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gap> START_TEST("rational.tst");
#
gap> M := [
> [ 1, 1, 2 ],
> [ -1, -1, 3 ],
> [ 1, -2, 4 ],
> ];;
gap> gr := [ [ 0, 0, 1 ] ];;
gap> cone := NmzCone(["integral_closure", M, "grading", gr]);;
gap> NmzCompute(cone);
true
gap> tmp := NmzKnownConeProperties(cone);;
gap> RemoveSet(tmp, "NumberLatticePoints");
gap> Perform(tmp, Display);
ClassGroup
Deg1Elements
EmbeddingDim
ExtremeRays
Generators
Grading
GradingDenom
HilbertBasis
HilbertQuasiPolynomial
HilbertSeries
InternalIndex
IsDeg1ExtremeRays
IsDeg1HilbertBasis
IsInhomogeneous
IsIntegrallyClosed
IsPointed
IsTriangulationNested
IsTriangulationPartial
MaximalSubspace
Multiplicity
OriginalMonoidGenerators
Rank
Sublattice
SupportHyperplanes
TriangulationDetSum
TriangulationSize
UnitGroupIndex
gap> Display(NmzTriangulation(cone));
[ [ rec(
Excluded := [ ],
height := 0,
key := [ 0, 1, 2 ],
mult := 0,
vol := 15 ) ], [ [ 1, 1, 2 ], [ -1, -1, 3 ], [ 1, -2, 4 ] ] ]
gap> Display(NmzExtremeRays(cone));
[ [ 1, 1, 2 ],
[ -1, -1, 3 ],
[ 1, -2, 4 ] ]
gap> Display(NmzSupportHyperplanes(cone));
[ [ -8, 2, 3 ],
[ 1, -1, 0 ],
[ 2, 7, 3 ] ]
gap> Display(NmzHilbertBasis(cone));
[ [ 0, 0, 1 ],
[ 1, 1, 2 ],
[ -1, -1, 3 ],
[ 0, -1, 3 ],
[ 1, 0, 3 ],
[ 1, -2, 4 ],
[ 1, -1, 4 ],
[ 0, -2, 5 ] ]
gap> Display(NmzDeg1Elements(cone));
[ [ 0, 0, 1 ] ]
gap> Display(NmzSublattice(cone));
[ [ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ],
[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 0, 0, 1 ] ], 1 ]
gap> Display(NmzOriginalMonoidGenerators(cone));
[ [ 1, 1, 2 ],
[ -1, -1, 3 ],
[ 1, -2, 4 ] ]
gap> _NmzPrintSomeConeProperties(cone, [
> "Generators",
> "ExtremeRays",
> "SupportHyperplanes",
> "HilbertBasis",
> "Deg1Elements",
> "Sublattice",
> "NumberLatticePoints",
> "OriginalMonoidGenerators",
> ]);
BasicTriangulation = fail
ClassGroup = [ 0, 3, 15 ]
EhrhartQuasiPolynomial = [ [ 48, 28, 15 ], [ 11, 22, 15 ], [ -20, 28, 15 ],
[ 39, 22, 15 ], [ 32, 28, 15 ], [ -5, 22, 15 ], [ 12, 28, 15 ],
[ 23, 22, 15 ], [ 16, 28, 15 ], [ 27, 22, 15 ], [ -4, 28, 15 ],
[ 7, 22, 15 ], 48 ]
EmbeddingDim = 3
Grading = [ 0, 0, 1 ]
GradingDenom = 1
HilbertQuasiPolynomial = [ 5/16*t^2+7/12*t+1, 5/16*t^2+11/24*t+11/48,
5/16*t^2+7/12*t-5/12, 5/16*t^2+11/24*t+13/16, 5/16*t^2+7/12*t+2/3,
5/16*t^2+11/24*t-5/48, 5/16*t^2+7/12*t+1/4, 5/16*t^2+11/24*t+23/48,
5/16*t^2+7/12*t+1/3, 5/16*t^2+11/24*t+9/16, 5/16*t^2+7/12*t-1/12,
5/16*t^2+11/24*t+7/48 ]
HilbertQuasiPolynomial = [ 5/16*t^2+7/12*t+1, 5/16*t^2+11/24*t+11/48,
5/16*t^2+7/12*t-5/12, 5/16*t^2+11/24*t+13/16, 5/16*t^2+7/12*t+2/3,
5/16*t^2+11/24*t-5/48, 5/16*t^2+7/12*t+1/4, 5/16*t^2+11/24*t+23/48,
5/16*t^2+7/12*t+1/3, 5/16*t^2+11/24*t+9/16, 5/16*t^2+7/12*t-1/12,
5/16*t^2+11/24*t+7/48 ]
HilbertSeries = [ 2*t^12+t^11+t^10+t^9+t^8+2*t^7+2*t^6-t^5+2*t^4+3*t^3+1,
[ [ 1, 1 ], [ 2, 1 ], [ 12, 1 ] ] ]
InternalIndex = 15
IsDeg1ExtremeRays = false
IsDeg1HilbertBasis = false
IsInhomogeneous = false
IsIntegrallyClosed = false
IsPointed = true
IsTriangulationNested = false
IsTriangulationPartial = false
MaximalSubspace = [ ]
Multiplicity = 5/8
Rank = 3
TriangulationDetSum = 15
TriangulationSize = 1
UnitGroupIndex = 1
gap> Display(NmzConeDecomposition(cone));
[ [ rec(
Excluded := [ false, false, false ],
height := 0,
key := [ 0, 1, 2 ],
mult := 0,
vol := 15 ) ], [ [ 1, 1, 2 ], [ -1, -1, 3 ], [ 1, -2, 4 ] ] ]
gap> ForAll(NmzConeDecomposition(cone), IsBlistRep);
false
#
gap> NmzStanleyDec(cone);
[ [ [ [ 0, 1, 2 ],
[ [ 0, 0, 0 ], [ 1, 11, 10 ], [ 2, 7, 5 ], [ 3, 3, 0 ],
[ 4, 14, 10 ], [ 5, 10, 5 ], [ 6, 6, 0 ], [ 7, 2, 10 ],
[ 8, 13, 5 ], [ 9, 9, 0 ], [ 10, 5, 10 ], [ 11, 1, 5 ],
[ 12, 12, 0 ], [ 13, 8, 10 ], [ 14, 4, 5 ] ] ] ],
[ [ 1, 1, 2 ], [ -1, -1, 3 ], [ 1, -2, 4 ] ] ]
#
gap> (_NmzVersion() < [3, 7, 0]) or (NmzFVector(cone) = [ 1, 3, 3, 1 ]);
true
gap> (_NmzVersion() < [3, 7, 0]) or (NmzFaceLattice(cone) =
> [ [ [ false, false, false ], 0 ], [ [ true, false, false ], 1 ],
> [ [ false, true, false ], 1 ], [ [ true, true, false ], 2 ],
> [ [ false, false, true ], 1 ], [ [ true, false, true ], 2 ],
> [ [ false, true, true ], 2 ], [ [ true, true, true ], 3 ] ]);
true
#
gap> STOP_TEST("rational.tst", 0);
[ Dauer der Verarbeitung: 0.17 Sekunden
(vorverarbeitet)
]
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