@@ -73,51 +73,61 @@ gap> Display(NmzOriginalMonoidGenerators(cone));
7373[ [ 1 , 1 , 2 ] ,
7474 [ - 1 , - 1 , 3 ] ,
7575 [ 1 , - 2 , 4 ] ]
76- gap> _NmzPrintSomeConeProperties(cone, [
77- > " Generators" ,
78- > " ExtremeRays" ,
79- > " SupportHyperplanes" ,
80- > " HilbertBasis" ,
81- > " Deg1Elements" ,
82- > " Sublattice" ,
83- > " NumberLatticePoints" ,
84- > " OriginalMonoidGenerators" ,
85- > ] );
86- BasicTriangulation = fail
87- ClassGroup = [ 0 , 3 , 15 ]
88- EhrhartQuasiPolynomial = [ [ 48 , 28 , 15 ] , [ 11 , 22 , 15 ] , [ - 20 , 28 , 15 ] ,
89- [ 39 , 22 , 15 ] , [ 32 , 28 , 15 ] , [ - 5 , 22 , 15 ] , [ 12 , 28 , 15 ] ,
90- [ 23 , 22 , 15 ] , [ 16 , 28 , 15 ] , [ 27 , 22 , 15 ] , [ - 4 , 28 , 15 ] ,
91- [ 7 , 22 , 15 ] , 48 ]
92- EmbeddingDim = 3
93- Grading = [ 0 , 0 , 1 ]
94- GradingDenom = 1
95- HilbertQuasiPolynomial = [ 5 / 16 * t^ 2 + 7 / 12 * t+ 1 , 5 / 16 * t^ 2 + 11 / 24 * t+ 11 / 48 ,
96- 5 / 16 * t^ 2 + 7 / 12 * t- 5 / 12 , 5 / 16 * t^ 2 + 11 / 24 * t+ 13 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t+ 2 / 3 ,
97- 5 / 16 * t^ 2 + 11 / 24 * t- 5 / 48 , 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 4 , 5 / 16 * t^ 2 + 11 / 24 * t+ 23 / 48 ,
98- 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 3 , 5 / 16 * t^ 2 + 11 / 24 * t+ 9 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t- 1 / 12 ,
99- 5 / 16 * t^ 2 + 11 / 24 * t+ 7 / 48 ]
100- HilbertQuasiPolynomial = [ 5 / 16 * t^ 2 + 7 / 12 * t+ 1 , 5 / 16 * t^ 2 + 11 / 24 * t+ 11 / 48 ,
101- 5 / 16 * t^ 2 + 7 / 12 * t- 5 / 12 , 5 / 16 * t^ 2 + 11 / 24 * t+ 13 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t+ 2 / 3 ,
102- 5 / 16 * t^ 2 + 11 / 24 * t- 5 / 48 , 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 4 , 5 / 16 * t^ 2 + 11 / 24 * t+ 23 / 48 ,
103- 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 3 , 5 / 16 * t^ 2 + 11 / 24 * t+ 9 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t- 1 / 12 ,
104- 5 / 16 * t^ 2 + 11 / 24 * t+ 7 / 48 ]
105- HilbertSeries = [ 2 * t^ 12 + t^ 11 + t^ 10 + t^ 9 + t^ 8 + 2 * t^ 7 + 2 * t^ 6 - t^ 5 + 2 * t^ 4 + 3 * t^ 3 + 1 ,
76+ gap> NmzConeProperty(cone, " BasicTriangulation" );
77+ fail
78+ gap> NmzConeProperty(cone, " ClassGroup" );
79+ [ 0 , 3 , 15 ]
80+ gap> NmzConeProperty(cone, " EhrhartQuasiPolynomial" );
81+ [ [ 48 , 28 , 15 ] , [ 11 , 22 , 15 ] , [ - 20 , 28 , 15 ] , [ 39 , 22 , 15 ] ,
82+ [ 32 , 28 , 15 ] , [ - 5 , 22 , 15 ] , [ 12 , 28 , 15 ] , [ 23 , 22 , 15 ] ,
83+ [ 16 , 28 , 15 ] , [ 27 , 22 , 15 ] , [ - 4 , 28 , 15 ] , [ 7 , 22 , 15 ] , 48 ]
84+ gap> NmzConeProperty(cone, " EmbeddingDim" );
85+ 3
86+ gap> NmzConeProperty(cone, " Grading" );
87+ [ 0 , 0 , 1 ]
88+ gap> NmzConeProperty(cone, " GradingDenom" );
89+ 1
90+ gap> NmzConeProperty(cone, " HilbertQuasiPolynomial" );
