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, 18 Jun 2021 10:54:18 +0200Is it possible to compute a Gröbner basis of an ideal of a graded commutative algebra in SageMathhttps://ask.sagemath.org/question/57617/is-it-possible-to-compute-a-grobner-basis-of-an-ideal-of-a-graded-commutative-algebra-in-sagemath/Let me start by saying that I am a newbie to Sage.
Let us say I have a graded commutative algebra `A` using the command
`GradedCommutativeAlgebra`, and an ideal `I` of `A`.
For instance, something like the following (but this is just a toy example!):
sage: A.<x,y,z> = GradedCommutativeAlgebra(QQ, degrees=((1,1), (2,1), (3,2))
sage: I = A.ideal([z*y - x*y*y])
I would like to get a Gröbner basis of `I` from SageMath
(not for the previous example, which is immediate).
I know how to do this for polynomial algebras, but for graded
commutative algebras constructed using `GradedCommutativeAlgebra`
this does not seem to work. Is it possible?
Thanks in advance!
EDIT: I slightly changed the previous example to avoid any misunderstanding. I remark that, if one forgets the multidegree of the algebras, the algebras I am interested in (and produced by the command `GradedCommutativeAlgebra`) are super commutative for the underlying Z/2Z grading. In particular, in the previous example, we have `z*z = 0` in `A`, because `z` has total odd degree, and `z*y = - y * z` in `A`, since `y` also has odd degree.EstanislaoFri, 18 Jun 2021 10:54:18 +0200https://ask.sagemath.org/question/57617/Is there any easy way to parallel gröbnerbasis computations in sage?https://ask.sagemath.org/question/33534/is-there-any-easy-way-to-parallel-grobnerbasis-computations-in-sage/Hi, I have a problem I am currently working on where I wish to eliminate variables from a system of polynomials. I have managed to do it in several cases, but for large systems to check my hypothesis the memory usage becomes very large, and the computations take a long time. Therefore I wondered if there is any easy way to optimalize the gröbner basis computation in sage. I am currently using the .elimination_ideal([]) environment, but it turns out to be very ineffective in the examples I am computing. I figured out that one of the limitations is that the eliminate function runs on only one core of the computer. So I therefore thought that in order to speed up the computations, then one could parallelize the function. However, it turns out that all current environments on sage including @fork, @parallel and parallelism.set() does not help at all in this case, since the process still runs on only one core.
Any good ideas out there? mathguyTue, 24 May 2016 14:26:36 +0200https://ask.sagemath.org/question/33534/