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Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Product/total_degree_start_systems.adb, Revision 1.1

1.1     ! maekawa     1: with text_io;                           use text_io;
        !             2: with Standard_Random_Numbers;           use Standard_Random_Numbers;
        !             3: with Standard_Complex_Numbers;          use Standard_Complex_Numbers;
        !             4: with Standard_Complex_Numbers_Polar;    use Standard_Complex_Numbers_Polar;
        !             5: with Standard_Natural_Vectors;
        !             6: with Standard_Complex_Polynomials;      use Standard_Complex_Polynomials;
        !             7:
        !             8: package body Total_Degree_Start_Systems is
        !             9:
        !            10:   procedure Total_Degree_Info is
        !            11:
        !            12:   -- DESCRIPTION :
        !            13:   --   Displays information about the total degree on screen.
        !            14:
        !            15:     i : array(1..5) of string(1..65);
        !            16:
        !            17:   begin
        !            18:     i(1):="  The  total  degree  is  the  product  of  the  degrees  of  the";
        !            19:     i(2):="polynomials in the system.  The i-th equation of the start system";
        !            20:     i(3):="is a univariate polynomial in the i-th unknown of the same degree";
        !            21:     i(4):="as  the i-th polynomial in the system that has to be solved.  The";
        !            22:     i(5):="total degree equals the number of solutions of the start system. ";
        !            23:     for k in i'range loop
        !            24:       put_line(i(k));
        !            25:     end loop;
        !            26:   end Total_Degree_Info;
        !            27:
        !            28:   procedure Start_Solutions
        !            29:                ( level : in natural;
        !            30:                  q : in Poly_Sys; c : in Vector; s : in out Solution;
        !            31:                  qsols,qsols_last : in out Solution_List ) is
        !            32:
        !            33:   -- DESCRIPTION :
        !            34:   --   All solutions to the polynomial system q are computed.
        !            35:   --   The parameter level indicates the current component in the recursive
        !            36:   --   application of the rule of de Moivre.
        !            37:
        !            38:     d : natural;
        !            39:
        !            40:   begin
        !            41:     if level <= s.n
        !            42:      then d := Degree(q(level));
        !            43:           for j in 1..d loop
        !            44:             s.v(level) := Root(c(level),d,j);
        !            45:             Start_Solutions(level+1,q,c,s,qsols,qsols_last);
        !            46:           end loop;
        !            47:      else s.t := Create(0.0);
        !            48:           s.m := 1;
        !            49:           s.err := 0.0; s.rco := 1.0; s.res := 0.0;
        !            50:           Append(qsols,qsols_last,s);
        !            51:     end if;
        !            52:   end Start_Solutions;
        !            53:
        !            54:   procedure Start_System
        !            55:                ( p : in Poly_Sys; q : in out Poly_Sys; c : in Vector;
        !            56:                  qsols : in out Solution_List ) is
        !            57:
        !            58:     t : Term;
        !            59:     n : natural := p'length;
        !            60:     s : Solution(n);
        !            61:     last : Solution_List := qsols;
        !            62:
        !            63:   begin
        !            64:     for i in p'range loop
        !            65:       t.dg := new Standard_Natural_Vectors.Vector'(1..n => 0);
        !            66:       t.dg(i) := Degree(p(i));
        !            67:       t.cf := Create(1.0);
        !            68:       q(i) := Create(t);
        !            69:       Clear(t);
        !            70:       t.dg := new Standard_Natural_Vectors.Vector'(1..n => 0);
        !            71:       t.cf := -c(i);
        !            72:       Add(q(i),t);
        !            73:       Clear(t);
        !            74:     end loop;
        !            75:     Start_Solutions(1,q,c,s,qsols,last);
        !            76:   end Start_System;
        !            77:
        !            78:   procedure Start_System
        !            79:                ( p : in Poly_Sys; q : in out Poly_Sys;
        !            80:                  qsols : in out Solution_List ) is
        !            81:
        !            82:     n : natural := p'length;
        !            83:     c : Vector(1..n);
        !            84:
        !            85:   begin
        !            86:     for i in c'range loop
        !            87:       c(i) := Random1;
        !            88:     end loop;
        !            89:     Start_System(p,q,c,qsols);
        !            90:   end Start_System;
        !            91:
        !            92: end Total_Degree_Start_Systems;