JLWSGaussianInteger

jws.spad line 995 [edit on github]

JL Wolfram Symbolic gaussian integers using Wolfram Symbolic Transport Protocol.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> % if JLWSInteger has Field

from RightModule Fraction Integer

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

from RightModule Integer

*: (%, JLWSInteger) -> %

from RightModule JLWSInteger

*: (Fraction Integer, %) -> % if JLWSInteger has Field

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

/: (%, %) -> % if JLWSInteger has Field

from Field

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % if JLWSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> % if JLWSInteger has TranscendentalFunctionCategory and JLWSInteger has RadicalCategory

from RadicalCategory

^: (%, Integer) -> % if JLWSInteger has Field

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if JLWSInteger has RealNumberSystem

from ComplexCategory JLWSInteger

acos: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acosh: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acot: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acoth: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acsc: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acsch: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

argument: % -> JLWSInteger if JLWSInteger has TranscendentalFunctionCategory

from ComplexCategory JLWSInteger

asec: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asech: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

asin: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asinh: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

atanh: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

basis: () -> Vector %

from FramedModule JLWSInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial JLWSInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

charthRoot: % -> % if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> JLWSExpression

coerce(x): convenience function.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> % if JLWSInteger has RetractableTo Fraction Integer or JLWSInteger has Field

from Algebra Fraction Integer

coerce: Integer -> %

coerce(x): convenience function.

coerce: JLWSInteger -> %

from Algebra JLWSInteger

commutator: (%, %) -> %

from NonAssociativeRng

complex: (JLWSInteger, JLWSInteger) -> %

from ComplexCategory JLWSInteger

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory JLWSInteger

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

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: % -> SparseUnivariatePolynomial JLWSInteger

from ConvertibleTo SparseUnivariatePolynomial JLWSInteger

convert: % -> String

from ConvertibleTo String

convert: % -> Vector JLWSInteger

from FramedModule JLWSInteger

convert: SparseUnivariatePolynomial JLWSInteger -> %

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

convert: Vector JLWSInteger -> %

from FramedModule JLWSInteger

coordinates: % -> Vector JLWSInteger

from FramedModule JLWSInteger

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

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

coordinates: (Vector %, Vector %) -> Matrix JLWSInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

coordinates: Vector % -> Matrix JLWSInteger

from FramedModule JLWSInteger

cos: % -> % if JLWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

cosh: % -> % if JLWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

cot: % -> % if JLWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

coth: % -> % if JLWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> % if JLWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

csch: % -> % if JLWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

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

definingPolynomial: () -> SparseUnivariatePolynomial JLWSInteger

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

derivationCoordinates: (Vector %, JLWSInteger -> JLWSInteger) -> Matrix JLWSInteger if JLWSInteger has Field

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial 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

discreteLog: % -> NonNegativeInteger if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

discreteLog: (%, %) -> Union(NonNegativeInteger, failed) if JLWSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

discriminant: () -> JLWSInteger

from FramedAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

discriminant: Vector % -> JLWSInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

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

from EuclideanDomain

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

from Eltable(JLWSInteger, %)

enumerate: () -> List % if JLWSInteger has Finite

from Finite

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)

exp: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

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

from PrincipalIdealDomain

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

from EntireRing

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

from ComplexCategory JLWSInteger

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

factorsOfCyclicGroupSize: () -> List Record(factor: Integer, exponent: NonNegativeInteger) if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

hash: % -> SingleInteger if JLWSInteger has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if JLWSInteger has Hashable

from Hashable

imag: % -> JLWSInteger

from ComplexCategory JLWSInteger

imaginary: () -> %

from ComplexCategory JLWSInteger

index: PositiveInteger -> % if JLWSInteger has Finite

from Finite

init: % if JLWSInteger has FiniteFieldCategory

from StepThrough

inv: % -> % if JLWSInteger has Field

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

jWSGI: (JLWSInteger, JLWSInteger) -> %

jWSGI(re, im) constructs a JLWSGaussianInteger from real part re and imaginary part im.

jWSInterpret: (String, String) -> %

from JLWSObject

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

lift: % -> SparseUnivariatePolynomial JLWSInteger

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

log: % -> % if JLWSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

lookup: % -> PositiveInteger if JLWSInteger has Finite

from Finite

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

from FullyEvalableOver JLWSInteger

minimalPolynomial: % -> SparseUnivariatePolynomial JLWSInteger if JLWSInteger has Field

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

nextItem: % -> Union(%, failed) if JLWSInteger has FiniteFieldCategory

from StepThrough

norm: % -> JLWSInteger

from ComplexCategory JLWSInteger

nothing?: % -> Boolean

from JLObjectType

nthRoot: (%, Integer) -> % if JLWSInteger has TranscendentalFunctionCategory and JLWSInteger has RadicalCategory

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if JLWSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

pi: () -> % if JLWSInteger has TranscendentalFunctionCategory

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

polarCoordinates: % -> Record(r: JLWSInteger, phi: JLWSInteger) if JLWSInteger has TranscendentalFunctionCategory and JLWSInteger has RealNumberSystem

from ComplexCategory JLWSInteger

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if JLWSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

primeFrobenius: (%, NonNegativeInteger) -> % if JLWSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

random: () -> % if JLWSInteger has Finite

from Finite

random: JLWSInteger -> %

random(n) returns a gaussian integer where real part is in the range 0..n as the imagniray part.

