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/