[Indigo]<AlgebraStructures>NewAlgebraStructures>ASAlgebraicNumberStructure.mesa!1

ASAlgebraicNumberStructure.mesa

Last Edited by: Arnon, June 10, 1985 4:19:22 pm PDT

DIRECTORY

Rope USING [ROPE],

IO,

AlgebraClasses,

RatIntervals,

ASPolynomialStructure;

ASAlgebraicNumberStructure: CEDAR DEFINITIONS

= BEGIN

Element Representation

AlgebraicNumber: TYPE = AlgebraClasses.Object;

AlgebraicNumberData: TYPE = REF AlgebraicNumberDataRec;

AlgebraicNumberDataRec: TYPE = RECORD [

minimalPolynomial: ASPolynomialStructure.Polynomial, -- a monic elt of minPolyRing irreducible over groundField, where minPolyRing is a ring of univariate polynomials over any groundField.

isolatingInterval: ASRatIntervals.RatInterval ← NIL -- NonNIL iff groundField real; isolating interval for the unique root of minimalPolynomial which is this real algebraic number.

];

Structure Instance Data

FieldOfAlgebraicNumbersData: TYPE = REF FieldOfAlgebraicNumbersDataRec;

FieldOfAlgebraicNumbersDataRec: TYPE = RECORD [

groundField: AlgebraClasses.Object,

minPolyRing: AlgebraClasses.Object,

real: BOOL

];

Structure Constructor

MakeFieldOfAlgebraicNumbers: PROC [minPolyRing: AlgebraClasses.Object, real: BOOL] RETURNS [fieldOfAlgebraicNumbers: AlgebraClasses.Object];

Structure Operations

PrintName: AlgebraClasses.ToRopeOp;

ShortPrintName: AlgebraClasses.ToRopeOp;

IsFieldOfAlgebraicNumbers: PROC [structure: AlgebraClasses.Object] RETURNS [BOOL];

GroundField: AlgebraClasses.UnaryOp;

selector: groundField

MinPolyRing: AlgebraClasses.UnaryOp;

selector: minPolyRing

StructureData: AlgebraClasses.UnaryToListOp;

selector: returns LIST[groundField, minPolyRing] of a FieldOfAlgebraicNumbers Structure

Element Conversion and IO

Recast: AlgebraClasses.BinaryOp;

CanRecast: AlgebraClasses.BinaryPredicate;

ToExpr: AlgebraClasses.ToExprOp;

LegalFirstChar: AlgebraClasses.LegalFirstCharOp;

Read: AlgebraClasses.ReadOp;

FromRope: AlgebraClasses.FromRopeOp;

ToRope: AlgebraClasses.ToRopeOp;

Write: AlgebraClasses.WriteOp;

Element Constructor

MakeAlgebraicNumber: AlgebraClasses.BinaryImbedOp;

data1 = minimalPolynomial, a monic elt of structure.minPolyRing irreducible over groundField, where minPolyRing is a ring of univariate polynomials over any groundField. data2 = isolatingInterval; If structure.real, then groundField = structure.groundField is a real field, and isolatingInterval is an isolating interval for the unique root of minimalPolynomial which is this (real) algebraic number.

Element Operations

BinaryOp: AlgebraClasses.BinaryOp;

UnaryOp: AlgebraClasses.UnaryOp;

END.