WSGaussianInteger

jws.spad line 1005 [edit on github]

Julia Wolfram Symbolic gaussian integers using the MathLink Julia package.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

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

from RightModule Fraction Integer

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

from RightModule Integer

*: (%, WSInteger) -> %

from RightModule WSInteger

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

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

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

from Field

=: (%, %) -> Boolean

from BasicType

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

from ElementaryFunctionCategory

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

from RadicalCategory

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

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if WSInteger has RealNumberSystem

from ComplexCategory WSInteger

acos: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acosh: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acot: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acoth: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acsc: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acsch: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

argument: % -> WSInteger if WSInteger has TranscendentalFunctionCategory

from ComplexCategory WSInteger

asec: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asech: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

asin: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asinh: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

atanh: % -> % if WSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

basis: () -> Vector %

from FramedModule WSInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial WSInteger

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

charthRoot: % -> % if WSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: % -> WSExpression

coerce(x): convenience function.

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

from Algebra Fraction Integer

coerce: Integer -> %

coerce(x): convenience function.

coerce: WSInteger -> %

from CoercibleFrom WSInteger

commutator: (%, %) -> %

from NonAssociativeRng

complex: (WSInteger, WSInteger) -> %

from ComplexCategory WSInteger

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory WSInteger

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

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: % -> SparseUnivariatePolynomial WSInteger

from ConvertibleTo SparseUnivariatePolynomial WSInteger

convert: % -> String

from ConvertibleTo String

convert: % -> Vector WSInteger

from FramedModule WSInteger

convert: SparseUnivariatePolynomial WSInteger -> %

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

convert: Vector WSInteger -> %

from FramedModule WSInteger

coordinates: % -> Vector WSInteger

from FramedModule WSInteger

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

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

coordinates: Vector % -> Matrix WSInteger

from FramedModule WSInteger

cos: % -> % if WSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

cosh: % -> % if WSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

cot: % -> % if WSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

coth: % -> % if WSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if WSInteger has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> % if WSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

csch: % -> % if WSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

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

definingPolynomial: () -> SparseUnivariatePolynomial WSInteger

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial 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

discreteLog: % -> NonNegativeInteger if WSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from FieldOfPrimeCharacteristic

discriminant: () -> WSInteger

from FramedAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

discriminant: Vector % -> WSInteger

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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

from EuclideanDomain

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

from Eltable(WSInteger, %)

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

from Finite

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)

exp: % -> % if WSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

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

from PrincipalIdealDomain

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

from EntireRing

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

from ComplexCategory WSInteger

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

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

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

hash: % -> SingleInteger if WSInteger has Hashable

from Hashable

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

from Hashable

imag: % -> WSInteger

from ComplexCategory WSInteger

imaginary: () -> %

from ComplexCategory WSInteger

index: PositiveInteger -> % if WSInteger has Finite

from Finite

init: % if WSInteger has FiniteFieldCategory

from StepThrough

inv: % -> % if WSInteger 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

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

jWSGI: (WSInteger, WSInteger) -> %

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

jWSInterpret: (String, String) -> %

from WSObject

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 WSInteger

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

log: % -> % if WSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

lookup: % -> PositiveInteger if WSInteger has Finite

from Finite

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

from FullyEvalableOver WSInteger

minimalPolynomial: % -> SparseUnivariatePolynomial WSInteger if WSInteger has Field

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

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

from StepThrough

norm: % -> WSInteger

from ComplexCategory WSInteger

nothing?: % -> Boolean

from JLObjectType

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

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if WSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if WSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

pi: () -> % if WSInteger has TranscendentalFunctionCategory

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

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

from ComplexCategory WSInteger

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if WSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

