WSRational

jws.spad line 308 [edit on github]

Julia Wolfram Symbolic rational numbers using the MathLink Julia package.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> % if WSInteger has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, WSInteger) -> %

from RightModule WSInteger

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NMInteger, %) -> %

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

*: (WSInteger, %) -> %

from LeftModule WSInteger

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (WSInteger, WSInteger) -> %

from QuotientFieldCategory WSInteger

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from OrderedAbelianGroup

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean

from EntireRing

associator: (%, %, %) -> %

from NonAssociativeRng

ceiling: % -> WSInteger

from QuotientFieldCategory WSInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

charthRoot: % -> Union(%, failed) if % has CharacteristicNonZero and WSInteger has PolynomialFactorizationExplicit or WSInteger has CharacteristicNonZero

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: % -> WSExpression

coerce(q) coerces q. Convenience function.

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

coerce(z): coerces(z). Convenience function.

coerce: Symbol -> % if WSInteger has RetractableTo Symbol

from CoercibleFrom Symbol

coerce: WSInteger -> %

from CoercibleFrom WSInteger

commutator: (%, %) -> %

from NonAssociativeRng

conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and WSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> Fraction Integer

convert(q) returns q as a Fraction(Integer)

convert: % -> InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float if WSInteger has ConvertibleTo Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> String

from ConvertibleTo String

D: % -> %

from DifferentialRing

D: (%, List Symbol) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, WSInteger -> WSInteger) -> %

from DifferentialExtension WSInteger

D: (%, WSInteger -> WSInteger, NonNegativeInteger) -> %

from DifferentialExtension WSInteger

denom: % -> WSInteger

from QuotientFieldCategory WSInteger

denominator: % -> %

from QuotientFieldCategory WSInteger

differentiate: % -> %

from DifferentialRing

differentiate: (%, List Symbol) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if WSInteger has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, WSInteger -> WSInteger) -> %

from DifferentialExtension WSInteger

differentiate: (%, WSInteger -> WSInteger, NonNegativeInteger) -> %

from DifferentialExtension WSInteger

divide: (%, %) -> Record(quotient: %, remainder: %)

from EuclideanDomain

elt: (%, WSInteger) -> % if WSInteger has Eltable(WSInteger, WSInteger)

from Eltable(WSInteger, %)

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

eval: (%, Equation WSInteger) -> % if WSInteger has Evalable WSInteger

from Evalable WSInteger

eval: (%, List Equation WSInteger) -> % if WSInteger has Evalable WSInteger

from Evalable WSInteger

eval: (%, List Symbol, List WSInteger) -> % if WSInteger has InnerEvalable(Symbol, WSInteger)

from InnerEvalable(Symbol, WSInteger)

eval: (%, List WSInteger, List WSInteger) -> % if WSInteger has Evalable WSInteger

from InnerEvalable(WSInteger, WSInteger)

eval: (%, Symbol, WSInteger) -> % if WSInteger has InnerEvalable(Symbol, WSInteger)

from InnerEvalable(Symbol, WSInteger)

eval: (%, WSInteger, WSInteger) -> % if WSInteger has Evalable WSInteger

from InnerEvalable(WSInteger, WSInteger)

expressIdealMember: (List %, %) -> Union(List %, failed)

from PrincipalIdealDomain

exquo: (%, %) -> Union(%, failed)

from EntireRing

extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if WSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if WSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

floor: % -> WSInteger

from QuotientFieldCategory WSInteger

fractionPart: % -> %

from QuotientFieldCategory WSInteger

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %

from PolynomialFactorizationExplicit

init: %

from StepThrough

inv: % -> %

from DivisionRing

jlAbout: % -> Void

from JLObjectType

jlApply: (String, %) -> %

from JLObjectType

jlApply: (String, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %, %) -> %

from JLObjectType

jlDisplay: % -> Void

from JLObjectType

jlDump: JLObject -> Void

from JLObjectType

jlEval: % -> %

from WSObject

jlHead: % -> WSSymbol

from WSObject

jlId: % -> JLInt64

from JLObjectType

jlNumeric: % -> %

from WSObject

jlNumeric: (%, PositiveInteger) -> %

from WSObject

jlObject: () -> String

from JLObjectType

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlSymbolic: % -> String

from WSObject

jlType: % -> String

from JLObjectType

jWSInterpret: (String, String) -> %

from WSObject

jWSRat: Fraction Integer -> %

jWSRat(q) constructs q as a WSRational.

latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)

from LeftOreRing

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

map: (WSInteger -> WSInteger, %) -> %

from FullyEvalableOver WSInteger

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

multiEuclidean: (List %, %) -> Union(List %, failed)

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

negative?: % -> Boolean

from OrderedAbelianGroup

nextItem: % -> Union(%, failed)

from StepThrough

nothing?: % -> Boolean

from JLObjectType

numer: % -> WSInteger

from QuotientFieldCategory WSInteger

numerator: % -> %

from QuotientFieldCategory WSInteger

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if WSInteger has PatternMatchable Float

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %)

from PatternMatchable Integer

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

positive?: % -> Boolean

from OrderedAbelianGroup

prime?: % -> Boolean

from UniqueFactorizationDomain

principalIdeal: List % -> Record(coef: List %, generator: %)

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if WSInteger has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix WSInteger, vec: Vector WSInteger)

from LinearlyExplicitOver WSInteger

reducedSystem: Matrix % -> Matrix Integer if WSInteger has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix WSInteger

from LinearlyExplicitOver WSInteger

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> Symbol if WSInteger has RetractableTo Symbol

from RetractableTo Symbol

retract: % -> WSInteger

from RetractableTo WSInteger

retractIfCan: % -> Union(Fraction Integer, failed)

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(Symbol, failed) if WSInteger has RetractableTo Symbol

from RetractableTo Symbol

retractIfCan: % -> Union(WSInteger, failed)

from RetractableTo WSInteger

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer

from OrderedAbelianGroup

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if WSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if WSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

string: % -> String

from JLType

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

toString: % -> String

from WSObject

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %)

from EntireRing

wholePart: % -> WSInteger

from QuotientFieldCategory WSInteger

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra WSInteger

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(WSInteger, WSInteger)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if WSInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom Symbol if WSInteger has RetractableTo Symbol

CoercibleFrom WSInteger

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if WSInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo String

DifferentialExtension WSInteger

DifferentialRing

DivisionRing

Eltable(WSInteger, %) if WSInteger has Eltable(WSInteger, WSInteger)

EntireRing

EuclideanDomain

Evalable WSInteger if WSInteger has Evalable WSInteger

Field

FullyEvalableOver WSInteger

FullyLinearlyExplicitOver WSInteger

FullyPatternMatchable WSInteger

GcdDomain

InnerEvalable(Symbol, WSInteger) if WSInteger has InnerEvalable(Symbol, WSInteger)

InnerEvalable(WSInteger, WSInteger) if WSInteger has Evalable WSInteger

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftModule Fraction Integer

LeftModule WSInteger

LeftOreRing

LinearlyExplicitOver Integer if WSInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver WSInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module WSInteger

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra WSInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedMonoid

OrderedRing

OrderedSemiGroup

OrderedSet

PartialDifferentialRing Symbol if WSInteger has PartialDifferentialRing Symbol

PartialOrder

Patternable WSInteger

PatternMatchable Float if WSInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if WSInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

QuotientFieldCategory WSInteger

RealConstant

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo Symbol if WSInteger has RetractableTo Symbol

RetractableTo WSInteger

RightModule %

RightModule Fraction Integer

RightModule Integer if WSInteger has LinearlyExplicitOver Integer

RightModule WSInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown

WSNumber

WSObject

WSRing