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