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Normaliz :: intclToricRing(MonomialSubalgebra,allComputations=>...)

intclToricRing(MonomialSubalgebra,allComputations=>...) -- integral closure of a toric ring

Synopsis

Description

The toric ring S is the monomial subalgebra given. The function computes the integral closure T of S in the surrounding polynomial ring. If the option allComputations is set to true, all data that has been computed by Normaliz is stored in a RationalCone in the CacheTable of the monomial subalgebra returned.

i1 : R=ZZ/37[x,y,t];
i2 : S=createMonomialSubalgebra {x^3, x^2*y, y^3, x*y^2};
i3 : T=intclToricRing(allComputations=>true,S)

     ZZ
o3 = --[y, x]
     37

o3 : monomial subalgebra of R
i4 : T.cache#"cone"

o4 = RationalCone{cgr => | 0 |                                        }
                         | 4 |
                  equ => | 0 0 1 |
                  gen => | 0 1 0 |
                         | 1 0 0 |
                  inv => HashTable{ => (1, 1)                        }
                                   class group => 1 : (0)
                                   degree 1 elements => 2
                                   dim max subspace => 0
                                   embedding dim => 3
                                   external index => 1
                                   graded => true
                                   grading denom => 1
                                   grading => (1, 1, 0)
                                   hilbert basis elements => 2
                                   hilbert quasipolynomial denom => 1
                                   hilbert series denom => (1, 1)
                                   hilbert series num => 1 : (1)
                                   inhomogeneous => false
                                   integrally closed => false
                                   internal index => 3
                                   multiplicity denom => 1
                                   multiplicity => 1
                                   number extreme rays => 2
                                   number support hyperplanes => 2
                                   rank => 2
                                   size triangulation => 1
                                   sum dets => 1
                  sup => | 0 1 0 |
                         | 1 0 0 |

o4 : RationalCone

Further information

Functions with optional argument named allComputations :