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Annotation of OpenXM_contrib/PHC/Ada/Math_Lib/Polynomials/generic_laurent_polynomials.ads, Revision 1.1

1.1     ! maekawa     1: with Abstract_Ring;
        !             2: with Standard_Integer_Vectors;
        !             3:
        !             4: generic
        !             5:
        !             6:   with package Ring is new Abstract_Ring(<>);
        !             7:
        !             8: package Generic_Laurent_Polynomials is
        !             9:
        !            10: -- DESCRIPTION :
        !            11: --   This package represents Laurent polynomials in several variables with
        !            12: --   coefficients over any ring, to be specified by instantiation.
        !            13: --   The exponents can be negative.
        !            14:
        !            15:   use Ring;
        !            16:
        !            17: -- DATA STRUCTURES :
        !            18:
        !            19:   type Degrees is new Standard_Integer_Vectors.Link_to_Vector;
        !            20:
        !            21:   type Term is record
        !            22:     cf : number;     -- coefficient of the term
        !            23:     dg : Degrees;    -- the degrees of the term
        !            24:   end record;
        !            25:
        !            26:   type Poly is private;
        !            27:
        !            28:   Null_Poly : constant Poly;    -- represents zero in the polynomial ring
        !            29:   One_Poly : constant Poly;     -- represents one in the polynomial ring
        !            30:
        !            31: -- CONSTRUCTORS :
        !            32:
        !            33:   function Create ( n : natural ) return Poly;
        !            34:   function Create ( n : number ) return Poly;
        !            35:
        !            36:   function Create ( t : Term ) return Poly;
        !            37:
        !            38:   procedure Copy ( t1 : in Term; t2 : in out Term );    -- makes a deep copy
        !            39:   procedure Copy ( p: in Poly; q : in out Poly );
        !            40:
        !            41: -- SELECTORS :
        !            42:
        !            43:   function Equal ( t1,t2 : Term )  return boolean;
        !            44:   function Equal ( p,q : Poly )  return boolean;
        !            45:
        !            46:   function Number_of_Unknowns ( p : Poly ) return natural;
        !            47:   function Number_of_Terms    ( p : Poly ) return natural;
        !            48:
        !            49:   function Degree ( p : Poly ) return integer;              -- return deg(p);
        !            50:
        !            51:   function Maximal_Degree ( p : Poly; i : natural ) return integer;
        !            52:              -- returns maximal degree of xi in p;
        !            53:   function Maximal_Degrees ( p : Poly ) return Degrees;
        !            54:              -- Maximal_Degrees(p)(i) = Maximal_Degree(p,i)
        !            55:   function Minimal_Degree ( p : Poly; i : natural ) return integer;
        !            56:              -- returns minimal degree of xi in p;
        !            57:   function Minimal_Degrees ( p : Poly ) return Degrees;
        !            58:              -- Minimal_Degrees(p)(i) = Minimal_Degree(p,i)
        !            59:
        !            60:   function "<" ( d1,d2 : Degrees ) return boolean;          -- return d1 < d2
        !            61:   function ">" ( d1,d2 : Degrees ) return boolean;          -- return d1 > d2
        !            62:
        !            63:   function Coeff ( p : Poly; d : Degrees ) return number;
        !            64:    -- Ex.: Coeff(c1*x^2+c2*x*y^3,(1 2))=c2;  Coeff(c1*x^2+c2,(1 0))=zero;
        !            65:
        !            66: -- ARITHMETICAL OPERATIONS :
        !            67:
        !            68:   function "+" ( p : Poly; t : Term ) return Poly;      -- return p+t;
        !            69:   function "+" ( t : Term; p : Poly ) return Poly;      -- return t+p;
        !            70:   function "+" ( p : Poly ) return Poly;                -- returns copy of p;
        !            71:   function "+" ( p,q : Poly ) return Poly;              -- return p+q;
        !            72:   function "-" ( p : Poly; t : Term ) return Poly;      -- return p-t;
        !            73:   function "-" ( t : Term; p : Poly ) return Poly;      -- return t-p;
        !            74:   function "-" ( p : Poly ) return Poly;                -- return -p;
        !            75:   function "-" ( p,q : Poly ) return Poly;              -- return p-q;
        !            76:   function "*" ( p : Poly; a : number ) return Poly;    -- return a*p;
        !            77:   function "*" ( a : number; p : Poly ) return Poly;    -- return p*a;
        !            78:   function "*" ( p : Poly; t : Term ) return Poly;      -- return p*t;
        !            79:   function "*" ( t : Term; p : Poly ) return Poly;      -- return t*p;
        !            80:   function "*" ( p,q : Poly ) return Poly;              -- return p*q;
        !            81:
        !            82:   procedure Add ( p : in out Poly; t : in Term );       -- p := p + t;
        !            83:   procedure Add ( p : in out Poly; q : in Poly );       -- p := p + q;
        !            84:   procedure Sub ( p : in out Poly; t : in Term );       -- p := p - t;
        !            85:   procedure Min ( p : in out Poly );                    -- p := -p;
        !            86:   procedure Sub ( p : in out Poly; q : in Poly );       -- p := p - q;
        !            87:   procedure Mul ( p : in out Poly; a : in number );     -- p := p * a;
        !            88:   procedure Mul ( p : in out Poly; t : in Term );       -- p := p * t;
        !            89:   procedure Mul ( p : in out Poly; q : in Poly );       -- p := p * q;
        !            90:
        !            91:   function  Diff ( p : Poly; i : integer ) return Poly;
        !            92:   procedure Diff ( p : in out Poly; i : in integer );
        !            93:     -- symbolic differentiation w.r.t. the i-th unknown of p
        !            94:
        !            95: -- ITERATORS : run through all terms of p and apply the generic procedure.
        !            96:
        !            97:   generic
        !            98:     with procedure process ( t : in out Term; continue : out boolean );
        !            99:   procedure Changing_Iterator ( p : in out Poly );  -- t can be changed
        !           100:   generic
        !           101:     with procedure process ( t : in Term; continue : out boolean );
        !           102:   procedure Visiting_Iterator ( p : in Poly );      -- t can only be read
        !           103:
        !           104: -- DESTRUCTORS : deallocate memory.
        !           105:
        !           106:   procedure Clear ( t : in out Term );
        !           107:   procedure Clear ( p : in out Poly );
        !           108:
        !           109: private
        !           110:
        !           111:   type Poly_Rep;
        !           112:   type Poly is access Poly_Rep;
        !           113:
        !           114:   Null_Poly : constant Poly := null;
        !           115:
        !           116:   One_Term : constant Term := (one,null);
        !           117:   One_Poly : constant Poly := Create(One_Term);
        !           118:
        !           119: end Generic_Laurent_Polynomials;