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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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gap> START_TEST("NormalizInterface: dual.tst");

#
gap> # Based on dual.in
gap> M := [
> [ 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,  1,  0,  0,  0,  0 ],
> [ 0,  1,  0,  0,  0,  0,  0 ],
> [ 0,  1,  0,  1,  1,  0, -1 ],
> [ 0,  1,  0,  0,  1,  1, -1 ],
> [ 0,  1,  1,  0,  0,  1, -1 ],
> [ 0,  0,  1,  1,  1,  0, -1 ],
> [ 0,  0,  1,  1,  0,  1, -1 ],
> [ 0,  1,  1,  1,  1,  1, -2 ],
> [ 1,  0,  0,  0,  0,  0,  0 ],
> [ 1,  1,  1,  1,  1,  1, -3 ],
> [ 1,  0,  0,  1,  0,  1, -1 ],
> [ 1,  0,  0,  0,  1,  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,  1,  0,  0,  0, -1 ],
> [ 1,  1,  1,  1,  0,  1, -2 ],
> [ 1,  1,  1,  0,  1,  1, -2 ],
> [ 1,  1,  1,  1,  1,  0, -2 ],
> [ 1,  1,  0,  1,  1,  1, -2 ],
> ];;
gap> cone := NmzCone(["inequalities", 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 ]
MaximalSubspace = [  ]
Grading = [ 1, 1, 1, 1, 1, 1, -2 ]
TriangulationSize = 69
TriangulationDetSum = 72
GradingDenom = 1
Multiplicity = 72
Rank = 7
EmbeddingDim = 7
IsPointed = true
IsDeg1ExtremeRays = true
IsDeg1HilbertBasis = 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("dual.tst", 0);