allComputations

Description

allComputations is an option for normaliz, intclToricRing, normalToricRing, intclMonIdeal, torusInvariants, finiteDiagInvariants, diagInvariants, intersectionValRings, intersectionValRingIdeals. Its default value is false. If it is set to true, the cone in the cache table of the monomial subalgebra returned contains not only the generators, but all the data that have been computed by Normaliz (what this includes depends on the type and the options set, see output files written by Normaliz).

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

Functions with optional argument named allComputations :

diagInvariants(Matrix,Matrix,Ring,allComputations=>...) -- see diagInvariants -- ring of invariants of a diagonalizable group action
ehrhartRing(List,allComputations=>...) -- Ehrhart ring
ehrhartRing(List,RingElement,allComputations=>...) -- Ehrhart ring
finiteDiagInvariants(Matrix,Ring,allComputations=>...) -- see finiteDiagInvariants -- ring of invariants of a finite group action
intclMonIdeal(Ideal,allComputations=>...) -- normalization of Rees algebra
intclMonIdeal(Ideal,RingElement,allComputations=>...) -- normalization of Rees algebra
intclToricRing(List,allComputations=>...) -- integral closure of a toric ring
intclToricRing(MonomialSubalgebra,allComputations=>...) -- integral closure of a toric ring
intersectionValRingIdeals(Matrix,Ring,allComputations=>...) -- see intersectionValRingIdeals -- intersection of valuation ideals
intersectionValRings(Matrix,Ring,allComputations=>...) -- see intersectionValRings -- intersection of ring of valuations
normaliz(List,allComputations=>...) -- see normaliz(List) -- calls Normaliz with several input matrices
normaliz(Matrix,String,allComputations=>...) -- see normaliz(Matrix,String) -- calls Normaliz
normaliz(Matrix,ZZ,allComputations=>...) (missing documentation)
normalToricRing(Ideal,Thing,allComputations=>...) -- see normalToricRing(Ideal,Thing) -- normalization of a toric ring given by a binomial ideal
normalToricRing(List,allComputations=>...) -- normalization of a toric ring
normalToricRing(MonomialSubalgebra,allComputations=>...) -- normalization of a toric ring
torusInvariants(Matrix,Ring,allComputations=>...) -- see torusInvariants -- ring of invariants of torus action

For the programmer

The object allComputations is a symbol.