JuliaWSGaussianInteger

jws.spad line 995 [edit on github]

Julia Wolfram Symbolic gaussian integers using Wolfram Symbolic Transport Protocol.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

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

from RightModule Fraction Integer

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

from RightModule Integer

*: (%, JuliaWSInteger) -> %

from RightModule JuliaWSInteger

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

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (JuliaWSInteger, %) -> %

from LeftModule JuliaWSInteger

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

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

from Field

=: (%, %) -> Boolean

from BasicType

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

from ElementaryFunctionCategory

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

from RadicalCategory

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

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if JuliaWSInteger has RealNumberSystem

from ComplexCategory JuliaWSInteger

acos: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acosh: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acot: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acoth: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

acsc: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

acsch: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

argument: % -> JuliaWSInteger if JuliaWSInteger has TranscendentalFunctionCategory

from ComplexCategory JuliaWSInteger

asec: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asech: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

asin: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

asinh: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcTrigonometricFunctionCategory

atanh: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ArcHyperbolicFunctionCategory

basis: () -> Vector %

from FramedModule JuliaWSInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial JuliaWSInteger

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

charthRoot: % -> % if JuliaWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JuliaWSExpression

coerce: % -> OutputForm

from CoercibleTo OutputForm

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

from Algebra Fraction Integer

coerce: Integer -> %

coerce(x): convenience function.

coerce: JuliaWSInteger -> %

from CoercibleFrom JuliaWSInteger

commutator: (%, %) -> %

from NonAssociativeRng

complex: (JuliaWSInteger, JuliaWSInteger) -> %

from ComplexCategory JuliaWSInteger

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory JuliaWSInteger

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

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: % -> SparseUnivariatePolynomial JuliaWSInteger

from ConvertibleTo SparseUnivariatePolynomial JuliaWSInteger

convert: % -> String

from ConvertibleTo String

convert: % -> Vector JuliaWSInteger

from FramedModule JuliaWSInteger

convert: SparseUnivariatePolynomial JuliaWSInteger -> %

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

convert: Vector JuliaWSInteger -> %

from FramedModule JuliaWSInteger

coordinates: % -> Vector JuliaWSInteger

from FramedModule JuliaWSInteger

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

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

coordinates: Vector % -> Matrix JuliaWSInteger

from FramedModule JuliaWSInteger

cos: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

cosh: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

cot: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

coth: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if JuliaWSInteger has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

csch: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

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

definingPolynomial: () -> SparseUnivariatePolynomial JuliaWSInteger

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial 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

discreteLog: % -> NonNegativeInteger if JuliaWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from FieldOfPrimeCharacteristic

discriminant: () -> JuliaWSInteger

from FramedAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

discriminant: Vector % -> JuliaWSInteger

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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

from EuclideanDomain

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

from Eltable(JuliaWSInteger, %)

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

from Finite

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)

exp: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

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

from PrincipalIdealDomain

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

from EntireRing

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

from ComplexCategory JuliaWSInteger

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

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

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

hash: % -> SingleInteger if JuliaWSInteger has Hashable

from Hashable

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

from Hashable

imag: % -> JuliaWSInteger

from ComplexCategory JuliaWSInteger

imaginary: () -> %

from ComplexCategory JuliaWSInteger

index: PositiveInteger -> % if JuliaWSInteger has Finite

from Finite

init: % if JuliaWSInteger has FiniteFieldCategory

from StepThrough

inv: % -> % if JuliaWSInteger has Field

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

jWSGI: (JuliaWSInteger, JuliaWSInteger) -> %

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

jWSInterpret: (String, String) -> %

from JuliaWSObject

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 JuliaWSInteger

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

log: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from ElementaryFunctionCategory

lookup: % -> PositiveInteger if JuliaWSInteger has Finite

from Finite

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

from FullyEvalableOver JuliaWSInteger

minimalPolynomial: % -> SparseUnivariatePolynomial JuliaWSInteger if JuliaWSInteger has Field

