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### Is it possible to compute a Gröbner basis of an ideal of a graded commutative algebra in SageMath

Hi,

Let me start by saying that I 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([zz - xxyy])

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?

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### Is it possible to compute a Gröbner basis of an ideal of a graded commutative algebra in SageMath

Hi,

Let me start by saying that I a newbie to Sage.

Let us say I have a graded commutative algebra A A using the command "GradedCommutativeAlgebra", command GradedCommutativeAlgebra, and an ideal I I of A. 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)) (3,2))
sage: I=A.ideal([zz I = A.ideal([z*z - xxyy])x*x*y*y])


I would like to get a Gröbner basis of I from SageMath SageMath (not for the previous example, which is immediate). immediate).

I know how to do this for polynomial algebras, but for graded graded commutative algebras constructed using "GradedCommutativeAlgebra" GradedCommutativeAlgebra this does not seem to work. Is it possible?

### 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*z - x*x*y*y])


I would like to get a Gröbner basis of I 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?

### 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*z A.ideal([z*y - x*x*y*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?

### 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?

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.