Is it possible to compute a Gröbner 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.
Do you really mean to use these super-commutative algebras ? or rather a standard grading, where commutation between variables does not involve their degrees ?