# 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 ?