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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Implift/volumes.ads, Revision 1.1

1.1     ! maekawa     1: with Lists_of_Integer_Vectors;           use Lists_of_Integer_Vectors;
        !             2: with Arrays_of_Integer_Vector_Lists;     use Arrays_of_Integer_Vector_Lists;
        !             3: with Trees_of_Vectors;                   use Trees_of_Vectors;
        !             4:
        !             5: package Volumes is
        !             6:
        !             7: -- DESCRIPTION :
        !             8: --   This package contains a routine to compute the volume
        !             9: --   of a polytope and two routines for computing the mixed volume.
        !            10:
        !            11:   function Volume ( n : natural; l : List ) return natural;
        !            12:
        !            13:   function Volume ( n : natural; l : List;
        !            14:                     tv : Tree_of_Vectors ) return natural;
        !            15:
        !            16:   procedure Volume ( n : in natural; l : in List;
        !            17:                      tv : in out Tree_of_Vectors; vlm : out natural );
        !            18:
        !            19:   -- DESCRIPTION :
        !            20:   --   Computes n! times the volume of the polytope generated
        !            21:   --   by the points in l; n equals the dimension of the space.
        !            22:   --   The tree of degrees tv maintains the directions used to
        !            23:   --   compute the volume.  Once tv has been constructed, the volume
        !            24:   --   can be computed more efficiently.
        !            25:
        !            26:   -- REMARK :
        !            27:   --   The tree of vectors contains directions normal to the polytope
        !            28:   --   generated by a list wl where the first element of the list
        !            29:   --   consists of all zeroes; so eventually l has been shifted.
        !            30:
        !            31:   function Mixed_Volume ( n : natural; al : Array_of_Lists ) return natural;
        !            32:
        !            33:   function Mixed_Volume ( n : natural; al : Array_of_Lists;
        !            34:                           tv : Tree_of_Vectors ) return natural;
        !            35:
        !            36:   procedure Mixed_Volume ( n : in natural; al : in Array_of_Lists;
        !            37:                            tv : in out Tree_of_Vectors; mv : out natural );
        !            38:
        !            39:   -- DESCRIPTION :
        !            40:   --   Computes the mixed volume of the polytopes generated
        !            41:   --   by the points in al; n equals the dimension of the space.
        !            42:   --   The tree of vectors tv maintains the directions used to
        !            43:   --   compute the mixed volume.  Once tv has been constructed,
        !            44:   --   the mixed volume can be computed more efficiently.
        !            45:
        !            46: end Volumes;