JLWSAPComplex prec

jws.spad line 1342 [edit on github]

Julia Wolfram Symbolic arbitrary precision complex numbers using Wolfram Symbolic Transport Protocol.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

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

from RightModule Integer

*: (%, JLWSAPReal prec) -> %

from RightModule JLWSAPReal prec

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (JLWSAPReal prec, %) -> %

from LeftModule JLWSAPReal prec

*: (JLWSInteger, %) -> %

n * z multiplies n by z.

*: (NMInteger, %) -> %

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from ComplexCategory JLWSAPReal prec

acos: % -> %

from ArcTrigonometricFunctionCategory

acosh: % -> %

from ArcHyperbolicFunctionCategory

acot: % -> %

from ArcTrigonometricFunctionCategory

acoth: % -> %

from ArcHyperbolicFunctionCategory

acsc: % -> %

from ArcTrigonometricFunctionCategory

acsch: % -> %

from ArcHyperbolicFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

argument: % -> JLWSAPReal prec

from ComplexCategory JLWSAPReal prec

asec: % -> %

from ArcTrigonometricFunctionCategory

asech: % -> %

from ArcHyperbolicFunctionCategory

asin: % -> %

from ArcTrigonometricFunctionCategory

asinh: % -> %

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> %

from ArcTrigonometricFunctionCategory

atan: (%, %) -> %

atan(z1,z2) computes the arc tangent of z2/z1.

atanh: % -> %

from ArcHyperbolicFunctionCategory

basis: () -> Vector %

from FramedModule JLWSAPReal prec

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

charthRoot: % -> % if JLWSAPReal prec has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

Chi: % -> %

from LiouvillianFunctionCategory

Ci: % -> %

from LiouvillianFunctionCategory

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> JLWSExpression

coerce(cplx) coerces cplx. Convenience function.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Complex Integer -> %

coerce(gi) coerces gi. Convenience function.

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

coerce(i): convenience function.

coerce: JLWSAPReal prec -> %

from CoercibleFrom JLWSAPReal prec

coerce: JLWSInteger -> %

coerce(int): coerces int. Convenience function.

commutator: (%, %) -> %

from NonAssociativeRng

complex: (JLWSAPReal prec, JLWSAPReal prec) -> %

complex(re, im) returns the complex number from real part re and imaginary part im.

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory JLWSAPReal prec

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

convert: % -> InputForm if JLWSAPReal prec has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if JLWSAPReal prec has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> SparseUnivariatePolynomial JLWSAPReal prec

from ConvertibleTo SparseUnivariatePolynomial JLWSAPReal prec

convert: % -> String

from ConvertibleTo String

convert: % -> Vector JLWSAPReal prec

from FramedModule JLWSAPReal prec

convert: SparseUnivariatePolynomial JLWSAPReal prec -> %

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

convert: Vector JLWSAPReal prec -> %

from FramedModule JLWSAPReal prec

coordinates: % -> Vector JLWSAPReal prec

from FramedModule JLWSAPReal prec

coordinates: (%, Vector %) -> Vector JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

coordinates: (Vector %, Vector %) -> Matrix JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

coordinates: Vector % -> Matrix JLWSAPReal prec

from FramedModule JLWSAPReal prec

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if JLWSAPReal prec has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

D: (%, JLWSAPReal prec -> JLWSAPReal prec) -> %

from DifferentialExtension JLWSAPReal prec

D: (%, JLWSAPReal prec -> JLWSAPReal prec, NonNegativeInteger) -> %

from DifferentialExtension JLWSAPReal prec

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

definingPolynomial: () -> SparseUnivariatePolynomial JLWSAPReal prec

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

derivationCoordinates: (Vector %, JLWSAPReal prec -> JLWSAPReal prec) -> Matrix JLWSAPReal prec

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

differentiate: % -> %

from DifferentialRing

differentiate: (%, JLWSAPReal prec -> JLWSAPReal prec) -> %

from DifferentialExtension JLWSAPReal prec

differentiate: (%, JLWSAPReal prec -> JLWSAPReal prec, NonNegativeInteger) -> %

from DifferentialExtension JLWSAPReal prec

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

dilog: % -> %

from LiouvillianFunctionCategory

discreteLog: % -> NonNegativeInteger if JLWSAPReal prec has FiniteFieldCategory

from FiniteFieldCategory

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

from FieldOfPrimeCharacteristic

discriminant: () -> JLWSAPReal prec

from FramedAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

discriminant: Vector % -> JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

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

from EuclideanDomain

Ei: % -> %

from LiouvillianFunctionCategory

elt: (%, JLWSAPReal prec) -> % if JLWSAPReal prec has Eltable(JLWSAPReal prec, JLWSAPReal prec)

from Eltable(JLWSAPReal prec, %)

enumerate: () -> List % if JLWSAPReal prec has Finite

from Finite

erf: % -> %

from LiouvillianFunctionCategory

erf: (%, %) -> %

erf(z) the error function of z.

