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 | 1 | initial version |
Strictly speaking, the Stanley-Reisner ideal or ring is not defined for all polytopes, but simplicial ones, where one then looks at the boundary complex of the polytope.
You can get the Stanley-Reisner ideal like so:
sage: P = Polyhedron(vertices=[[1,0,0,0],[-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[0,-1,-1,-1]])
sage: BC = P.boundary_complex()
sage: SRR = BC.stanley_reisner_ring()
sage: I = SRR.defining_ideal()
sage: I
Ideal (x1*x2*x3*x4, x0*x5) of Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5 over Integer Ring
| | 2 | No.2 Revision |
Strictly speaking, the Stanley-Reisner ideal or ring is not defined for all polytopes, but simplicial ones, where one then looks at the boundary complex of the polytope.
You can get the Stanley-Reisner ideal like so:
sage: P = Polyhedron(vertices=[[1,0,0,0],[-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[0,-1,-1,-1]])
sage: BC = P.boundary_complex()
sage: SRR = BC.stanley_reisner_ring()
sage: I = SRR.defining_ideal()
sage: I
Ideal (x1*x2*x3*x4, x0*x5) of Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5 over Integer RingRing
| | 3 | No.3 Revision |
Strictly speaking, the Stanley-Reisner ideal or ring is not defined for all polytopes, but simplicial ones, where one then looks at the boundary complex of the polytope.
You can get the Stanley-Reisner ideal like so:
sage: P = Polyhedron(vertices=[[1,0,0,0],[-1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[0,-1,-1,-1]])
sage: BC = P.boundary_complex()
sage: SRR = BC.stanley_reisner_ring()
sage: I = SRR.defining_ideal()
sage: SRR.defining_ideal(); I
Ideal (x1*x2*x3*x4, x0*x5) of Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5 over Integer Ring
