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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;