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

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

from StepThrough

norm: % -> JuliaWSInteger

from ComplexCategory JuliaWSInteger

nothing?: % -> Boolean

from JuliaObjectType

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

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if JuliaWSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if JuliaWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

pi: () -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

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

from ComplexCategory JuliaWSInteger

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if JuliaWSInteger has FiniteFieldCategory

from FieldOfPrimeCharacteristic

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

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if JuliaWSInteger has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if JuliaWSInteger has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

random: () -> % if JuliaWSInteger has Finite

from Finite

random: JuliaWSInteger -> %

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

rank: () -> PositiveInteger

from FramedModule JuliaWSInteger

rational?: % -> Boolean

from ComplexCategory JuliaWSInteger

rational: % -> Fraction Integer

from ComplexCategory JuliaWSInteger

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

from ComplexCategory JuliaWSInteger

real: % -> JuliaWSInteger

from ComplexCategory JuliaWSInteger

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

reduce: SparseUnivariatePolynomial JuliaWSInteger -> %

from MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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

regularRepresentation: % -> Matrix JuliaWSInteger

from FramedAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

rem: (%, %) -> %

from EuclideanDomain

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

from FiniteFieldCategory

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

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

represents: Vector JuliaWSInteger -> %

from FramedModule JuliaWSInteger

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

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JuliaWSInteger

from RetractableTo JuliaWSInteger

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JuliaWSInteger, failed)

from RetractableTo JuliaWSInteger

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sech: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

sin: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

sinh: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

size: () -> NonNegativeInteger if JuliaWSInteger has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

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

from RadicalCategory

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

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

from FiniteFieldCategory

tan: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from TrigonometricFunctionCategory

tanh: % -> % if JuliaWSInteger has TranscendentalFunctionCategory

from HyperbolicFunctionCategory

toString: % -> String

from JuliaWSObject

trace: % -> JuliaWSInteger

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

traceMatrix: () -> Matrix JuliaWSInteger

from FramedAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

traceMatrix: Vector % -> Matrix JuliaWSInteger

from FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

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 JuliaWSInteger has Field

Algebra JuliaWSInteger

arbitraryPrecision if JuliaWSInteger has arbitraryPrecision

ArcHyperbolicFunctionCategory if JuliaWSInteger has TranscendentalFunctionCategory

ArcTrigonometricFunctionCategory if JuliaWSInteger has TranscendentalFunctionCategory

BasicType

BiModule(%, %)

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

BiModule(JuliaWSInteger, JuliaWSInteger)

CancellationAbelianMonoid

canonicalsClosed if JuliaWSInteger has Field

canonicalUnitNormal if JuliaWSInteger has Field

CharacteristicNonZero if JuliaWSInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer if JuliaWSInteger has RetractableTo Fraction Integer

CoercibleFrom Integer

CoercibleFrom JuliaWSInteger

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory JuliaWSInteger

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if JuliaWSInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial JuliaWSInteger

ConvertibleTo String

DifferentialExtension JuliaWSInteger

DifferentialRing

DivisionRing if JuliaWSInteger has Field

ElementaryFunctionCategory if JuliaWSInteger has TranscendentalFunctionCategory

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

EntireRing

EuclideanDomain

Evalable JuliaWSInteger if JuliaWSInteger has Evalable JuliaWSInteger

Field if JuliaWSInteger has Field

FieldOfPrimeCharacteristic if JuliaWSInteger has FiniteFieldCategory

Finite if JuliaWSInteger has Finite

FiniteFieldCategory if JuliaWSInteger has FiniteFieldCategory

FiniteRankAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

FramedAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

FramedModule JuliaWSInteger

FullyEvalableOver JuliaWSInteger

FullyLinearlyExplicitOver JuliaWSInteger

FullyPatternMatchable JuliaWSInteger

FullyRetractableTo JuliaWSInteger

GcdDomain

Hashable if JuliaWSInteger has Hashable

HyperbolicFunctionCategory if JuliaWSInteger has TranscendentalFunctionCategory

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 if JuliaWSInteger has Field

LeftModule JuliaWSInteger

LeftOreRing

LinearlyExplicitOver Integer if JuliaWSInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver JuliaWSInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer if JuliaWSInteger has Field

Module JuliaWSInteger

MonogenicAlgebra(JuliaWSInteger, SparseUnivariatePolynomial JuliaWSInteger)

Monoid

multiplicativeValuation

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer if JuliaWSInteger has Field

NonAssociativeAlgebra JuliaWSInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if JuliaWSInteger has PartialDifferentialRing Symbol

Patternable JuliaWSInteger

PatternMatchable Float if JuliaWSInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if JuliaWSInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory if JuliaWSInteger has RadicalCategory and JuliaWSInteger has TranscendentalFunctionCategory

RetractableTo Fraction Integer if JuliaWSInteger has RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JuliaWSInteger

RightModule %

RightModule Fraction Integer if JuliaWSInteger has Field

RightModule Integer if JuliaWSInteger has LinearlyExplicitOver Integer

RightModule JuliaWSInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if JuliaWSInteger has FiniteFieldCategory

TranscendentalFunctionCategory if JuliaWSInteger has TranscendentalFunctionCategory

TrigonometricFunctionCategory if JuliaWSInteger has TranscendentalFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown