# Revision history [back]

The Stanley_reisner_ideal function exists in SageMath for a rational polyhedral fan or for the toric variety associated to a rational polyhedral fan:

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:          [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: fan.Stanley_Reisner_ideal(PolynomialRing(QQ, 5, 'A, B, C, D, E'))
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


Hope this helps.

The Stanley_reisner_idealStanley_Reisner_ideal function exists in SageMath for a rational polyhedral fan or for the toric variety associated to a rational polyhedral fan:

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:          [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: fan.Stanley_Reisner_ideal(PolynomialRing(QQ, 5, 'A, B, C, D, E'))
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


Hope this helps.

The Stanley_Reisner_ideal function exists in SageMath for a rational polyhedral fan or for the toric variety associated to a rational polyhedral fan:

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:          [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: fan.Stanley_Reisner_ideal(PolynomialRing(QQ, 5, 'A, B, C, D, E'))
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


or for the toric variety associated to a rational polyhedral fan:

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:           [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: X = ToricVariety(fan, coordinate_names='A B C D E', base_field=GF(5))
sage: SR = X.Stanley_Reisner_ideal(); SR
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


Hope this helps.

The Stanley_Reisner_ideal function exists in SageMath for a rational polyhedral fan :

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:          [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: fan.Stanley_Reisner_ideal(PolynomialRing(QQ, 5, 'A, B, C, D, E'))
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:           [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: X = ToricVariety(fan, coordinate_names='A B C D E', base_field=GF(5))
sage: SR = X.Stanley_Reisner_ideal(); SR
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


Note that you may also compute the Stanley-Reisner ring of a simplicial complex:

sage: X = 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)


Hope this helps.

The Stanley_Reisner_ideal function exists in SageMath for a rational polyhedral fan :

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:          [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: fan.Stanley_Reisner_ideal(PolynomialRing(QQ, 5, 'A, B, C, D, E'))
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:           [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: X = ToricVariety(fan, coordinate_names='A B C D E', base_field=GF(5))
sage: SR = X.Stanley_Reisner_ideal(); SR
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


Note that you may also compute the Stanley-Reisner ring of a simplicial complex:. Here the method is not using capital letter:

sage: X = 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)


Hope this helps.

The Stanley_Reisner_ideal function exists in SageMath for a rational polyhedral fan :

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:          [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: fan.Stanley_Reisner_ideal(PolynomialRing(QQ, 5, 'A, B, C, D, E'))
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field

sage: fan = Fan([[0,1,3], [3,4], [2,0], [1,2,4]],
....:           [(-3, -2, 1), (0, 0, 1), (3, -2, 1), (-1, -1, 1), (1, -1, 1)])
sage: X = ToricVariety(fan, coordinate_names='A B C D E', base_field=GF(5))
sage: SR = X.Stanley_Reisner_ideal(); SR
Ideal (A*E, C*D, A*B*C, B*D*E) of
Multivariate Polynomial Ring in A, B, C, D, E over Rational Field


Note that you may also compute the Stanley-Reisner ring of a simplicial complex. Here the method is not using capital letter:letters:

sage: X = 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)


Hope this helps.