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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?

Thanks in advance!

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.

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?

Thanks in advance! advance!

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?

Thanks in advance!

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?

Thanks in advance!

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!

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.