[Cyan]<ISLCedar>Math>Polynomial.mesa!1

Polynomial.Mesa

Operations for dealing with univariate polynomials with real coefficients.

Michael Plass, August 18, 1983 3:20 pm

Polynomial: DEFINITIONS =

BEGIN

Ref: TYPE = REF PolynomialRec;

PolynomialRec: TYPE = RECORD

[Coeff: SEQUENCE maxDegreePlusOne:NAT OF REAL];

RealRootRec: TYPE = RECORD [nRoots: NAT, realRoot: SEQUENCE n:NAT OF REAL];

ShortRealRootRec: TYPE = RECORD [nRoots: NAT, realRoot: ARRAY [0..5) OF REAL];

DivideResult: TYPE = RECORD [quotient, remainder: Ref];

Create: PROC [maxDegree: NAT] RETURNS [Ref]; -- returns a zero polynomial

Degree: PROC [poly: Ref] RETURNS [NAT]; -- for finding what the degree really is

Eval: PROC [f: Ref, x: REAL] RETURNS [REAL];

Copy: PROC [dest, source: Ref]; -- MaxDegree[dest] <= Degree[source]

The following are useful for creating polynomials of low degree.

Constant: PROC[ARRAY [0..0] OF REAL] RETURNS [Ref];

Linear: PROC[ARRAY [0..1] OF REAL] RETURNS [Ref];

Quadratic: PROC[ARRAY [0..2] OF REAL] RETURNS [Ref];

Cubic: PROC[ARRAY [0..3] OF REAL] RETURNS [Ref];

Quartic: PROC[ARRAY [0..4] OF REAL] RETURNS [Ref];

Quintic: PROC[ARRAY [0..5] OF REAL] RETURNS [Ref];

Add: PROC [dest, source: Ref];

Sum: PROC [a, b: Ref] RETURNS [Ref];

Subtract: PROC [dest, source: Ref];

Difference: PROC [a, b: Ref] RETURNS [Ref];

Product: PROC [a, b: Ref] RETURNS [Ref];

Divide: PROC [a, b: Ref] RETURNS [DivideResult];

DivideByLinear: PROC [f: Ref, c: REAL] RETURNS [value: REAL];

replaces f by f DIV (x-c)

Gcd: PROC [a, b: REF] RETURNS [Ref];

Differentiate: PROC [poly: Ref];

Derivative: PROC [poly: Ref] RETURNS [Ref];

EvalDeriv: PROC [f: Ref, x: REAL] RETURNS [REAL];

Integrate: PROC [poly: Ref]; -- watch out for growing degrees

Integral: PROC [poly: Ref] RETURNS [Ref];

EvalIntegral: PROC [f: Ref, x: REAL] RETURNS [REAL]; -- Definite integral from 0 to t

RealRoots: PROC [poly: Ref] RETURNS [REF RealRootRec];

CheapRealRoots: PROC [poly: Ref] RETURNS [ShortRealRootRec];

For when the degree is five or less.

END.