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

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if WSInteger has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if WSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

random: () -> % if WSInteger has Finite

from Finite

random: WSInteger -> %

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

rank: () -> PositiveInteger

from FramedModule WSInteger

rational?: % -> Boolean

from ComplexCategory WSInteger

rational: % -> Fraction Integer

from ComplexCategory WSInteger

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

from ComplexCategory WSInteger

real: % -> WSInteger

from ComplexCategory WSInteger

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

reduce: SparseUnivariatePolynomial WSInteger -> %

from MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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

regularRepresentation: % -> Matrix WSInteger

from FramedAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

rem: (%, %) -> %

from EuclideanDomain

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

from FiniteFieldCategory

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

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

represents: Vector WSInteger -> %

from FramedModule WSInteger

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

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> WSInteger

from RetractableTo WSInteger

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(WSInteger, failed)

from RetractableTo WSInteger

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if WSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sech: % -> % if WSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

sin: % -> % if WSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sinh: % -> % if WSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

size: () -> NonNegativeInteger if WSInteger has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

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

from RadicalCategory

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

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

from FiniteFieldCategory

tan: % -> % if WSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

tanh: % -> % if WSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

toString: % -> String

from WSObject

trace: % -> WSInteger

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

traceMatrix: () -> Matrix WSInteger

from FramedAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

traceMatrix: Vector % -> Matrix WSInteger

from FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

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 WSInteger has Field

Algebra WSInteger

arbitraryPrecision if WSInteger has arbitraryPrecision

ArcHyperbolicFunctionCategory if WSInteger has TranscendentalFunctionCategory

ArcTrigonometricFunctionCategory if WSInteger has TranscendentalFunctionCategory

BasicType

BiModule(%, %)

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

BiModule(WSInteger, WSInteger)

CancellationAbelianMonoid

canonicalsClosed if WSInteger has Field

canonicalUnitNormal if WSInteger has Field

CharacteristicNonZero if WSInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer if WSInteger has RetractableTo Fraction Integer

CoercibleFrom Integer

CoercibleFrom WSInteger

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory WSInteger

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if WSInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial WSInteger

ConvertibleTo String

DifferentialExtension WSInteger

DifferentialRing

DivisionRing if WSInteger has Field

ElementaryFunctionCategory if WSInteger has TranscendentalFunctionCategory

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

EntireRing

EuclideanDomain

Evalable WSInteger if WSInteger has Evalable WSInteger

Field if WSInteger has Field

FieldOfPrimeCharacteristic if WSInteger has FiniteFieldCategory

Finite if WSInteger has Finite

FiniteFieldCategory if WSInteger has FiniteFieldCategory

FiniteRankAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

FramedAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

FramedModule WSInteger

FullyEvalableOver WSInteger

FullyLinearlyExplicitOver WSInteger

FullyPatternMatchable WSInteger

FullyRetractableTo WSInteger

GcdDomain

Hashable if WSInteger has Hashable

HyperbolicFunctionCategory if WSInteger has TranscendentalFunctionCategory

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 if WSInteger has Field

LeftModule WSInteger

LeftOreRing

LinearlyExplicitOver Integer if WSInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver WSInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer if WSInteger has Field

Module WSInteger

MonogenicAlgebra(WSInteger, SparseUnivariatePolynomial WSInteger)

Monoid

multiplicativeValuation

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer if WSInteger has Field

NonAssociativeAlgebra WSInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if WSInteger has PartialDifferentialRing Symbol

Patternable WSInteger

PatternMatchable Float if WSInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if WSInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory if WSInteger has TranscendentalFunctionCategory and WSInteger has RadicalCategory

RetractableTo Fraction Integer if WSInteger has RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo WSInteger

RightModule %

RightModule Fraction Integer if WSInteger has Field

RightModule Integer if WSInteger has LinearlyExplicitOver Integer

RightModule WSInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if WSInteger has FiniteFieldCategory

TranscendentalFunctionCategory if WSInteger has TranscendentalFunctionCategory

TrigonometricFunctionCategory if WSInteger has TranscendentalFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown

WSNumber

WSObject

WSRing