JuliaWSRational

jws.spad line 305 [edit on github]

Julia Wolfram Symbolic rational numbers using Wolfram Symbolic Transport Protocol.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

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

from RightModule Integer

*: (%, JuliaWSInteger) -> %

from RightModule JuliaWSInteger

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (JuliaWSInteger, %) -> %

from LeftModule JuliaWSInteger

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (JuliaWSInteger, JuliaWSInteger) -> %

from QuotientFieldCategory JuliaWSInteger

<=: (%, %) -> 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 OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

ceiling: % -> JuliaWSInteger

from QuotientFieldCategory JuliaWSInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JuliaWSExpression

coerce(q) coerces q. Convenience function.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

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

coerce: JuliaWSInteger -> %

from Algebra JuliaWSInteger

coerce: Symbol -> % if JuliaWSInteger has RetractableTo Symbol

from CoercibleFrom Symbol

commutator: (%, %) -> %

from NonAssociativeRng

conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and JuliaWSInteger 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 JuliaWSInteger has ConvertibleTo Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> String

from ConvertibleTo String

D: % -> %

from DifferentialRing

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

from DifferentialExtension JuliaWSInteger

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

from DifferentialExtension JuliaWSInteger

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

denom: % -> JuliaWSInteger

from QuotientFieldCategory JuliaWSInteger

denominator: % -> %

from QuotientFieldCategory JuliaWSInteger

differentiate: % -> %

from DifferentialRing

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

from DifferentialExtension JuliaWSInteger

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

from DifferentialExtension JuliaWSInteger

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from EuclideanDomain

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

from Eltable(JuliaWSInteger, %)

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable JuliaWSInteger

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

from InnerEvalable(JuliaWSInteger, JuliaWSInteger)

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

from Evalable JuliaWSInteger

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

from InnerEvalable(JuliaWSInteger, JuliaWSInteger)

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

from InnerEvalable(Symbol, JuliaWSInteger)

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

from InnerEvalable(Symbol, JuliaWSInteger)

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 JuliaWSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

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

from PolynomialFactorizationExplicit

floor: % -> JuliaWSInteger

from QuotientFieldCategory JuliaWSInteger

fractionPart: % -> %

from QuotientFieldCategory JuliaWSInteger

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

init: %

from StepThrough

inv: % -> %

from DivisionRing

jlAbout: % -> Void

from JuliaObjectType

jlApply: (String, %) -> %

from JuliaObjectType

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

from JuliaObjectType

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

from JuliaObjectType

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

from JuliaObjectType

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

from JuliaObjectType

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

from JuliaObjectType

jlEval: % -> %

from JuliaWSObject

jlHead: % -> JuliaWSSymbol

from JuliaWSObject

jlId: % -> String

from JuliaObjectType

jlNumeric: % -> %

from JuliaWSObject

jlNumeric: (%, PositiveInteger) -> %

from JuliaWSObject

jlRef: % -> SExpression

from JuliaObjectType

jlref: String -> %

from JuliaObjectType

jlSymbolic: % -> String

from JuliaWSObject

jlType: % -> String

from JuliaObjectType

jWSInterpret: (String, String) -> %

from JuliaWSObject

jWSRat: Fraction Integer -> %

jWSRat(q) constructs q as a JuliaWSRational.

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: (JuliaWSInteger -> JuliaWSInteger, %) -> %

from FullyEvalableOver JuliaWSInteger

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

negative?: % -> Boolean

from OrderedRing

nextItem: % -> Union(%, failed)

from StepThrough

nothing?: % -> Boolean

from JuliaObjectType

numer: % -> JuliaWSInteger

from QuotientFieldCategory JuliaWSInteger

numerator: % -> %

from QuotientFieldCategory JuliaWSInteger

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

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

from PatternMatchable Float

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

from PatternMatchable Integer

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

positive?: % -> Boolean

from OrderedRing

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 JuliaWSInteger has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver JuliaWSInteger

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

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JuliaWSInteger

from LinearlyExplicitOver JuliaWSInteger

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JuliaWSInteger

from RetractableTo JuliaWSInteger

retract: % -> Symbol if JuliaWSInteger has RetractableTo Symbol

from RetractableTo Symbol

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JuliaWSInteger, failed)

from RetractableTo JuliaWSInteger

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

from RetractableTo Symbol

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer

from OrderedRing

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

string: % -> String

from JuliaObjectType

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

from CancellationAbelianMonoid

toString: % -> String

from JuliaWSObject

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

wholePart: % -> JuliaWSInteger

from QuotientFieldCategory JuliaWSInteger

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra JuliaWSInteger

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(JuliaWSInteger, JuliaWSInteger)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if JuliaWSInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JuliaWSInteger

CoercibleFrom Symbol if JuliaWSInteger has RetractableTo Symbol

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if JuliaWSInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo String

DifferentialExtension JuliaWSInteger

DifferentialRing

DivisionRing

Eltable(JuliaWSInteger, %) if JuliaWSInteger has Eltable(JuliaWSInteger, JuliaWSInteger)

EntireRing

EuclideanDomain

Evalable JuliaWSInteger if JuliaWSInteger has Evalable JuliaWSInteger

Field

FullyEvalableOver JuliaWSInteger

FullyLinearlyExplicitOver JuliaWSInteger

FullyPatternMatchable JuliaWSInteger

GcdDomain

InnerEvalable(JuliaWSInteger, JuliaWSInteger) if JuliaWSInteger has Evalable JuliaWSInteger

InnerEvalable(Symbol, JuliaWSInteger) if JuliaWSInteger has InnerEvalable(Symbol, JuliaWSInteger)

IntegralDomain

JuliaObjectRing

JuliaObjectType

JuliaRing

JuliaType

JuliaWSNumber

JuliaWSObject

JuliaWSRing

LeftModule %

LeftModule Fraction Integer

LeftModule JuliaWSInteger

LeftOreRing

LinearlyExplicitOver Integer if JuliaWSInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver JuliaWSInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module JuliaWSInteger

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra JuliaWSInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedRing

OrderedSet

PartialDifferentialRing Symbol if JuliaWSInteger has PartialDifferentialRing Symbol

PartialOrder

Patternable JuliaWSInteger

PatternMatchable Float if JuliaWSInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if JuliaWSInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

QuotientFieldCategory JuliaWSInteger

RealConstant

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JuliaWSInteger

RetractableTo Symbol if JuliaWSInteger has RetractableTo Symbol

RightModule %

RightModule Fraction Integer

RightModule Integer if JuliaWSInteger has LinearlyExplicitOver Integer

RightModule JuliaWSInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown