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Normaliz
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_normaliz.out
-- -*- M2-comint -*- hash: 12535740247240577957 i1 : setNmzOption("allf",true); i2 : eq=matrix {{1, 1, 1, -1, -1, -1, 0, 0, 0}, {1, 1, 1, 0, 0, 0, -1, -1, -1}, {0, 1, 1, -1, 0, 0, -1, 0, 0}, {1, 0, 1, 0, -1, 0, 0, -1, 0}, {1, 1, 0, 0, 0, -1, 0, 0, -1}, {0, 1, 1, 0, -1, 0, 0, 0, -1}, {1, 1, 0, 0, -1, 0, -1, 0, 0}}; 7 9 o2 : Matrix ZZ <-- ZZ i3 : rc=normaliz(eq,"equations") o3 = RationalCone{"gen" => | 0 2 1 2 1 0 1 0 2 | } | 1 0 2 2 1 0 0 2 1 | | 1 1 1 1 1 1 1 1 1 | | 1 2 0 0 1 2 2 0 1 | | 2 0 1 0 1 2 1 2 0 | "inv" => HashTable{"" => (1, 1, 1) } "class group" => (1, 2, 2) "degree 1 elements" => 5 "dim max subspace" => 0 "embedding dim" => 9 "external index" => 1 "graded" => true "grading denom" => 3 "grading" => (1, 1, 1, 0, 0, 0, 0, 0, 0) "hilbert basis elements" => 5 "hilbert quasipolynomial denom" => 1 "hilbert series denom" => (1, 1, 1) "hilbert series num" => (1, 2, 1) "inhomogeneous" => false "multiplicity denom" => 1 "multiplicity" => 4 "number extreme rays" => 4 "number support hyperplanes" => 4 "rank" => 3 "size triangulation" => 2 "sum dets" => 4 o3 : RationalCone i4 : arc=normaliz(allComputations=>true,eq,"equations"); i5 : arc#"gen" o5 = | 0 2 1 2 1 0 1 0 2 | | 1 0 2 2 1 0 0 2 1 | | 1 1 1 1 1 1 1 1 1 | | 1 2 0 0 1 2 2 0 1 | | 2 0 1 0 1 2 1 2 0 | 5 9 o5 : Matrix ZZ <-- ZZ i6 : arc#"ext" o6 = | 0 2 1 2 1 0 1 0 2 | | 1 0 2 2 1 0 0 2 1 | | 1 2 0 0 1 2 2 0 1 | | 2 0 1 0 1 2 1 2 0 | 4 9 o6 : Matrix ZZ <-- ZZ i7 : arc#"inv" o7 = HashTable{"" => (1, 1, 1) } "class group" => (1, 2, 2) "degree 1 elements" => 5 "dim max subspace" => 0 "embedding dim" => 9 "external index" => 1 "graded" => true "grading denom" => 3 "grading" => (1, 1, 1, 0, 0, 0, 0, 0, 0) "hilbert basis elements" => 5 "hilbert quasipolynomial denom" => 1 "hilbert series denom" => (1, 1, 1) "hilbert series num" => (1, 2, 1) "inhomogeneous" => false "multiplicity denom" => 1 "multiplicity" => 4 "number extreme rays" => 4 "number support hyperplanes" => 4 "rank" => 3 "size triangulation" => 2 "sum dets" => 4 o7 : HashTable i8 :
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