# normalToricRing(MonomialSubalgebra,allComputations=>...) -- normalization of a toric ring

## Synopsis

• Usage:
normalToricRing S
• Inputs:
• Outputs:

## Description

The toric ring S is the monomial subalgebra given. The function computes the normalization T of S, which is the integral closure in its field of fractions. 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=normalToricRing(allComputations=> true, S) ZZ 3 2 2 3 o3 = --[y , x*y , x y, x ] 37 o3 : monomial subalgebra of R i4 : T.cache#"cone" o4 = RationalCone{cgr => | 1 1 0 3 | } equ => | 0 0 1 | gen => | 0 3 0 | | 1 2 0 | | 2 1 0 | | 3 0 0 | inv => HashTable{ => (1, 1) } class group => (0, 3) degree 1 elements => 4 dim max subspace => 0 embedding dim => 3 external index => 3 graded => true grading denom => 3 grading => (1, 1, 0) hilbert basis elements => 4 hilbert quasipolynomial denom => 1 hilbert series denom => (1, 1) hilbert series num => (1, 2) inhomogeneous => false integrally closed => true internal index => 1 multiplicity denom => 1 multiplicity => 3 number extreme rays => 2 number support hyperplanes => 2 rank => 2 size triangulation => 3 sum dets => 3 sup => | 0 1 0 | | 1 0 0 | o4 : RationalCone