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

1.1     ! maekawa     1: with Standard_Integer_Vectors;           use Standard_Integer_Vectors;
        !             2: with Standard_Complex_Laur_Polys;        use Standard_Complex_Laur_Polys;
        !             3: with Standard_Complex_Laur_Systems;      use Standard_Complex_Laur_Systems;
        !             4: with Lists_of_Integer_Vectors;           use Lists_of_Integer_Vectors;
        !             5: with Integer_Mixed_Subdivisions;         use Integer_Mixed_Subdivisions;
        !             6: with Arrays_of_Integer_Vector_Lists;     use Arrays_of_Integer_Vector_Lists;
        !             7:
        !             8: package Integer_Lifting_Utilities is
        !             9:
        !            10: -- DESCRIPTION :
        !            11: --   This package provides some utilities for dealing with lifting functions.
        !            12:
        !            13:   function Adaptive_Lifting ( l : Array_of_Lists ) return Vector;
        !            14:
        !            15:   -- DESCRIPTION :
        !            16:   --   Returns upper bounds for a random lifting, depending on the lengths
        !            17:   --   of the lists in l.
        !            18:
        !            19: --  function Select_Subsystem ( p : Laur_Sys; mix : Vector; mic : Mixed_Cell )
        !            20: --                            return Laur_Sys;
        !            21:
        !            22:   -- DESCRIPTION :
        !            23:   --   Given a Laurent polynomial system and a mixed cell,
        !            24:   --   the corresponding subsystem will be returned.
        !            25:
        !            26:   -- ON ENTRY :
        !            27:   --   p          a Laurent polynomial system;
        !            28:   --   mix        type of mixture: occurencies of the supports;
        !            29:   --   mic        a mixed cell.
        !            30:
        !            31:   -- REQUIRED :
        !            32:   --   The polynomials in p must be ordered according to the type of mixture.
        !            33:
        !            34:   function Perform_Lifting
        !            35:                ( n : natural; l : List; p : Poly ) return Poly;
        !            36:   function Perform_Lifting
        !            37:                ( n : natural; mix : Vector; lifted : Array_of_Lists;
        !            38:                  p : Laur_Sys ) return Laur_Sys;
        !            39:
        !            40:   -- DESCRIPTION :
        !            41:   --   Construction of the polyhedral homotopy, given the lifted supports.
        !            42:   --   The p will be lifted according to the lifted points, i.e. each
        !            43:   --   monomial whose exponent vector corresponds to a vector in the
        !            44:   --   lifted points (except for the last entry of course), will be
        !            45:   --   extended with an additional unknown, with as exponent, the
        !            46:   --   lifting value of that vector.
        !            47:
        !            48:   function Copy_Lifting ( lifted : List; pt : Link_to_Vector )
        !            49:                         return Link_to_Vector;
        !            50:
        !            51:   -- DESCRIPTION :
        !            52:   --   Searches the corresponding point in the list lifted and returns
        !            53:   --   the lifted point.  If the corresponding point has not been found,
        !            54:   --   then the original point pt will be returned.
        !            55:
        !            56:   function Copy_Lifting ( lifted,pts : List ) return List;
        !            57:
        !            58:   -- DESCRIPTION :
        !            59:   --   Copies the lifting on the points lifted to the points in pts,
        !            60:   --   i.e., each point in pts will get the same lifting as the corresponding
        !            61:   --   lifted point in the list lifted.
        !            62:
        !            63:   procedure Search_Lifting ( l : in List; pt : in Vector;
        !            64:                              found : out boolean; lif : out integer );
        !            65:
        !            66:   -- DESCRIPTION :
        !            67:   --   Searches the lifting of the point in the lifted list l.
        !            68:   --   If found, then lif equals the lifting, otherwise lif is meaningless.
        !            69:
        !            70:   function Search_and_Lift ( l : List; pt : Vector ) return Vector;
        !            71:
        !            72:   -- DESCRIPTION :
        !            73:   --   Given a lifted list of points and a unlifted vector, the function
        !            74:   --   either returns the corresponding lifted vector from the list, or
        !            75:   --   the same point, when there is no lifted point in l whose projection
        !            76:   --   equals the given point pt.
        !            77:
        !            78:   function Induced_Lifting ( mixsub : Mixed_Subdivision; k : natural;
        !            79:                              pt : Vector ) return Vector;
        !            80:   function Induced_Lifting
        !            81:                ( n : natural; mix : Vector; points : Array_of_Lists;
        !            82:                  mixsub : Mixed_Subdivision ) return Array_of_Lists;
        !            83:
        !            84:   -- DESCRIPTION :
        !            85:   --   Given a mixed subdivision for a tuple of supports,
        !            86:   --   then the lifted points will be returned as induced by the
        !            87:   --   subdivision.   When points do not occur in the mixed subdivision,
        !            88:   --   they will be lifted conservatively.
        !            89:
        !            90:   procedure Constant_Lifting
        !            91:                ( l : in List; liftval : in natural;
        !            92:                  lifted,lifted_last : in out List );
        !            93:
        !            94:   -- DESCRIPTION :
        !            95:   --   Gives all points in l the constant lifting liftval,
        !            96:   --   and appends them to the list lifted, where lifted_last is
        !            97:   --   a pointer to the last element of lifted.
        !            98:
        !            99:   procedure Constant_Lifting
        !           100:                ( al : in Array_of_Lists; liftval : in natural;
        !           101:                  lifted,lifted_last : in out Array_of_Lists );
        !           102:
        !           103:   -- DESCRIPTION :
        !           104:   --   Gives all points in al(i) the constant lifting liftval,
        !           105:   --   and appends them to the lists lifted(i), where lifted_last(i) is
        !           106:   --   a pointer to the last element of lifted(i).
        !           107:
        !           108:   function Conservative_Lifting
        !           109:                ( mic : Mixed_Cell; k : natural; point : Vector ) return integer;
        !           110:   function Conservative_Lifting
        !           111:                ( mixsub : Mixed_Subdivision; k : natural; point : Vector )
        !           112:                return integer;
        !           113:
        !           114:   -- DESCRIPTION :
        !           115:   --   Returns the value of the conservative lifting function of the point
        !           116:   --   to be considered w.r.t. the kth polytope.
        !           117:
        !           118:   -- REQUIRED :
        !           119:   --   The given point must already be in the lifted space and its last
        !           120:   --   coordinate must contain already a lower bound for the lifting value.
        !           121:
        !           122:   function Lower_Lifting ( mic : Mixed_Cell; k : natural; point : Vector )
        !           123:                          return integer;
        !           124:
        !           125:   -- DESCRIPTION :
        !           126:   --   Returns a lower bound on the lifting value.  In case that the point
        !           127:   --   belongs to the kth component of the cell, the value zero is returned.
        !           128:   --   Otherwise, the conservative lifting value of the point w.r.t. the
        !           129:   --   cell is returned.
        !           130:
        !           131:   -- REQUIRED :
        !           132:   --   The point must be already in lifted space.
        !           133:
        !           134:   function Lower_Lifting ( mixsub : Mixed_Subdivision; k : natural;
        !           135:                            point : Vector ) return integer;
        !           136:
        !           137:   -- DESCRIPTION :
        !           138:   --   Applies the lower lifting function to all cells in the subdivision.
        !           139:   --   Stops when the lower bound equals the lifting value of the point
        !           140:   --   equals the lifting of the point given on entry.
        !           141:
        !           142: end Integer_Lifting_Utilities;