Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Symmetry/faces_of_symmetric_polytopes.ads, Revision 1.1.1.1
1.1 maekawa 1: with Integer_Faces_of_Polytope; use Integer_Faces_of_Polytope;
2: with Symmetry_Group; use Symmetry_Group;
3:
4: package Faces_of_Symmetric_Polytopes is
5:
6: -- DESCRIPTION :
7: -- This package contains some routines to construct the tuple of
8: -- generating faces of symmetric polytopes.
9: -- When the group representation is not given as parameter,
10: -- full permutation symmetry is assumed.
11: -- If `Lifted'-routines are called, then the permutations will leave
12: -- the lifting value invariant.
13:
14: -- ON A FACE : group * faces -> invariant subgroup
15:
16: function Stabilizer ( v : List_of_Permutations; f : Face )
17: return List_of_Permutations;
18: function Stabilizer_Lifted ( v : List_of_Permutations; f : Face )
19: return List_of_Permutations;
20:
21: -- DESCRIPTION :
22: -- Returns those permutations that leave the face invariant.
23:
24: -- ON FACES : group * faces -> invariant faces
25:
26: function Invariant_Faces ( v : List_of_Permutations;
27: f : Faces ) return Faces;
28:
29: function Invariant_Lifted_Faces ( v : List_of_Permutations;
30: f : Faces ) return Faces;
31:
32: -- DESCRIPTION :
33: -- Returns those faces which are invariant under the permutations.
34: -- To check this for the full permutation group, the list of
35: -- generators of the group should be supplied.
36:
37: -- ON FACES : group * faces -> generated faces
38:
39: function Generated_Faces ( v : List_of_Permutations; f : Faces )
40: return Faces;
41:
42: function Generated_Lifted_Faces
43: ( v : List_of_Permutations; f : Faces )
44: return Faces;
45:
46: -- DESCRIPTION :
47: -- Returns those faces that generate all faces in f.
48: -- For the full permutation group, supply the generators of the group.
49:
50: -- ON FACES : group * faces -> generators of faces
51:
52: function Generating_Faces ( f : Faces ) return Faces;
53: function Generating_Faces ( v : List_of_Permutations; f : Faces )
54: return Faces;
55:
56: function Generating_Lifted_Faces ( f : Faces ) return Faces;
57: function Generating_Lifted_Faces
58: ( v : List_of_Permutations; f : Faces )
59: return Faces;
60:
61: -- DESCRIPTION :
62: -- Returns those faces that generate all faces in f.
63:
64: -- ON TUPLES OF FACES : group * faces -> invariant faces
65:
66: function Invariant_Faces ( v : List_of_Permutations;
67: af : Array_of_Faces ) return Array_of_Faces;
68:
69: function Invariant_Lifted_Faces ( v : List_of_Permutations;
70: af : Array_of_Faces ) return Array_of_Faces;
71:
72: -- DESCRIPTION :
73: -- Returns for each component those faces which are invariant under the
74: -- permutations. To check this for the full permutation group, the list
75: -- of generators of the group should be supplied.
76: -- It is assumed that the tuple is invariant under v.
77:
78: -- ON TUPLES OF FACES : group * faces -> generators of faces
79:
80: function Generating_Faces ( af : Array_of_Faces ) return Array_of_Faces;
81: function Generating_Faces ( v : List_of_Permutations; af : Array_of_Faces )
82: return Array_of_Faces;
83: function Generating_Faces ( v,w : List_of_Permutations; af : Array_of_Faces )
84: return Array_of_Faces;
85:
86: function Generating_Lifted_Faces
87: ( af : Array_of_Faces ) return Array_of_Faces;
88: function Generating_Lifted_Faces
89: ( v : List_of_Permutations; af : Array_of_Faces )
90: return Array_of_Faces;
91: function Generating_Lifted_Faces
92: ( v,w : List_of_Permutations; af : Array_of_Faces )
93: return Array_of_Faces;
94:
95: -- DESCRIPTION :
96: -- Returns the generating faces of the tuple. When w is left out,
97: -- it is assumed that the tuple is invariant. When both v and w are not
98: -- supplied, then it is assumed that the tuple is equi-invariant w.r.t.
99: -- the full permutation group.
100:
101: end Faces_of_Symmetric_Polytopes;
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