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];
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i2 : L={x^3, x^2*y, y^3, x*y^2};
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i3 : T=intclToricRing(allComputations=>true,L)
ZZ
o3 = --[y, x]
37
o3 : monomial subalgebra of R
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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
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