JLWSRational

jws.spad line 305 [edit on github]

JL 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 JLWSInteger has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, JLWSInteger) -> %

from RightModule JLWSInteger

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (JLWSInteger, %) -> %

from LeftModule JLWSInteger

*: (NMInteger, %) -> %

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (JLWSInteger, JLWSInteger) -> %

from QuotientFieldCategory JLWSInteger

<=: (%, %) -> 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: % -> JLWSInteger

from QuotientFieldCategory JLWSInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> JLWSExpression

coerce(q) coerces q. Convenience function.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

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

coerce: JLWSInteger -> %

from Algebra JLWSInteger

coerce: Symbol -> % if JLWSInteger has RetractableTo Symbol

from CoercibleFrom Symbol

commutator: (%, %) -> %

from NonAssociativeRng

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

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> String

from ConvertibleTo String

D: % -> %

from DifferentialRing

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

from DifferentialExtension JLWSInteger

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

from DifferentialExtension JLWSInteger

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

denom: % -> JLWSInteger

from QuotientFieldCategory JLWSInteger

denominator: % -> %

from QuotientFieldCategory JLWSInteger

differentiate: % -> %

from DifferentialRing

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

from DifferentialExtension JLWSInteger

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

from DifferentialExtension JLWSInteger

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from EuclideanDomain

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

from Eltable(JLWSInteger, %)

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable JLWSInteger

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

from InnerEvalable(JLWSInteger, JLWSInteger)

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

from Evalable JLWSInteger

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

from InnerEvalable(JLWSInteger, JLWSInteger)

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

from InnerEvalable(Symbol, JLWSInteger)

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

from InnerEvalable(Symbol, JLWSInteger)

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 JLWSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

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

from PolynomialFactorizationExplicit

floor: % -> JLWSInteger

from QuotientFieldCategory JLWSInteger

fractionPart: % -> %

from QuotientFieldCategory JLWSInteger

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

jlEval: % -> %

from JLWSObject

jlHead: % -> JLWSSymbol

from JLWSObject

jlId: % -> JLInt64

from JLObjectType

jlNumeric: % -> %

from JLWSObject

jlNumeric: (%, PositiveInteger) -> %

from JLWSObject

jlObject: () -> String

from JLObjectType

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlSymbolic: % -> String

from JLWSObject

jlType: % -> String

from JLObjectType

jWSInterpret: (String, String) -> %

from JLWSObject

jWSRat: Fraction Integer -> %

jWSRat(q) constructs q as a JLWSRational.

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: (JLWSInteger -> JLWSInteger, %) -> %

from FullyEvalableOver JLWSInteger

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

negative?: % -> Boolean

from OrderedRing

nextItem: % -> Union(%, failed)

from StepThrough

nothing?: % -> Boolean

from JLObjectType

numer: % -> JLWSInteger

from QuotientFieldCategory JLWSInteger

numerator: % -> %

from QuotientFieldCategory JLWSInteger

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

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

from PatternMatchable Float

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

from PatternMatchable Integer

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

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 JLWSInteger has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver JLWSInteger

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

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JLWSInteger

from LinearlyExplicitOver JLWSInteger

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JLWSInteger

from RetractableTo JLWSInteger

retract: % -> Symbol if JLWSInteger has RetractableTo Symbol

from RetractableTo Symbol

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JLWSInteger, failed)

from RetractableTo JLWSInteger

retractIfCan: % -> Union(Symbol, failed) if JLWSInteger 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 JLWSInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

string: % -> String

from JLType

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

from CancellationAbelianMonoid

toString: % -> String

from JLWSObject

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

wholePart: % -> JLWSInteger

from QuotientFieldCategory JLWSInteger

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra JLWSInteger

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(JLWSInteger, JLWSInteger)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if JLWSInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JLWSInteger

CoercibleFrom Symbol if JLWSInteger has RetractableTo Symbol

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if JLWSInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo String

DifferentialExtension JLWSInteger

DifferentialRing

DivisionRing

Eltable(JLWSInteger, %) if JLWSInteger has Eltable(JLWSInteger, JLWSInteger)

EntireRing

EuclideanDomain

Evalable JLWSInteger if JLWSInteger has Evalable JLWSInteger

Field

FullyEvalableOver JLWSInteger

FullyLinearlyExplicitOver JLWSInteger

FullyPatternMatchable JLWSInteger

GcdDomain

InnerEvalable(JLWSInteger, JLWSInteger) if JLWSInteger has Evalable JLWSInteger

InnerEvalable(Symbol, JLWSInteger) if JLWSInteger has InnerEvalable(Symbol, JLWSInteger)

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

JLWSNumber

JLWSObject

JLWSRing

LeftModule %

LeftModule Fraction Integer

LeftModule JLWSInteger

LeftOreRing

LinearlyExplicitOver Integer if JLWSInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver JLWSInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module JLWSInteger

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra JLWSInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedRing

OrderedSet

PartialDifferentialRing Symbol if JLWSInteger has PartialDifferentialRing Symbol

PartialOrder

Patternable JLWSInteger

PatternMatchable Float if JLWSInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if JLWSInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

QuotientFieldCategory JLWSInteger

RealConstant

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JLWSInteger

RetractableTo Symbol if JLWSInteger has RetractableTo Symbol

RightModule %

RightModule Fraction Integer

RightModule Integer if JLWSInteger has LinearlyExplicitOver Integer

RightModule JLWSInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown