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

## Synopsis

• Usage:
intclToricRing S
• Inputs:
• Outputs:

## 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