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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Stalift/mixed_volume_computation.ads, Revision 1.1

1.1     ! maekawa     1: with text_io;                            use text_io;
        !             2: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             3: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
        !             4: with Arrays_of_Integer_Vector_Lists;     use Arrays_of_Integer_Vector_Lists;
        !             5: with Integer_Mixed_Subdivisions;         use Integer_Mixed_Subdivisions;
        !             6:
        !             7: package Mixed_Volume_Computation is
        !             8:
        !             9: -- DESCRIPTION :
        !            10: --   This package offers a number of routines for the computation
        !            11: --   of the mixed volume of a system of polynomial equations.
        !            12:
        !            13: -- UTILITIES :
        !            14:
        !            15:   procedure Compute_Mixture ( supports : in out Array_of_Lists;
        !            16:                               mix,perms : out Link_to_Vector );
        !            17:   -- DESCRIPTION :
        !            18:   --   Computes the type of mixture of the supports of a system.
        !            19:
        !            20:   -- ON ENTRY :
        !            21:   --   supports   the supports of a polynomial system.
        !            22:
        !            23:   -- ON RETURN :
        !            24:   --   supports   a permuted array of supports, so that the same
        !            25:   --              supports stand all toghether;
        !            26:   --   mix        mix(k) indicates number of occurrencies of the kth support;
        !            27:   --   perms      perms(k) gives the place of the kth support,
        !            28:   --              after permutation to make supports correspond with mix.
        !            29:
        !            30:   function Compute_Index ( k : natural; mix : Vector ) return natural;
        !            31:
        !            32:   -- DESCRIPTION :
        !            33:   --   Given k, an entry in the supports, the number this function returns
        !            34:   --   indicates the number of different support, w.r.t. the type of  mixture.
        !            35:
        !            36:   function Compute_Permutation
        !            37:                   ( n : natural; mix : Vector; supports : Array_of_Lists )
        !            38:                   return Link_to_Vector;
        !            39:
        !            40:   -- DESCRIPTION :
        !            41:   --   Given the type of mixture and the support, the permutation vector
        !            42:   --   will be computed.
        !            43:
        !            44:   -- ON RETURN :
        !            45:   --   perms        perms(k) gives the place of the kth support,
        !            46:   --                after permutation to make supports correspond with mix.
        !            47:
        !            48:   function Typed_Lists ( mix : Vector; points : Array_of_Lists )
        !            49:                        return Array_of_Lists;
        !            50:
        !            51:   -- DESCRIPTION :
        !            52:   --   Returns a tuple of lists where each list occurs only once,
        !            53:   --   according to the given type of mixture.
        !            54:
        !            55:   function Permute ( p : Poly_Sys; perm : Link_to_Vector ) return Poly_Sys;
        !            56:   function Permute ( supports : Array_of_Lists ; perm : Link_to_Vector )
        !            57:                    return Array_of_Lists;
        !            58:
        !            59:   -- DESCRIPTION :
        !            60:   --   Permutes the polynomials in the system or the supports,
        !            61:   --   according to the vector perm.
        !            62:
        !            63: -- MIXED VOLUME COMPUTATION, GIVEN A SUBDIVISION :
        !            64:
        !            65:   function Mixed_Volume ( n : natural; mix : Vector;
        !            66:                           mic : Mixed_Cell ) return natural;
        !            67:   function Mixed_Volume ( n : natural; mix : Vector;
        !            68:                           mixsub : Mixed_Subdivision ) return natural;
        !            69:
        !            70:   -- DESCRIPTION :
        !            71:   --   Computes the mixed volume based on a mixed cell and subdivision.
        !            72:   --   When the cells are not fine enough, they will be refined but will
        !            73:   --   be lost after returning the result.
        !            74:
        !            75:   procedure Mixed_Volume ( n : in natural; mix : in Vector;
        !            76:                            mic : in out Mixed_Cell; mv : out natural );
        !            77:   procedure Mixed_Volume ( n : in natural; mix : in Vector;
        !            78:                            mixsub : in out Mixed_Subdivision;
        !            79:                            mv : out natural );
        !            80:
        !            81:   -- DESCRIPTION :
        !            82:   --   Computes the mixed volume based on a mixed cell and subdivision.
        !            83:   --   When the cells are not fine enough, they will be refined by lifting.
        !            84:   --   The refinement is stored in the subdivision field of the cells.
        !            85:
        !            86: -- MIXED VOLUME COMPUTATIONS, GIVEN THE SUPPORTS :
        !            87:
        !            88:   function Mixed_Volume ( n : natural; supports : Array_of_Lists )
        !            89:                        return natural;
        !            90:
        !            91:   function Mixed_Volume ( file : file_type; n : natural;
        !            92:                           supports : Array_of_Lists ) return natural;
        !            93:
        !            94:   function Mixed_Volume ( n : natural; mix : Vector;
        !            95:                           supports : Array_of_Lists ) return natural;
        !            96:
        !            97:   function Mixed_Volume ( file : file_type; n : natural; mix : Vector;
        !            98:                           supports : Array_of_Lists ) return natural;
        !            99:
        !           100:   procedure Mixed_Volume ( n : in natural; mix : in Vector;
        !           101:                            supports : in Array_of_Lists;
        !           102:                            lifted : out Array_of_Lists;
        !           103:                            mixsub : out Mixed_Subdivision; mv : out natural );
        !           104:
        !           105:   procedure Mixed_Volume ( file : in file_type; n : in natural;
        !           106:                            mix : in Vector; supports : in Array_of_Lists;
        !           107:                            lifted : out Array_of_Lists;
        !           108:                            mixsub : out Mixed_Subdivision; mv : out natural );
        !           109:
        !           110:   -- DESCRIPTION :
        !           111:   --   All these routines compute the mixed volume of support lists.
        !           112:
        !           113:   -- ON ENTRY :
        !           114:   --   file       if specified, then the mixed subdivision will be
        !           115:   --              written on file;
        !           116:   --   n          the dimension of the system;
        !           117:   --   mix        mix(k) is the number of times the kth support occurs;
        !           118:   --   supports   the supports of a system of n polynomials in n unknowns.
        !           119:
        !           120:   -- ON RETURN :
        !           121:   --   lifted     array of listed points;
        !           122:   --   mixsub     mixed subdivision used;
        !           123:   --   mv         the mixed volume.
        !           124:
        !           125: end Mixed_Volume_Computation;