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

- Usage:
    `intclToricRing S`
- Inputs:
  - a monomial subalgebra, the toric ring
- Outputs:
  - a monomial subalgebra, the integral closure of the toric ring

## 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)

    o3 = MonomialSubalgebra{cache => CacheTable{...1...}}
                            generators => {y, x}
                            ring => R

    o3 : MonomialSubalgebra 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

## Functions with optional argument named allComputations:

- diagInvariants(...,allComputations=>...) (missing documentation)
- ehrhartRing(...,allComputations=>...) (missing documentation)
- finiteDiagInvariants(...,allComputations=>...) (missing documentation)
- intclMonIdeal(...,allComputations=>...) (missing documentation)
- intclToricRing(...,allComputations=>...) (missing documentation)
- intersectionValRingIdeals(...,allComputations=>...) (missing documentation)
- intersectionValRings(...,allComputations=>...) (missing documentation)
- normaliz(...,allComputations=>...) (missing documentation)
- normalToricRing(...,allComputations=>...) (missing documentation)
- torusInvariants(...,allComputations=>...) (missing documentation)

## Further information

- Default value: false
- Method: intclToricRing(MonomialSubalgebra) -- integral closure of a toric ring
- Option key: allComputations

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Normaliz.m2:1657:0.