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/How do I define a homomorphism of a graded commutative algebra?https://ask.sagemath.org/question/44109/how-do-i-define-a-homomorphism-of-a-graded-commutative-algebra/ I am working on implementing morphisms of graded commutative algebras. I have two graded commutative algebra, A with generators <w,x> and B with generators <y,z> . I define H the set of homomorphisms from A to B. Then, I want to define the homomorphisms f such that f(w)=y and f(x)=0 but I get an error:
sage: H = Hom(A,B)
sage: H([y,0])
TypeError: images do not define a valid homomorphism
BelénMon, 29 Oct 2018 10:26:05 +0100https://ask.sagemath.org/question/44109/Partially commutative monoid of a graphhttps://ask.sagemath.org/question/41756/partially-commutative-monoid-of-a-graph/I am interested in the free partially commutative monoid associated to a graph whose definition can be seen here www.sciencedirect.com/science/article/pii/0304397591903556 and here https://en.m.wikipedia.org/wiki/Trace_monoid.
Basically I need a free monoid in which some variables commutes.
My questions are
1. whether this notion is already implemented in Sage?
2. If not how to implement this in Sage?GA316Sun, 25 Mar 2018 17:54:57 +0200https://ask.sagemath.org/question/41756/