LoadPackage("NormalizInterface"); # the cone generated by (2,1) and (1,3) C := NmzCone(["integral_closure",[[2,1],[1,3]]]); NmzHasConeProperty(C,"HilbertBasis"); NmzHasConeProperty(C,"SupportHyperplanes"); NmzConeProperty(C,"HilbertBasis"); NmzHasConeProperty(C,"SupportHyperplanes"); # also computed when Hilbert basis was computed NmzConeProperty(C,"SupportHyperplanes"); # the cone given by the equation x + 2y - 3z = 0 in the non-negative orthant D := NmzCone(["equations",[[1,2,-3]]]); NmzCompute(D,["DualMode","HilbertSeries"]); NmzHilbertBasis(D); NmzConeProperty(D,"HilbertSeries"); # not yet implemented NmzHasConeProperty(D,"SupportHyperplanes"); NmzConeProperty(D,"SupportHyperplanes"); NmzEquations(D); # the polyhedron given by the equation x + 2y -3z + 1 = 0 in the non-negative orthant P := NmzCone(["inhom_equations",[[1,2,-3,1]], "grading", [[1,1,1]]]); NmzIsInhomogeneous(D); NmzIsInhomogeneous(P); NmzHilbertBasis(P); NmzConeProperty(P,"ModuleGenerators");