The toric ring S is the monomial subalgebra of the basering generated by the monomials in the list L. 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];
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i2 : L={x^3, x^2*y, y^3, x*y^2};
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i3 : T=normalToricRing(allComputations=> true, L)
ZZ 3 2 2 3
o3 = --[x , x y, x*y , y ]
37
o3 : monomial subalgebra of R
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i4 : T.cache#"cone"
o4 = RationalCone{cgr => | 1 1 0 3 | }
equ => | 0 0 1 |
gen => | 3 0 0 |
| 2 1 0 |
| 1 2 0 |
| 0 3 0 |
inv => HashTable{height 1 elements => 4 }
hilbert basis elements => 4
homogeneous => true
homogeneous weights => (1, 1, 0)
index => 1
multiplicity => 3
number extreme rays => 2
number support hyperplanes => 2
rank => 2
sup => | 0 1 0 |
| 1 0 0 |
typ => | 0 3 |
| 1 2 |
| 2 1 |
| 3 0 |
o4 : RationalCone
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