erfc: % -> %

erfc(z) returns the complementary error function of z.

erfi: % -> %

from LiouvillianFunctionCategory

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable JLWSAPReal prec

eval: (%, JLWSAPReal prec, JLWSAPReal prec) -> % if JLWSAPReal prec has Evalable JLWSAPReal prec

from InnerEvalable(JLWSAPReal prec, JLWSAPReal prec)

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

from Evalable JLWSAPReal prec

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

from InnerEvalable(JLWSAPReal prec, JLWSAPReal prec)

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

from InnerEvalable(Symbol, JLWSAPReal prec)

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

from InnerEvalable(Symbol, JLWSAPReal prec)

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the JLWSAPReal ℯ (%e or exp(1)).

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

from PrincipalIdealDomain

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

from EntireRing

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

from ComplexCategory JLWSAPReal prec

extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLWSAPReal prec has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

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

from FiniteFieldCategory

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLWSAPReal prec has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

fresnelC: % -> %

from LiouvillianFunctionCategory

fresnelS: % -> %

from LiouvillianFunctionCategory

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

hash: % -> SingleInteger if JLWSAPReal prec has Hashable

from Hashable

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

from Hashable

imag: % -> JLWSAPReal prec

from ComplexCategory JLWSAPReal prec

imaginary: () -> %

from ComplexCategory JLWSAPReal prec

index: PositiveInteger -> % if JLWSAPReal prec has Finite

from Finite

init: % if JLWSAPReal prec has FiniteFieldCategory

from StepThrough

integral: (%, SegmentBinding %) -> %

from PrimitiveFunctionCategory

integral: (%, Symbol) -> %

from PrimitiveFunctionCategory

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

jlApprox?: (%, %) -> Boolean

jlApprox?(x,y) computes inexact equality comparison with WS default parameters (Equal).

jlDisplay: % -> Void

from JLObjectType

jlDump: JLObject -> 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

jWSComplex: (JLWSAPReal prec, JLWSAPReal prec) -> %

jWSComplex(re, im) constructs a JLWSComplex from real part re and imaginary part im.

jWSComplex: JLWSAPReal prec -> %

jWSComplex(re) constructs a JLWSComplex with real part re.

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

li: % -> %

from LiouvillianFunctionCategory

lift: % -> SparseUnivariatePolynomial JLWSAPReal prec

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

log10: % -> %

log10(z) compute logarithm of z in base 10.

log2: % -> %

log2(z) compute logarithm of z in base 2.

log: % -> %

from ElementaryFunctionCategory

lookup: % -> PositiveInteger if JLWSAPReal prec has Finite

from Finite

map: (JLWSAPReal prec -> JLWSAPReal prec, %) -> %

from FullyEvalableOver JLWSAPReal prec

minimalPolynomial: % -> SparseUnivariatePolynomial JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

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

from StepThrough

norm: % -> JLWSAPReal prec

from ComplexCategory JLWSAPReal prec

nothing?: % -> Boolean

from JLObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if JLWSAPReal prec has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if JLWSAPReal prec has FiniteFieldCategory

from FiniteFieldCategory

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

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if JLWSAPReal prec has PatternMatchable Integer

from PatternMatchable Integer

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

polarCoordinates: % -> Record(r: JLWSAPReal prec, phi: JLWSAPReal prec)

from ComplexCategory JLWSAPReal prec

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if JLWSAPReal prec has FiniteFieldCategory

from FieldOfPrimeCharacteristic

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

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if JLWSAPReal prec has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if JLWSAPReal prec has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

random: () -> % if JLWSAPReal prec has Finite

from Finite

rank: () -> PositiveInteger

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

rational?: % -> Boolean if JLWSAPReal prec has IntegerNumberSystem

from ComplexCategory JLWSAPReal prec

rational: % -> Fraction Integer if JLWSAPReal prec has IntegerNumberSystem

from ComplexCategory JLWSAPReal prec

rationalIfCan: % -> Union(Fraction Integer, failed) if JLWSAPReal prec has IntegerNumberSystem

from ComplexCategory JLWSAPReal prec

real: % -> JLWSAPReal prec

from ComplexCategory JLWSAPReal prec

recip: % -> Union(%, failed)

from MagmaWithUnit

reduce: Fraction SparseUnivariatePolynomial JLWSAPReal prec -> Union(%, failed)

