JLComplexF64

julia.spad line 608 [edit on github]

JLComplexF64 implements complex 64 bits floating point arithmetic. Only basic arithmetic is supported. Convenience domain.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> % if JLFloat64 has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, JLFloat64) -> %

from RightModule JLFloat64

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (JLFloat64, %) -> %

from LeftModule JLFloat64

*: (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 JLFloat64

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: % -> JLFloat64

from ComplexCategory JLFloat64

asec: % -> %

from ArcTrigonometricFunctionCategory

asech: % -> %

from ArcHyperbolicFunctionCategory

asin: % -> %

from ArcTrigonometricFunctionCategory

asinh: % -> %

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> %

from ArcTrigonometricFunctionCategory

atanh: % -> %

from ArcHyperbolicFunctionCategory

basis: () -> Vector %

from FramedModule JLFloat64

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

charthRoot: % -> % if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

charthRoot: % -> Union(%, failed) if JLFloat64 has CharacteristicNonZero or % has CharacteristicNonZero and JLFloat64 has PolynomialFactorizationExplicit

from CharacteristicNonZero

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JLFloat64 -> %

from Algebra JLFloat64

commutator: (%, %) -> %

from NonAssociativeRng

complex: (JLFloat64, JLFloat64) -> %

from ComplexCategory JLFloat64

conditionP: Matrix % -> Union(Vector %, failed) if JLFloat64 has FiniteFieldCategory or % has CharacteristicNonZero and JLFloat64 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory JLFloat64

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

convert: % -> InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if JLFloat64 has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> SparseUnivariatePolynomial JLFloat64

from ConvertibleTo SparseUnivariatePolynomial JLFloat64

convert: % -> String

from ConvertibleTo String

convert: % -> Vector JLFloat64

from FramedModule JLFloat64

convert: SparseUnivariatePolynomial JLFloat64 -> %

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

convert: Vector JLFloat64 -> %

from FramedModule JLFloat64

coordinates: % -> Vector JLFloat64

from FramedModule JLFloat64

coordinates: (%, Vector %) -> Vector JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

coordinates: (Vector %, Vector %) -> Matrix JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

coordinates: Vector % -> Matrix JLFloat64

from FramedModule JLFloat64

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

D: (%, JLFloat64 -> JLFloat64) -> %

from DifferentialExtension JLFloat64

D: (%, JLFloat64 -> JLFloat64, NonNegativeInteger) -> %

from DifferentialExtension JLFloat64

D: (%, List Symbol) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

definingPolynomial: () -> SparseUnivariatePolynomial JLFloat64

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

derivationCoordinates: (Vector %, JLFloat64 -> JLFloat64) -> Matrix JLFloat64

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

differentiate: % -> %

from DifferentialRing

differentiate: (%, JLFloat64 -> JLFloat64) -> %

from DifferentialExtension JLFloat64

differentiate: (%, JLFloat64 -> JLFloat64, NonNegativeInteger) -> %

from DifferentialExtension JLFloat64

differentiate: (%, List Symbol) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if JLFloat64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

discreteLog: % -> NonNegativeInteger if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

discreteLog: (%, %) -> Union(NonNegativeInteger, failed) if JLFloat64 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

discriminant: () -> JLFloat64

from FramedAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

discriminant: Vector % -> JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

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

from EuclideanDomain

elt: (%, JLFloat64) -> % if JLFloat64 has Eltable(JLFloat64, JLFloat64)

from Eltable(JLFloat64, %)

enumerate: () -> List % if JLFloat64 has Finite

from Finite

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

eval: (%, Equation JLFloat64) -> % if JLFloat64 has Evalable JLFloat64

from Evalable JLFloat64

eval: (%, JLFloat64, JLFloat64) -> % if JLFloat64 has Evalable JLFloat64

from InnerEvalable(JLFloat64, JLFloat64)

eval: (%, List Equation JLFloat64) -> % if JLFloat64 has Evalable JLFloat64

from Evalable JLFloat64

eval: (%, List JLFloat64, List JLFloat64) -> % if JLFloat64 has Evalable JLFloat64

from InnerEvalable(JLFloat64, JLFloat64)

eval: (%, List Symbol, List JLFloat64) -> % if JLFloat64 has InnerEvalable(Symbol, JLFloat64)

from InnerEvalable(Symbol, JLFloat64)

eval: (%, Symbol, JLFloat64) -> % if JLFloat64 has InnerEvalable(Symbol, JLFloat64)

from InnerEvalable(Symbol, JLFloat64)

exp: % -> %

from ElementaryFunctionCategory

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

from PrincipalIdealDomain

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

from EntireRing

exquo: (%, JLFloat64) -> Union(%, failed)

from ComplexCategory JLFloat64

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat64 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

factorsOfCyclicGroupSize: () -> List Record(factor: Integer, exponent: NonNegativeInteger) if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat64 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

hash: % -> SingleInteger if JLFloat64 has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if JLFloat64 has Hashable

from Hashable

imag: % -> JLFloat64

from ComplexCategory JLFloat64

imaginary: () -> %

from ComplexCategory JLFloat64

index: PositiveInteger -> % if JLFloat64 has Finite

from Finite

init: % if JLFloat64 has FiniteFieldCategory

from StepThrough

inv: % -> %

from DivisionRing

jcf64: (JLFloat64, JLFloat64) -> %

jcf64(r,i) coerce real part r and imaginary part i to a JLComplexF64.

jcf64: JLFloat64 -> %

jcf64(r) coerces the real part r.

jlApprox?: (%, %) -> Boolean

jlApprox?(x,y) computes inexact equality comparison with default parameters. Two numbers compare equal if their relative distance or their absolute distance is within tolerance bounds. Applied component-wise.

