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

1.1     ! maekawa     1: with text_io;                            use text_io;
        !             2: with Standard_Integer_Vectors;
        !             3: with Standard_Floating_Vectors;
        !             4: with Standard_Complex_VecVecs;
        !             5: with Standard_Complex_Laur_Systems;      use Standard_Complex_Laur_Systems;
        !             6: with Standard_Complex_Laur_SysFun;       use Standard_Complex_Laur_SysFun;
        !             7: with Standard_Complex_Laur_Jacomats;     use Standard_Complex_Laur_Jacomats;
        !             8: with Exponent_Vectors;                   use Exponent_Vectors;
        !             9: with Arrays_of_Floating_Vector_Lists;    use Arrays_of_Floating_Vector_Lists;
        !            10: with Standard_Complex_Solutions;         use Standard_Complex_Solutions;
        !            11: with Floating_Mixed_Subdivisions;        use Floating_Mixed_Subdivisions;
        !            12:
        !            13: package Floating_Polyhedral_Continuation is
        !            14:
        !            15: -- DESCRIPTION :
        !            16: --   This package implements polyhedral homotopy continuation methods,
        !            17: --   based on mixed subdivision induced by floating-point lifting.
        !            18: --   The continuation is organized in three layers:
        !            19: --     1. inner normal, tracking of paths for one poly
        !            20: --     2. mixed cell, recursion is needed when the cell is not fine;
        !            21: --     3. mixed subdivision, for all cells in the subdivision.
        !            22: --   Each layer has two versions: a silent and a reporting version.
        !            23:
        !            24: -- FIRST LAYER : polyhedral continuation for one transformation.
        !            25:
        !            26:   procedure Mixed_Continuation
        !            27:                 ( mix : in Standard_Integer_Vectors.Vector;
        !            28:                   lifted : in Array_of_Lists; h : in Eval_Coeff_Laur_Sys;
        !            29:                   c : in Standard_Complex_VecVecs.VecVec;
        !            30:                   e : in Exponent_Vectors_Array;
        !            31:                   j : in Eval_Coeff_Jaco_Mat; m : in Mult_Factors;
        !            32:                   normal : in Standard_Floating_Vectors.Vector;
        !            33:                   sols : in out Solution_List );
        !            34:
        !            35:   procedure Mixed_Continuation
        !            36:                 ( file : in file_type;
        !            37:                   mix : in Standard_Integer_Vectors.Vector;
        !            38:                   lifted : in Array_of_Lists; h : in Eval_Coeff_Laur_Sys;
        !            39:                   c : in Standard_Complex_VecVecs.VecVec;
        !            40:                   e : in Exponent_Vectors_Array;
        !            41:                   j : in Eval_Coeff_Jaco_Mat; m : in Mult_Factors;
        !            42:                   normal : in Standard_Floating_Vectors.Vector;
        !            43:                   sols : in out Solution_List );
        !            44:
        !            45:   -- DESCRIPTION : polyhedral continuation with coefficient homotopy.
        !            46:
        !            47:   -- ON ENTRY :
        !            48:   --   file       file to write intermediate results on;
        !            49:   --   mix        type of mixture;
        !            50:   --   lifted     lifted supports of polynomial system, in original order;
        !            51:   --   h          coefficient homotopy;
        !            52:   --   c          coefficients of homotopy;
        !            53:   --   e          the exponent vectors of the unlifted system;
        !            54:   --   j          coefficient Jacobian matrix;
        !            55:   --   m          multiplication factors in coefficient Jacobian matrix;
        !            56:   --   normal     normal to a mixed cell;
        !            57:   --   sols       start solutions of the subsystem which corresponds
        !            58:   --              with the mixed cell with given inner normal.
        !            59:
        !            60:   -- ON RETURN :
        !            61:   --   sols       the solutions of p, which correspond to one mixed cell.
        !            62:
        !            63: -- SECOND LAYER : polyhedral continuaton for one mixed cell.
        !            64:
        !            65:   procedure Mixed_Solve
        !            66:                 ( p : in Laur_Sys; lifted : in Array_of_Lists;
        !            67:                   h : in Eval_Coeff_Laur_Sys;
        !            68:                   c : in Standard_Complex_VecVecs.VecVec;
        !            69:                   e : in Exponent_Vectors_Array;
        !            70:                   j : in Eval_Coeff_Jaco_Mat; m : in Mult_Factors;
        !            71:                   mix : in Standard_Integer_Vectors.Vector;
        !            72:                   mic : in Mixed_Cell;
        !            73:                   sols,sols_last : in out Solution_List );
        !            74:
        !            75:   procedure Mixed_Solve
        !            76:                 ( file : in file_type;
        !            77:                   p : in Laur_Sys; lifted : in Array_of_Lists;
        !            78:                   h : in Eval_Coeff_Laur_Sys;
        !            79:                   c : in Standard_Complex_VecVecs.VecVec;
        !            80:                   e : in Exponent_Vectors_Array;
        !            81:                   j : in Eval_Coeff_Jaco_Mat; m : in Mult_Factors;
        !            82:                   mix : in Standard_Integer_Vectors.Vector;
        !            83:                   mic : in Mixed_Cell;
        !            84:                   sols,sols_last : in out Solution_List );
        !            85:
        !            86:   -- DESCRIPTION :
        !            87:   --   Polyhedral coefficient-homotopy continuation for one mixed cell.
        !            88:
        !            89:   -- REQUIRED : polynomials in p must be ordered according to mix.
        !            90:
        !            91:   -- ON ENTRY :
        !            92:   --   file       a file to write intermediate results on;
        !            93:   --   p          non-lifted Laurent polynomial system;
        !            94:   --   lifted     lifted supports, with original order of points;
        !            95:   --   h          coefficient homotopy;
        !            96:   --   c          coefficients of homotopy;
        !            97:   --   e          the exponent vectors of the unlifted system;
        !            98:   --   j          coefficient Jacobian matrix;
        !            99:   --   m          multiplication factors in coefficient Jacobian matrix;
        !           100:   --   mix        type of mixture;
        !           101:   --   mic        a mixed cell.
        !           102:
        !           103:   -- ON RETURN :
        !           104:   --   sols       the solution list of p;
        !           105:   --   sols_last  pointer to last element of the list sols.
        !           106:
        !           107: -- THIRD LAYER : polyhedral continuation for a mixed subdivision.
        !           108:
        !           109:   procedure Mixed_Solve
        !           110:                 ( p : in Laur_Sys; lifted : in Array_of_Lists;
        !           111:                   h : in Eval_Coeff_Laur_Sys;
        !           112:                   c : in Standard_Complex_VecVecs.VecVec;
        !           113:                   e : in Exponent_Vectors_Array;
        !           114:                   j : in Eval_Coeff_Jaco_Mat; m : in Mult_Factors;
        !           115:                   mix : in Standard_Integer_Vectors.Vector;
        !           116:                   mixsub : in Mixed_Subdivision;
        !           117:                   sols : in out Solution_List );
        !           118:
        !           119:   procedure Mixed_Solve
        !           120:                 ( file : in file_type;
        !           121:                   p : in Laur_Sys; lifted : in Array_of_Lists;
        !           122:                   h : in Eval_Coeff_Laur_Sys;
        !           123:                   c : in Standard_Complex_VecVecs.VecVec;
        !           124:                   e : in Exponent_Vectors_Array;
        !           125:                   j : in Eval_Coeff_Jaco_Mat; m : in Mult_Factors;
        !           126:                   mix : in Standard_Integer_Vectors.Vector;
        !           127:                   mixsub : in Mixed_Subdivision;
        !           128:                   sols : in out Solution_List );
        !           129:
        !           130:   -- DESCRIPTION :
        !           131:   --   Polyhedral coefficient-homotopy continuation for a mixed subdivision.
        !           132:
        !           133:   -- REQUIRED : polynomials in p must be ordered according to mix.
        !           134:
        !           135:   -- ON ENTRY :
        !           136:   --   file       a file to write intermediate results on;
        !           137:   --   p          non-lifted Laurent polynomial system;
        !           138:   --   lifted     lifted supports, in original order;
        !           139:   --   h          coefficient homotopy;
        !           140:   --   c          coefficients of homotopy;
        !           141:   --   e          the exponent vectors of the unlifted system;
        !           142:   --   j          coefficient Jacobian matrix;
        !           143:   --   m          multiplication factors in coefficient Jacobian matrix;
        !           144:   --   mix        type of mixture;
        !           145:   --   mixsub     a collection of mixed cells.
        !           146:
        !           147:   -- ON RETURN :
        !           148:   --   sols       the solution list of p.
        !           149:
        !           150: end Floating_Polyhedral_Continuation;