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

reduce: SparseUnivariatePolynomial JLWSAPReal prec -> %

from MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JLWSAPReal prec has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver JLWSAPReal prec

reducedSystem: Matrix % -> Matrix Integer if JLWSAPReal prec has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JLWSAPReal prec

from LinearlyExplicitOver JLWSAPReal prec

regularRepresentation: % -> Matrix JLWSAPReal prec

from FramedAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

regularRepresentation: (%, Vector %) -> Matrix JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

rem: (%, %) -> %

from EuclideanDomain

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

from FiniteFieldCategory

represents: (Vector JLWSAPReal prec, Vector %) -> %

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

represents: Vector JLWSAPReal prec -> %

from FramedModule JLWSAPReal prec

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JLWSAPReal prec

from RetractableTo JLWSAPReal prec

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JLWSAPReal prec, failed)

from RetractableTo JLWSAPReal prec

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

Shi: % -> %

from LiouvillianFunctionCategory

Si: % -> %

from LiouvillianFunctionCategory

sin: % -> %

from TrigonometricFunctionCategory

sinc: % -> %

sinc(z) compues the unormalized sinc of z, sin(z)/z and 0 if z = 0.

sinh: % -> %

from HyperbolicFunctionCategory

size: () -> NonNegativeInteger if JLWSAPReal prec has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLWSAPReal prec has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

string: % -> String

from JLType

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

from CancellationAbelianMonoid

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

from FiniteFieldCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

toString: % -> String

from JLWSObject

toString: (%, JLWSExpression) -> String

toString(expr, form) returns the string representation of expr with WS language format form.

trace: % -> JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

traceMatrix: () -> Matrix JLWSAPReal prec

from FramedAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

traceMatrix: Vector % -> Matrix JLWSAPReal prec

from FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

urand01: () -> %

urand01() returns a unit square random complex number.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra JLWSAPReal prec

arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(JLWSAPReal prec, JLWSAPReal prec)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if JLWSAPReal prec has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JLWSAPReal prec

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory JLWSAPReal prec

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm if JLWSAPReal prec has ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if JLWSAPReal prec has ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial JLWSAPReal prec

ConvertibleTo String

DifferentialExtension JLWSAPReal prec

DifferentialRing

DivisionRing

ElementaryFunctionCategory

Eltable(JLWSAPReal prec, %) if JLWSAPReal prec has Eltable(JLWSAPReal prec, JLWSAPReal prec)

EntireRing

EuclideanDomain

Evalable JLWSAPReal prec if JLWSAPReal prec has Evalable JLWSAPReal prec

Field

FieldOfPrimeCharacteristic if JLWSAPReal prec has FiniteFieldCategory

Finite if JLWSAPReal prec has Finite

FiniteFieldCategory if JLWSAPReal prec has FiniteFieldCategory

FiniteRankAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

FramedAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

FramedModule JLWSAPReal prec

FullyEvalableOver JLWSAPReal prec

FullyLinearlyExplicitOver JLWSAPReal prec

FullyPatternMatchable JLWSAPReal prec

FullyRetractableTo JLWSAPReal prec

GcdDomain

Hashable if JLWSAPReal prec has Hashable

HyperbolicFunctionCategory

InnerEvalable(JLWSAPReal prec, JLWSAPReal prec) if JLWSAPReal prec has Evalable JLWSAPReal prec

InnerEvalable(Symbol, JLWSAPReal prec) if JLWSAPReal prec has InnerEvalable(Symbol, JLWSAPReal prec)

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

JLWSNumber

JLWSObject

JLWSRing

LeftModule %

LeftModule Fraction Integer

LeftModule JLWSAPReal prec

LeftOreRing

LinearlyExplicitOver Integer if JLWSAPReal prec has LinearlyExplicitOver Integer

LinearlyExplicitOver JLWSAPReal prec

LiouvillianFunctionCategory

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module JLWSAPReal prec

MonogenicAlgebra(JLWSAPReal prec, SparseUnivariatePolynomial JLWSAPReal prec)

Monoid

multiplicativeValuation if JLWSAPReal prec has IntegerNumberSystem

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra JLWSAPReal prec

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if JLWSAPReal prec has PartialDifferentialRing Symbol

Patternable JLWSAPReal prec

PatternMatchable Float

PatternMatchable Integer if JLWSAPReal prec has PatternMatchable Integer

PolynomialFactorizationExplicit if JLWSAPReal prec has PolynomialFactorizationExplicit

PrimitiveFunctionCategory

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JLWSAPReal prec

RightModule %

RightModule Fraction Integer

RightModule Integer if JLWSAPReal prec has LinearlyExplicitOver Integer

RightModule JLWSAPReal prec

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if JLWSAPReal prec has FiniteFieldCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown