generalize to free submodules if possiblearpitFri, 25 Jan 2019 07:16:59 +0100https://ask.sagemath.org/question/45174/vdim(std(I)) and vdim(I) returning different answers - Singularhttps://ask.sagemath.org/question/39756/vdimstdi-and-vdimi-returning-different-answers-singular/I thought std just put the ideal in a nicer format, so the answer should be independent. In this case I have 2 larger equation f_1, f_2 and I = jacob((f_1, f_2)). So it ends up being around 18 equations.
I get vdim(std(I)) is the expected answer while vdim(I) the answer is a bit to big.
Any help would be appreciated.
Ed CalFri, 24 Nov 2017 02:41:38 +0100https://ask.sagemath.org/question/39756/Dimensions of modules in branchinghttps://ask.sagemath.org/question/27011/dimensions-of-modules-in-branching/ For example, consider the following branching:
G2=WeylCharacterRing("G2",style="coroots")
adj=G2(0,1)
A1 = WeylCharacterRing("A1", style="coroots")
adj.branch(A1,rule="levi")
How can I find the dimensions of all representations that occur?
In this example, we obtain:
3*A1(0) + A1(2) + 2*A1(3)
and I would like to get:
3*1 + 3 + 2*4
(Note: If I try A1(1).degree() I obtain 1 which is wrong.)vit.tucekWed, 03 Jun 2015 16:55:46 +0200https://ask.sagemath.org/question/27011/How to build a basis for a vector space E(n+1) from a set of points given in E(n) (a vector space of rank n).https://ask.sagemath.org/question/10889/how-to-build-a-basis-for-a-vector-space-en1-from-a-set-of-points-given-in-en-a-vector-space-of-rank-n/I'm interested in how (and if) one can build a new dimension from a set of given dimensions. Specifically, if we are given a vector space E(n) of rank n, and a sample S of elements of E(n) (let us say, S arbitrarily big):
Can we build a vector basis for some E(n+1) of rank n+1?
I'm also interested in keywords or themes that study this kind of questions in maths (if any).
I've been looking up for Lie brackets, unstable operations in vector fields, and words such as involutivity and extension algebras.
Thank you.dimensionMon, 06 Jan 2014 08:22:17 +0100https://ask.sagemath.org/question/10889/Why do messages "// ** redefining ..." show up when computing the dimension of an ideal?https://ask.sagemath.org/question/10740/why-do-messages-redefining-show-up-when-computing-the-dimension-of-an-ideal/I was receiving these weird messages when running the following Sage code - but not every time: When I executed it again, it just went through without any messages.
S.<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11> =PolynomialRing(GF(2),11)
dims=Set([])
s=0
for j in newdivs:
s=s+1
if mod(s,10)==0:
print(s)
aux=j
sdivs=[]
for k in aux:
if k((0,0,0,0,0,0,0,0))==0:
sdivs.append(k)
sdivs.append(f1)
sdivs.append(f2)
sdivs.append(1+x9*(1+x3))
sdivs.append(1+x10*(1+x6))
sdivs.append(1+x11*(1+x4*x5))
IS=S.ideal(sdivs)
di=IS.dimension()
if di>4:
print di
dims=dims.union(Set([di]))
(To understand the code: f1 and f2 are two very long polynomials in S, and newdivs contains 500 of the factors of the 2x2-minors of the Jacobian matrix of f1 and f2...)
The first time I run it, I got this output:
// ** redefining # **
// ** redefining P **
// ** redefining i **
// ** redefining method **
// ** redefining Method **
// ** redefining k **
// ** redefining Minpoly **
// ** redefining was_minpoly **
// ** redefining Qideal **
// ** redefining was_qring **
// ** redefining BRlist **
// ** redefining ord_P **
// ** redefining ordstr_P **
// ** redefining nvars_P **
// ** redefining npars_P **
// ** redefining w **
// ** redefining neg **
// ** redefining opt **
// ** redefining s_opt **
// ** redefining p_opt **
// ** redefining algorithm **
// ** redefining conversion **
// ** redefining partovar **
// ** redefining order **
// ** redefining direct **
10
20
...
The second time, the messages with "// ** redefining" didn't show up anymore.
But maybe it is important to not ignore those messages, so what do they mean?
Thanks in advance!LolinaSat, 16 Nov 2013 16:07:58 +0100https://ask.sagemath.org/question/10740/