Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Symmetry/faces_of_symmetric_polytopes.ads, Revision 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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