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 JLFloat64

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

log: % -> %

from ElementaryFunctionCategory

lookup: % -> PositiveInteger if JLFloat64 has Finite

from Finite

map: (JLFloat64 -> JLFloat64, %) -> %

from FullyEvalableOver JLFloat64

minimalPolynomial: % -> SparseUnivariatePolynomial JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

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

from EuclideanDomain

nextItem: % -> Union(%, failed) if JLFloat64 has FiniteFieldCategory

from StepThrough

norm: % -> JLFloat64

from ComplexCategory JLFloat64

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if JLFloat64 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

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

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if JLFloat64 has PatternMatchable Integer

from PatternMatchable Integer

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

polarCoordinates: % -> Record(r: JLFloat64, phi: JLFloat64)

from ComplexCategory JLFloat64

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if JLFloat64 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

primeFrobenius: (%, NonNegativeInteger) -> % if JLFloat64 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

random: () -> % if JLFloat64 has Finite

from Finite

rank: () -> PositiveInteger

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

rational?: % -> Boolean if JLFloat64 has IntegerNumberSystem

from ComplexCategory JLFloat64

rational: % -> Fraction Integer if JLFloat64 has IntegerNumberSystem

from ComplexCategory JLFloat64

rationalIfCan: % -> Union(Fraction Integer, failed) if JLFloat64 has IntegerNumberSystem

from ComplexCategory JLFloat64

real: % -> JLFloat64

from ComplexCategory JLFloat64

recip: % -> Union(%, failed)

from MagmaWithUnit

reduce: Fraction SparseUnivariatePolynomial JLFloat64 -> Union(%, failed)

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

reduce: SparseUnivariatePolynomial JLFloat64 -> %

from MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JLFloat64 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix JLFloat64, vec: Vector JLFloat64)

from LinearlyExplicitOver JLFloat64

reducedSystem: Matrix % -> Matrix Integer if JLFloat64 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JLFloat64

from LinearlyExplicitOver JLFloat64

regularRepresentation: % -> Matrix JLFloat64

from FramedAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

regularRepresentation: (%, Vector %) -> Matrix JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

rem: (%, %) -> %

from EuclideanDomain

representationType: () -> Union(prime, polynomial, normal, cyclic) if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

represents: (Vector JLFloat64, Vector %) -> %

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

represents: Vector JLFloat64 -> %

from FramedModule JLFloat64

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JLFloat64

from RetractableTo JLFloat64

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JLFloat64, failed)

from RetractableTo JLFloat64

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

sin: % -> %

from TrigonometricFunctionCategory

sinh: % -> %

from HyperbolicFunctionCategory

size: () -> NonNegativeInteger if JLFloat64 has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if JLFloat64 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat64 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

string: % -> String

from JLType

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

from CancellationAbelianMonoid

tableForDiscreteLogarithm: Integer -> Table(PositiveInteger, NonNegativeInteger) if JLFloat64 has FiniteFieldCategory

from FiniteFieldCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

trace: % -> JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

traceMatrix: () -> Matrix JLFloat64

from FramedAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

traceMatrix: Vector % -> Matrix JLFloat64

from FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

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

Algebra JLFloat64

arbitraryPrecision if JLFloat64 has arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(JLFloat64, JLFloat64)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if JLFloat64 has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JLFloat64

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory JLFloat64

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if JLFloat64 has ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial JLFloat64

ConvertibleTo String

DifferentialExtension JLFloat64

DifferentialRing

DivisionRing

ElementaryFunctionCategory

Eltable(JLFloat64, %) if JLFloat64 has Eltable(JLFloat64, JLFloat64)

EntireRing

EuclideanDomain

Evalable JLFloat64 if JLFloat64 has Evalable JLFloat64

Field

FieldOfPrimeCharacteristic if JLFloat64 has FiniteFieldCategory

Finite if JLFloat64 has Finite

FiniteFieldCategory if JLFloat64 has FiniteFieldCategory

FiniteRankAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

FramedAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

FramedModule JLFloat64

FullyEvalableOver JLFloat64

FullyLinearlyExplicitOver JLFloat64

FullyPatternMatchable JLFloat64

FullyRetractableTo JLFloat64

GcdDomain

Hashable if JLFloat64 has Hashable

HyperbolicFunctionCategory

InnerEvalable(JLFloat64, JLFloat64) if JLFloat64 has Evalable JLFloat64

InnerEvalable(Symbol, JLFloat64) if JLFloat64 has InnerEvalable(Symbol, JLFloat64)

IntegralDomain

JLType

LeftModule %

LeftModule Fraction Integer

LeftModule JLFloat64

LeftOreRing

LinearlyExplicitOver Integer if JLFloat64 has LinearlyExplicitOver Integer

LinearlyExplicitOver JLFloat64

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module JLFloat64

MonogenicAlgebra(JLFloat64, SparseUnivariatePolynomial JLFloat64)

Monoid

multiplicativeValuation if JLFloat64 has IntegerNumberSystem

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra JLFloat64

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if JLFloat64 has PartialDifferentialRing Symbol

Patternable JLFloat64

PatternMatchable Float

PatternMatchable Integer if JLFloat64 has PatternMatchable Integer

PolynomialFactorizationExplicit if JLFloat64 has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JLFloat64

RightModule %

RightModule Fraction Integer

RightModule Integer if JLFloat64 has LinearlyExplicitOver Integer

RightModule JLFloat64

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if JLFloat64 has FiniteFieldCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown