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

## Synopsis

• Usage:
intclToricRing L
• Inputs:
• a list, generators of the toric ring
• Outputs:

## Description

The toric ring S is the subalgebra of the basering generated by the monomials in the list L. 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 : L={x^3, x^2*y, y^3, x*y^2}; i3 : T=intclToricRing(allComputations=>true,L) 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