Return to faces_of_symmetric_polytopes.ads CVS log

Up to [local] / OpenXM_contrib / PHC / Ada / Root_Counts / Symmetry

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;