# Revision history [back]

### Testing the Gorenstein and regular property for Stanley-Reisner rings using Sage

One can obtain in Sage the Stanley-Reisner ring of a simplicial complex as follows:

X = SimplicialComplex([[0,1,2], [0,2,3]]) X.stanley_reisner_ring()

There is also a given method to check whether the Stanley-Reisner ring is Cohen-Macaulay using Sage as follows: X.is_cohen_macaulay(QQ)

A natural question in commutative algebra is whether a Cohen-Macaulay ring is a Gorenstein ring or even a regular ring. Is there a method to check this for a given commutative ring with Sage or at least for Stanley-Reisner rings?

### Testing the Gorenstein and regular property for Stanley-Reisner rings using Sage

One can obtain in Sage the Stanley-Reisner ring of a simplicial complex as follows:

X = SimplicialComplex([[0,1,2], [0,2,3]]) [0,2,3]])

X.stanley_reisner_ring()

There is also a given method to check whether the Stanley-Reisner ring is Cohen-Macaulay using Sage as follows: X.is_cohen_macaulay(QQ)

A natural question in commutative algebra is whether a Cohen-Macaulay ring is a Gorenstein ring or even a regular ring. Is there a method to check this for a given commutative ring with Sage or at least for Stanley-Reisner rings?

### Testing the Gorenstein and regular property for Stanley-Reisner rings using Sage

One can obtain in Sage the Stanley-Reisner ring of a simplicial complex as follows:

X = SimplicialComplex([[0,1,2], [0,2,3]])

X.stanley_reisner_ring()

There is also a given method to check whether the Stanley-Reisner ring is Cohen-Macaulay using Sage as follows: X.is_cohen_macaulay(QQ)

A natural question in commutative algebra is whether a Cohen-Macaulay ring is a Gorenstein ring or even a regular ring.

Question: Is there a method to check this for a given commutative ring with Sage or at least for Stanley-Reisner rings?

### Testing the Gorenstein and regular property for Stanley-Reisner rings using Sage

One can obtain in Sage the Stanley-Reisner ring of a simplicial complex as follows:

X = SimplicialComplex([[0,1,2], [0,2,3]])

X.stanley_reisner_ring()

There is also a given method to check whether the Stanley-Reisner ring is Cohen-Macaulay using Sage as follows: X.is_cohen_macaulay(QQ)

A natural question in commutative algebra is whether a Cohen-Macaulay ring is a Gorenstein ring or even a regular ring.

Question: Is there a method to check this for the Gorenstein (and regular) property for a given commutative ring with Sage or (or at least for Stanley-Reisner rings?rings) with Sage?

### Testing the Gorenstein and regular property for Stanley-Reisner rings using Sage

One can obtain in Sage the Stanley-Reisner ring of a simplicial complex as follows:

X = SimplicialComplex([[0,1,2], [0,2,3]])

X.stanley_reisner_ring()

There is also a given method to check whether the Stanley-Reisner ring is Cohen-Macaulay using Sage as follows: X.is_cohen_macaulay(QQ)

A natural question in commutative algebra is whether a Cohen-Macaulay ring is a Gorenstein ring or even a regular ring.

Question: Is there a method to check for the Gorenstein (and regular) property for a given commutative ring (or at least for Stanley-Reisner rings) with Sage?

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### Testing the Gorenstein and regular property for Stanley-Reisner rings using Sage

One Sage can obtain in Sage construct the Stanley-Reisner ring of a simplicial complex as follows:complex:

sage: X = SimplicialComplex([[0,1,2], [0,2,3]])SimplicialComplex([[0, 1, 2], [0, 2, 3]])

sage: X.stanley_reisner_ring()
Quotient of Multivariate Polynomial Ring in x0, x1, x2, x3
over Integer Ring by the ideal (x1*x3)


Such rings in Sage have a method to check whether they are Cohen-Macaulay:

X.stanley_reisner_ring()

There is also a given method to check whether the Stanley-Reisner ring is Cohen-Macaulay using Sage as follows: X.is_cohen_macaulay(QQ)

sage: X.is_cohen_macaulay(QQ)
True


A natural question in commutative algebra is whether whether a Cohen-Macaulay ring is a Gorenstein ring or even a regular ring.

Question:

Question: Is there a method to check for the Gorenstein Gorenstein (and regular) property for a given commutative ring ring (or at least for Stanley-Reisner rings) with Sage?