GENERIC INTERFACE PolynomialBasic(R, V);

Arithmetic for Modula-3, see doc for details

FROM Arithmetic IMPORT Error;

TYPE
  (* this is not only a re-use because of laziness, more than this, a
     polynomial can be treated as vector and behaves like a vector of
     arbitrary size *)
  TBody = V.TBody;
  T = V.T;
  QuotRem = RECORD quot, rem: T END;

<* INLINE *>
PROCEDURE IsZero (x: T; ): BOOLEAN;
PROCEDURE Equal (x, y: T; ): BOOLEAN; (* x=y *)
PROCEDURE Compare (x, y: T; ):
  [-1 .. 1];                     (* a dummy to let Fraction module work *)

PROCEDURE Add (x, y: T; ): T;    (* x+y *)
PROCEDURE Sub (x, y: T; ): T;    (* x-y *)
CONST Neg = V.Neg;

CONST Scale = V.Scale;

PROCEDURE Mul (x, y: T; ): T;    (* x*y *)
PROCEDURE Div (x, y: T; ): T
  RAISES {Error};                (* x/y if possible, will fail for floating
                                    point numbers often *)
PROCEDURE Mod (x, y: T; ): T RAISES {Error}; (* x mod y *)
PROCEDURE DivMod (x, y: T; ): QuotRem RAISES {Error};

compute quotient x/y and remainder

PROCEDURE Eval (x : T;           (* evaluate this polynomial *)
                xi: R.T;         (* at this point *)
  ): R.T;

PROCEDURE Derive (x: T;          (* differentiate polynomial *)
  ): T;
PROCEDURE EvalDerivative
  (x : T;                        (* evaluate this polynomial *)
   xi: R.T;                      (* for this argument *)
   n : CARDINAL;                 (* with this number of derivatives *)
  ): REF ARRAY OF R.T;           (* returning x(xi), x'(xi)... *)

PROCEDURE Compose (x, y: T;      (* y(x) - apply y on the values of x *)
  ): T;

END PolynomialBasic.