91+ [ 5 / 16 * t^ 2 + 7 / 12 * t+ 1 , 5 / 16 * t^ 2 + 11 / 24 * t+ 11 / 48 , 5 / 16 * t^ 2 + 7 / 12 * t- 5 / 12 ,
92+ 5 / 16 * t^ 2 + 11 / 24 * t+ 13 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t+ 2 / 3 , 5 / 16 * t^ 2 + 11 / 24 * t- 5 / 48 ,
93+ 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 4 , 5 / 16 * t^ 2 + 11 / 24 * t+ 23 / 48 , 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 3 ,
94+ 5 / 16 * t^ 2 + 11 / 24 * t+ 9 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t- 1 / 12 , 5 / 16 * t^ 2 + 11 / 24 * t+ 7 / 48 ]
95+ gap> NmzConeProperty(cone, " HilbertQuasiPolynomial" );
96+ [ 5 / 16 * t^ 2 + 7 / 12 * t+ 1 , 5 / 16 * t^ 2 + 11 / 24 * t+ 11 / 48 , 5 / 16 * t^ 2 + 7 / 12 * t- 5 / 12 ,
97+ 5 / 16 * t^ 2 + 11 / 24 * t+ 13 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t+ 2 / 3 , 5 / 16 * t^ 2 + 11 / 24 * t- 5 / 48 ,
98+ 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 4 , 5 / 16 * t^ 2 + 11 / 24 * t+ 23 / 48 , 5 / 16 * t^ 2 + 7 / 12 * t+ 1 / 3 ,
99+ 5 / 16 * t^ 2 + 11 / 24 * t+ 9 / 16 , 5 / 16 * t^ 2 + 7 / 12 * t- 1 / 12 , 5 / 16 * t^ 2 + 11 / 24 * t+ 7 / 48 ]
100+ gap> NmzConeProperty(cone, " HilbertSeries" );
101+ [ 2 * t^ 12 + t^ 11 + t^ 10 + t^ 9 + t^ 8 + 2 * t^ 7 + 2 * t^ 6 - t^ 5 + 2 * t^ 4 + 3 * t^ 3 + 1 ,
106102 [ [ 1 , 1 ] , [ 2 , 1 ] , [ 12 , 1 ] ] ]
107- InternalIndex = 15
108- IsDeg1ExtremeRays = false
109- IsDeg1HilbertBasis = false
110- IsInhomogeneous = false
111- IsIntegrallyClosed = false
112- IsPointed = true
113- IsTriangulationNested = false
114- IsTriangulationPartial = false
115- MaximalSubspace = [ ]
116- Multiplicity = 5 / 8
117- Rank = 3
118- TriangulationDetSum = 15
119- TriangulationSize = 1
120- UnitGroupIndex = 1
103+ gap> NmzConeProperty(cone, " InternalIndex" );
104+ 15
105+ gap> NmzConeProperty(cone, " IsDeg1ExtremeRays" );
106+ false
107+ gap> NmzConeProperty(cone, " IsDeg1HilbertBasis" );
108+ false
109+ gap> NmzConeProperty(cone, " IsInhomogeneous" );
110+ false
111+ gap> NmzConeProperty(cone, " IsIntegrallyClosed" );
112+ false
113+ gap> NmzConeProperty(cone, " IsPointed" );
114+ true
115+ gap> NmzConeProperty(cone, " IsTriangulationNested" );
116+ false
117+ gap> NmzConeProperty(cone, " IsTriangulationPartial" );
118+ false
119+ gap> NmzConeProperty(cone, " MaximalSubspace" );
120+ [ ]
121+ gap> NmzConeProperty(cone, " Multiplicity" );
122+ 5 / 8
123+ gap> NmzConeProperty(cone, " Rank" );
124+ 3
125+ gap> NmzConeProperty(cone, " TriangulationDetSum" );
126+ 15
127+ gap> NmzConeProperty(cone, " TriangulationSize" );
128+ 1
129+ gap> NmzConeProperty(cone, " UnitGroupIndex" );
130+ 1
121131gap> Display(NmzConeDecomposition(cone));
122132[ [ rec (
123133 Excluded := [ false , false , false ] ,
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