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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346gap> START_TEST("NormalizInterface: rp2poly.tst");
#
gap> M := [
> [ 1, 1, 1, 0, 0, 0 ],
> [ 1, 1, 0, 1, 0, 0 ],
> [ 1, 0, 1, 0, 1, 0 ],
> [ 1, 0, 0, 1, 0, 1 ],
> [ 1, 0, 0, 0, 1, 1 ],
> [ 0, 1, 1, 0, 0, 1 ],
> [ 0, 1, 0, 1, 1, 0 ],
> [ 0, 1, 0, 0, 1, 1 ],
> [ 0, 0, 1, 1, 1, 0 ],
> [ 0, 0, 1, 1, 0, 1 ],
> ];;
gap> cone := NmzCone(["normalization", M]);;
gap> NmzCompute(cone);
true
gap> NmzPrintConeProperties(cone);
Generators =
[ [ 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0 ],
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 1, 1, 0, 0, 0 ] ]
ExtremeRays =
[ [ 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0 ],
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 1, 1, 0, 0, 0 ] ]
SupportHyperplanes =
[ [ -2, 1, 1, 1, 1, 1 ],
[ -1, -1, 2, 2, -1, 2 ],
[ -1, -1, 2, 2, 2, -1 ],
[ -1, 2, -1, -1, 2, 2 ],
[ -1, 2, -1, 2, 2, -1 ],
[ -1, 2, 2, -1, -1, 2 ],
[ 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0 ],
[ 1, -2, 1, 1, 1, 1 ],
[ 1, 0, 0, 0, 0, 0 ],
[ 1, 1, -2, 1, 1, 1 ],
[ 1, 1, 1, -2, 1, 1 ],
[ 1, 1, 1, 1, -2, 1 ],
[ 1, 1, 1, 1, 1, -2 ],
[ 2, -1, -1, -1, 2, 2 ],
[ 2, -1, -1, 2, -1, 2 ],
[ 2, -1, 2, -1, 2, -1 ],
[ 2, 2, -1, 2, -1, -1 ],
[ 2, 2, 2, -1, -1, -1 ] ]
HilbertBasis =
[ [ 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0 ],
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 1, 1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1 ] ]
Deg1Elements =
[ [ 0, 0, 1, 1, 0, 1 ],
[ 0, 0, 1, 1, 1, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 0 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 1, 0, 1, 0 ],
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 1, 1, 0, 0, 0 ] ]
Sublattice =
[ [ [ 1, 0, 0, 0, 0, -1 ], [ 0, 1, 0, 0, 0, -1 ], [ 0, 0, 1, 0, 0, -1 ],
[ 0, 0, 0, 1, 0, -1 ], [ 0, 0, 0, 0, 1, -1 ], [ 0, 0, 0, 0, 0, 3 ] ],
[ [ 3, 0, 0, 0, 0, 1 ], [ 0, 3, 0, 0, 0, 1 ], [ 0, 0, 3, 0, 0, 1 ],
[ 0, 0, 0, 3, 0, 1 ], [ 0, 0, 0, 0, 3, 1 ], [ 0, 0, 0, 0, 0, 1 ] ], 3 ]
OriginalMonoidGenerators =
[ [ 1, 1, 1, 0, 0, 0 ],
[ 1, 1, 0, 1, 0, 0 ],
[ 1, 0, 1, 0, 1, 0 ],
[ 1, 0, 0, 1, 0, 1 ],
[ 1, 0, 0, 0, 1, 1 ],
[ 0, 1, 1, 0, 0, 1 ],
[ 0, 1, 0, 1, 1, 0 ],
[ 0, 1, 0, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 0 ],
[ 0, 0, 1, 1, 0, 1 ] ]
MaximalSubspace = [ ]
Grading = [ 1/3, 1/3, 1/3, 1/3, 1/3, 1/3 ]
TriangulationSize = 18
TriangulationDetSum = 21
GradingDenom = 3
UnitGroupIndex = 1
InternalIndex = 1
Multiplicity = 21
Rank = 6
EmbeddingDim = 6
IsPointed = true
IsDeg1ExtremeRays = true
IsDeg1HilbertBasis = false
IsIntegrallyClosed = false
IsInhomogeneous = false
ClassGroup = [ 16 ]
HilbertSeries = [ t^4+4*t^3+11*t^2+4*t+1, [ [ 1, 6 ] ] ]
HilbertQuasiPolynomial = [ 7/40*t^5+7/8*t^4+53/24*t^3+25/8*t^2+157/60*t+1 ]
IsTriangulationNested = false
IsTriangulationPartial = false
#
gap> STOP_TEST("rp2poly.tst", 0);