GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
gap> START_TEST("NormalizInterface: rproj2.tst");
#
gap> M := [
> [ 1, 0, 0, 0, 0, 0, 0 ],
> [ 0, 1, 0, 0, 0, 0, 0 ],
> [ 0, 0, 1, 0, 0, 0, 0 ],
> [ 0, 0, 0, 1, 0, 0, 0 ],
> [ 0, 0, 0, 0, 1, 0, 0 ],
> [ 0, 0, 0, 0, 0, 1, 0 ],
> [ 1, 1, 1, 0, 0, 0, 1 ],
> [ 1, 1, 0, 1, 0, 0, 1 ],
> [ 1, 0, 1, 0, 1, 0, 1 ],
> [ 1, 0, 0, 1, 0, 1, 1 ],
> [ 1, 0, 0, 0, 1, 1, 1 ],
> [ 0, 1, 1, 0, 0, 1, 1 ],
> [ 0, 1, 0, 1, 1, 0, 1 ],
> [ 0, 1, 0, 0, 1, 1, 1 ],
> [ 0, 0, 1, 1, 1, 0, 1 ],
> [ 0, 0, 1, 1, 0, 1, 1 ],
> ];;
gap> cone := NmzCone(["integral_closure", M]);;
gap> NmzCompute(cone);
true
gap> NmzPrintConeProperties(cone);
Generators =
[ [ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1, 1 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ] ]
ExtremeRays =
[ [ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1, 1 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ] ]
SupportHyperplanes =
[ [ 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, -1 ],
[ 0, 0, 1, 1, 1, 0, -1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1, -1 ],
[ 0, 1, 0, 1, 1, 0, -1 ],
[ 0, 1, 1, 0, 0, 1, -1 ],
[ 0, 1, 1, 1, 1, 1, -2 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1, -1 ],
[ 1, 0, 0, 1, 0, 1, -1 ],
[ 1, 0, 1, 0, 1, 0, -1 ],
[ 1, 0, 1, 1, 1, 1, -2 ],
[ 1, 1, 0, 1, 0, 0, -1 ],
[ 1, 1, 0, 1, 1, 1, -2 ],
[ 1, 1, 1, 0, 0, 0, -1 ],
[ 1, 1, 1, 0, 1, 1, -2 ],
[ 1, 1, 1, 1, 0, 1, -2 ],
[ 1, 1, 1, 1, 1, 0, -2 ],
[ 1, 1, 1, 1, 1, 1, -3 ] ]
HilbertBasis =
[ [ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1, 1 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 1, 1, 1, 1, 2 ] ]
Deg1Elements =
[ [ 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 1, 1, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 1, 1, 1 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 1, 1, 0, 0, 0, 1 ] ]
Sublattice =
[
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0 ], [ 0, 0, 0, 0, 0, 0, 1 ] ], 1 ]
OriginalMonoidGenerators =
[ [ 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0 ],
[ 1, 1, 1, 0, 0, 0, 1 ],
[ 1, 1, 0, 1, 0, 0, 1 ],
[ 1, 0, 1, 0, 1, 0, 1 ],
[ 1, 0, 0, 1, 0, 1, 1 ],
[ 1, 0, 0, 0, 1, 1, 1 ],
[ 0, 1, 1, 0, 0, 1, 1 ],
[ 0, 1, 0, 1, 1, 0, 1 ],
[ 0, 1, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 1, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 1 ] ]
MaximalSubspace = [ ]
Grading = [ 1, 1, 1, 1, 1, 1, -2 ]
TriangulationSize = 69
TriangulationDetSum = 72
GradingDenom = 1
UnitGroupIndex = 1
InternalIndex = 1
Multiplicity = 72
Rank = 7
EmbeddingDim = 7
IsPointed = true
IsDeg1ExtremeRays = true
IsDeg1HilbertBasis = false
IsIntegrallyClosed = false
IsInhomogeneous = false
ClassGroup = [ 17 ]
HilbertSeries = [ 6*t^4+25*t^3+31*t^2+9*t+1, [ [ 1, 7 ] ] ]
HilbertQuasiPolynomial =
[ 1/10*t^6+41/60*t^5+13/6*t^4+49/12*t^3+71/15*t^2+97/30*t+1 ]
IsTriangulationNested = false
IsTriangulationPartial = false
#
gap> STOP_TEST("rproj2.tst", 0);