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File: [local] / OpenXM_contrib / PHC / Ada / Math_Lib / Polynomials / generic_polynomials.ads (download)
Revision 1.1.1.1 (vendor branch), Sun Oct 29 17:45:26 2000 UTC (23 years, 10 months ago) by maekawa
Import the second public release of PHCpack. OKed by Jan Verschelde. |
with Abstract_Ring; with Standard_Natural_Vectors; generic with package Ring is new Abstract_Ring(<>); package Generic_Polynomials is -- DESCRIPTION : -- This package represents polynomials in several variables with -- coefficients over any ring, to be specified by instantiation. use Ring; -- DATA STRUCTURES : type Degrees is new Standard_Natural_Vectors.Link_to_Vector; type Term is record cf : number; -- coefficient of the term dg : Degrees; -- the degrees of the term end record; type Poly is private; Null_Poly : constant Poly; -- represents zero in the polynomial ring One_Poly : constant Poly; -- represents one in the polynomial ring -- CONSTRUCTORS : function Create ( n : natural ) return Poly; function Create ( n : number ) return Poly; function Create ( t : Term ) return Poly; procedure Copy ( t1 : in Term; t2 : in out Term ); -- makes a deep copy procedure Copy ( p: in Poly; q : in out Poly ); -- SELECTORS : function Equal ( t1,t2 : Term ) return boolean; function Equal ( p,q : Poly ) return boolean; function Number_of_Unknowns ( p : Poly ) return natural; function Number_of_Terms ( p : Poly ) return natural; function Degree ( p : Poly ) return integer; -- return deg(p); function Degree ( p : Poly; i : integer ) return integer; -- return deg(p,xi); function "<" ( d1,d2 : Degrees ) return boolean; -- return d1 < d2 function ">" ( d1,d2 : Degrees ) return boolean; -- return d1 > d2 function Coeff ( p : Poly; d : Degrees ) return number; -- Ex.: Coeff(c1*x^2+c2*x*y^3,(1 2))=c2; Coeff(c1*x^2+c2,(1 0))=zero; -- ARITHMETICAL OPERATIONS : function "+" ( p : Poly; t : Term ) return Poly; -- return p+t; function "+" ( t : Term; p : Poly ) return Poly; -- return t+p; function "+" ( p : Poly ) return Poly; -- returns copy of p; function "+" ( p,q : Poly ) return Poly; -- return p+q; function "-" ( p : Poly; t : Term ) return Poly; -- return p-t; function "-" ( t : Term; p : Poly ) return Poly; -- return t-p; function "-" ( p : Poly ) return Poly; -- return -p; function "-" ( p,q : Poly ) return Poly; -- return p-q; function "*" ( p : Poly; a : number ) return Poly; -- return a*p; function "*" ( a : number; p : Poly ) return Poly; -- return p*a; function "*" ( p : Poly; t : Term ) return Poly; -- return p*t; function "*" ( t : Term; p : Poly ) return Poly; -- return t*p; function "*" ( p,q : Poly ) return Poly; -- return p*q; procedure Add ( p : in out Poly; t : in Term ); -- p := p + t; procedure Add ( p : in out Poly; q : in Poly ); -- p := p + q; procedure Sub ( p : in out Poly; t : in Term ); -- p := p - t; procedure Min ( p : in out Poly ); -- p := -p; procedure Sub ( p : in out Poly; q : in Poly ); -- p := p - q; procedure Mul ( p : in out Poly; a : in number ); -- p := p * a; procedure Mul ( p : in out Poly; t : in Term ); -- p := p * t; procedure Mul ( p : in out Poly; q : in Poly ); -- p := p * q; function Diff ( p : Poly; i : integer ) return Poly; procedure Diff ( p : in out Poly; i : in integer ); -- symbolic differentiation w.r.t. the i-th unknown of p -- ITERATORS : run through all terms of p and apply the generic procedure. generic with procedure process ( t : in out Term; continue : out boolean ); procedure Changing_Iterator ( p : in out Poly ); -- t can be changed generic with procedure process ( t : in Term; continue : out boolean ); procedure Visiting_Iterator ( p : in Poly ); -- t can only be read -- DESTRUCTORS : deallocate memory. procedure Clear ( d : in out Degrees ); procedure Clear ( t : in out Term ); procedure Clear ( p : in out Poly ); private type Poly_Rep; type Poly is access Poly_Rep; Null_Poly : constant Poly := null; One_Term : constant Term := (one,null); One_Poly : constant Poly := Create(One_Term); end Generic_Polynomials;