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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Polynomials/standard_complex_substitutors.ads, Revision 1.1.1.1

1.1       maekawa     1: with Standard_Complex_Numbers;           use Standard_Complex_Numbers;
                      2: with Standard_Complex_Vectors;           use Standard_Complex_Vectors;
                      3: with Standard_Complex_Polynomials;       use Standard_Complex_Polynomials;
                      4: with Standard_Complex_Poly_Systems;      use Standard_Complex_Poly_Systems;
                      5:
                      6: package Standard_Complex_Substitutors is
                      7:
                      8: -- DESCRIPTION :
                      9: --   This package contains routines for substituting
                     10: --   equations into polynomials and polynomial systems.
                     11:
                     12:   function  Substitute ( k : integer; c : Complex_Number; t : Term )
                     13:                        return Term;
                     14:   procedure Substitute ( k : in integer; c : in Complex_Number;
                     15:                          t : in out Term );
                     16:
                     17:   function  Substitute ( k : integer; c : Complex_Number; p : Poly )
                     18:                        return Poly;
                     19:   procedure Substitute ( k : in integer; c : in Complex_Number;
                     20:                          p : in out Poly );
                     21:
                     22:   function  Substitute ( k : integer; c : Complex_Number; p : Poly_Sys )
                     23:                        return Poly_Sys;
                     24:   procedure Substitute ( k : in integer; c : in Complex_Number;
                     25:                          p : in out Poly_Sys );
                     26:
                     27:    -- DESCRIPTION :
                     28:    --   These routines substitute the kth unknown of the term t or
                     29:    --   polynomial (system) p by a complex constant c.
                     30:
                     31:    -- ON ENTRY :
                     32:    --   k         an unknown in the polynomial p;
                     33:    --   c         a complex constant;
                     34:    --   t         a term;
                     35:    --   p         a polynomial (system).
                     36:
                     37:    -- ON RETURN :
                     38:    --   t         a term where the kth unknonw has been replaced by the
                     39:    --             complex constant c;
                     40:    --   p         a polynomial (system) where the kth unknown has been
                     41:    --             replaced by the complex constant c.
                     42:
                     43:   function  Substitute ( k : integer; h : Vector; p : Poly ) return Poly;
                     44:   procedure Substitute ( k : in integer; h : in Vector; p : in out Poly );
                     45:
                     46:   -- DESCRIPTION :
                     47:   --   These routines substitute the kth unknown of the polynomial p
                     48:   --   by a linear equation defined by h.
                     49:
                     50:   -- ON ENTRY :
                     51:   --   k          an unknown in the polynomial p;
                     52:   --   h          a vector h(0..n), n = Number_of_Unknowns(p),
                     53:   --              defines h(0) + h(1)*x1 + ... + h(n)*xn;
                     54:   --   p          a polynomial.
                     55:
                     56:   -- REQUIRED : h(k) /= 0.
                     57:
                     58:   -- ON RETURN :
                     59:   --   p          a polynomial where the kth unknown has been replaced
                     60:   --              by a linear equation defined by h.
                     61:
                     62:   function  Substitute ( k : integer; s,p : Poly ) return Poly;
                     63:   procedure Substitute ( k : in integer; s : in Poly; p : in out Poly );
                     64:
                     65:   -- DESCRIPTION :
                     66:   --   These routines substitute the kth unknown of the polynomial p
                     67:   --   by a polynomial s.
                     68:
                     69:   -- ON ENTRY :
                     70:   --   k          an unknown in the polynomial p;
                     71:   --   s          a polynomial so that xk = s;
                     72:   --   p          a polynomial.
                     73:
                     74:   -- ON RETURN :
                     75:   --   p          a polynomial where the kth unknown has been replaced
                     76:   --              by the polynomial s.
                     77:
                     78:   function  Substitute ( k : integer; h : Vector; p : Poly_Sys )
                     79:                        return Poly_Sys;
                     80:   procedure Substitute ( k : in integer; h : in Vector; p : in out Poly_Sys );
                     81:
                     82:   -- DESCRIPTION :
                     83:   --   These routines substitute the kth unknown of the polynomials in the
                     84:   --   system p by a linear equation defined by h.
                     85:
                     86:   -- ON ENTRY :
                     87:   --   k          an unknown in the polynomials in the system p;
                     88:   --   h          a vector h(0..n), n = Number_of_Unknowns(p(i)),
                     89:   --              defines h(0) + h(1)*x1 + ... + h(n)*xn;
                     90:   --   p          a polynomial system.
                     91:
                     92:   -- REQUIRED : h(k) /= 0
                     93:
                     94:   -- ON RETURN :
                     95:   --   p          a polynomial system where the kth unknown has been replaced
                     96:   --              by a linear equation defined by h.
                     97:
                     98:   function  Substitute ( k : integer; s : Poly; p : Poly_Sys ) return Poly_Sys;
                     99:   procedure Substitute ( k : in integer; s : in Poly; p : in out Poly_Sys );
                    100:
                    101:   -- DESCRIPTION :
                    102:   --   These routines substitute the kth unknown of the polynomials in p
                    103:   --   by a polynomial s.
                    104:
                    105:   -- ON ENTRY :
                    106:   --   k          an unknown in the polynomial p;
                    107:   --   s          a polynomial so that xk = s;
                    108:   --   p          a polynomial.
                    109:
                    110:   -- ON RETURN :
                    111:   --   p          a polynomial system where the kth unknown has been replaced
                    112:   --              by the polynomial s.
                    113:
                    114: end Standard_Complex_Substitutors;