rank: () -> PositiveInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

rational?: % -> Boolean

from ComplexCategory JLWSInteger

rational: % -> Fraction Integer

from ComplexCategory JLWSInteger

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

from ComplexCategory JLWSInteger

real: % -> JLWSInteger

from ComplexCategory JLWSInteger

recip: % -> Union(%, failed)

from MagmaWithUnit

reduce: Fraction SparseUnivariatePolynomial JLWSInteger -> Union(%, failed) if JLWSInteger has Field

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

reduce: SparseUnivariatePolynomial JLWSInteger -> %

from MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

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

regularRepresentation: % -> Matrix JLWSInteger

from FramedAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

regularRepresentation: (%, Vector %) -> Matrix JLWSInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

rem: (%, %) -> %

from EuclideanDomain

representationType: () -> Union(prime, polynomial, normal, cyclic) if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

represents: Vector JLWSInteger -> %

from FramedModule JLWSInteger

retract: % -> Fraction Integer if JLWSInteger has RetractableTo Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JLWSInteger

from RetractableTo JLWSInteger

retractIfCan: % -> Union(Fraction Integer, failed) if JLWSInteger has RetractableTo Fraction Integer

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JLWSInteger, failed)

from RetractableTo JLWSInteger

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if JLWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sech: % -> % if JLWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

sin: % -> % if JLWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sinh: % -> % if JLWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

size: () -> NonNegativeInteger if JLWSInteger has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

sqrt: % -> % if JLWSInteger has TranscendentalFunctionCategory and JLWSInteger has RadicalCategory

from RadicalCategory

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

tableForDiscreteLogarithm: Integer -> Table(PositiveInteger, NonNegativeInteger) if JLWSInteger has FiniteFieldCategory

from FiniteFieldCategory

tan: % -> % if JLWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

tanh: % -> % if JLWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

toString: % -> String

from JLWSObject

trace: % -> JLWSInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

traceMatrix: () -> Matrix JLWSInteger

from FramedAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

traceMatrix: Vector % -> Matrix JLWSInteger

from FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer if JLWSInteger has Field

Algebra JLWSInteger

arbitraryPrecision if JLWSInteger has arbitraryPrecision

ArcHyperbolicFunctionCategory if JLWSInteger has TranscendentalFunctionCategory

ArcTrigonometricFunctionCategory if JLWSInteger has TranscendentalFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer) if JLWSInteger has Field

BiModule(JLWSInteger, JLWSInteger)

CancellationAbelianMonoid

canonicalsClosed if JLWSInteger has Field

canonicalUnitNormal if JLWSInteger has Field

CharacteristicNonZero if JLWSInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer if JLWSInteger has RetractableTo Fraction Integer

CoercibleFrom Integer

CoercibleFrom JLWSInteger

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory JLWSInteger

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if JLWSInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial JLWSInteger

ConvertibleTo String

DifferentialExtension JLWSInteger

DifferentialRing

DivisionRing if JLWSInteger has Field

ElementaryFunctionCategory if JLWSInteger has TranscendentalFunctionCategory

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

EntireRing

EuclideanDomain

Evalable JLWSInteger if JLWSInteger has Evalable JLWSInteger

Field if JLWSInteger has Field

FieldOfPrimeCharacteristic if JLWSInteger has FiniteFieldCategory

Finite if JLWSInteger has Finite

FiniteFieldCategory if JLWSInteger has FiniteFieldCategory

FiniteRankAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

FramedAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

FramedModule JLWSInteger

FullyEvalableOver JLWSInteger

FullyLinearlyExplicitOver JLWSInteger

FullyPatternMatchable JLWSInteger

FullyRetractableTo JLWSInteger

GcdDomain

Hashable if JLWSInteger has Hashable

HyperbolicFunctionCategory if JLWSInteger has TranscendentalFunctionCategory

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 if JLWSInteger has Field

LeftModule JLWSInteger

LeftOreRing

LinearlyExplicitOver Integer if JLWSInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver JLWSInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer if JLWSInteger has Field

Module JLWSInteger

MonogenicAlgebra(JLWSInteger, SparseUnivariatePolynomial JLWSInteger)

Monoid

multiplicativeValuation

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer if JLWSInteger has Field

NonAssociativeAlgebra JLWSInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if JLWSInteger has PartialDifferentialRing Symbol

Patternable JLWSInteger

PatternMatchable Float if JLWSInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if JLWSInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory if JLWSInteger has TranscendentalFunctionCategory and JLWSInteger has RadicalCategory

RetractableTo Fraction Integer if JLWSInteger has RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JLWSInteger

RightModule %

RightModule Fraction Integer if JLWSInteger has Field

RightModule Integer if JLWSInteger has LinearlyExplicitOver Integer

RightModule JLWSInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if JLWSInteger has FiniteFieldCategory

TranscendentalFunctionCategory if JLWSInteger has TranscendentalFunctionCategory

TrigonometricFunctionCategory if JLWSInteger has TranscendentalFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown