Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Polynomials/standard_complex_substitutors.ads, Revision 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! 38: -- t a term where the kth unknonw has been replaced by the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;
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