JLComplexF32

julia.spad line 384 [edit on github]

JLComplexF32 implements complex 32 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 JLFloat32 has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, JLFloat32) -> %

from RightModule JLFloat32

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (JLFloat32, %) -> %

from LeftModule JLFloat32

*: (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 JLFloat32

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: % -> JLFloat32

from ComplexCategory JLFloat32

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 JLFloat32

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

charthRoot: % -> % if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

charthRoot: % -> Union(%, failed) if JLFloat32 has CharacteristicNonZero or % has CharacteristicNonZero and JLFloat32 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JLFloat32 -> %

from CoercibleFrom JLFloat32

commutator: (%, %) -> %

from NonAssociativeRng

complex: (JLFloat32, JLFloat32) -> %

from ComplexCategory JLFloat32

conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and JLFloat32 has PolynomialFactorizationExplicit or JLFloat32 has FiniteFieldCategory

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory JLFloat32

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

convert: % -> InputForm if JLFloat32 has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if JLFloat32 has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> SparseUnivariatePolynomial JLFloat32

from ConvertibleTo SparseUnivariatePolynomial JLFloat32

convert: % -> String

from ConvertibleTo String

convert: % -> Vector JLFloat32

from FramedModule JLFloat32

convert: SparseUnivariatePolynomial JLFloat32 -> %

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

convert: Vector JLFloat32 -> %

from FramedModule JLFloat32

coordinates: % -> Vector JLFloat32

from FramedModule JLFloat32

coordinates: (%, Vector %) -> Vector JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

coordinates: (Vector %, Vector %) -> Matrix JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

coordinates: Vector % -> Matrix JLFloat32

from FramedModule JLFloat32

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

D: (%, JLFloat32 -> JLFloat32) -> %

from DifferentialExtension JLFloat32

D: (%, JLFloat32 -> JLFloat32, NonNegativeInteger) -> %

from DifferentialExtension JLFloat32

D: (%, List Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

definingPolynomial: () -> SparseUnivariatePolynomial JLFloat32

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

derivationCoordinates: (Vector %, JLFloat32 -> JLFloat32) -> Matrix JLFloat32

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

differentiate: % -> %

from DifferentialRing

differentiate: (%, JLFloat32 -> JLFloat32) -> %

from DifferentialExtension JLFloat32

differentiate: (%, JLFloat32 -> JLFloat32, NonNegativeInteger) -> %

from DifferentialExtension JLFloat32

differentiate: (%, List Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if JLFloat32 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

discreteLog: % -> NonNegativeInteger if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

discreteLog: (%, %) -> Union(NonNegativeInteger, failed) if JLFloat32 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

discriminant: () -> JLFloat32

from FramedAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

discriminant: Vector % -> JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

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

from EuclideanDomain

elt: (%, JLFloat32) -> % if JLFloat32 has Eltable(JLFloat32, JLFloat32)

from Eltable(JLFloat32, %)

enumerate: () -> List % if JLFloat32 has Finite

from Finite

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

eval: (%, Equation JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from Evalable JLFloat32

eval: (%, JLFloat32, JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from InnerEvalable(JLFloat32, JLFloat32)

eval: (%, List Equation JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from Evalable JLFloat32

eval: (%, List JLFloat32, List JLFloat32) -> % if JLFloat32 has Evalable JLFloat32

from InnerEvalable(JLFloat32, JLFloat32)

eval: (%, List Symbol, List JLFloat32) -> % if JLFloat32 has InnerEvalable(Symbol, JLFloat32)

from InnerEvalable(Symbol, JLFloat32)

eval: (%, Symbol, JLFloat32) -> % if JLFloat32 has InnerEvalable(Symbol, JLFloat32)

from InnerEvalable(Symbol, JLFloat32)

exp: % -> %

from ElementaryFunctionCategory

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

from PrincipalIdealDomain

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

from EntireRing

exquo: (%, JLFloat32) -> Union(%, failed)

from ComplexCategory JLFloat32

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat32 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

factorsOfCyclicGroupSize: () -> List Record(factor: Integer, exponent: NonNegativeInteger) if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat32 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

hash: % -> SingleInteger if JLFloat32 has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if JLFloat32 has Hashable

from Hashable

imag: % -> JLFloat32

from ComplexCategory JLFloat32

imaginary: () -> %

from ComplexCategory JLFloat32

index: PositiveInteger -> % if JLFloat32 has Finite

from Finite

init: % if JLFloat32 has FiniteFieldCategory

from StepThrough

inv: % -> %

from DivisionRing

jcf32: (JLFloat32, JLFloat32) -> %

jcf32: JLFloat32 -> %

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 JLFloat32

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

log: % -> %

from ElementaryFunctionCategory

lookup: % -> PositiveInteger if JLFloat32 has Finite

from Finite

map: (JLFloat32 -> JLFloat32, %) -> %

from FullyEvalableOver JLFloat32

minimalPolynomial: % -> SparseUnivariatePolynomial JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

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

from EuclideanDomain

nextItem: % -> Union(%, failed) if JLFloat32 has FiniteFieldCategory

from StepThrough

norm: % -> JLFloat32

from ComplexCategory JLFloat32

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if JLFloat32 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

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

from PatternMatchable Float

patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if JLFloat32 has PatternMatchable Integer

from PatternMatchable Integer

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

polarCoordinates: % -> Record(r: JLFloat32, phi: JLFloat32)

from ComplexCategory JLFloat32

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if JLFloat32 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

primeFrobenius: (%, NonNegativeInteger) -> % if JLFloat32 has FiniteFieldCategory

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

random: () -> % if JLFloat32 has Finite

from Finite

rank: () -> PositiveInteger

from FramedModule JLFloat32

rational?: % -> Boolean if JLFloat32 has IntegerNumberSystem

from ComplexCategory JLFloat32

rational: % -> Fraction Integer if JLFloat32 has IntegerNumberSystem

from ComplexCategory JLFloat32

rationalIfCan: % -> Union(Fraction Integer, failed) if JLFloat32 has IntegerNumberSystem

from ComplexCategory JLFloat32

real: % -> JLFloat32

from ComplexCategory JLFloat32

recip: % -> Union(%, failed)

from MagmaWithUnit

reduce: Fraction SparseUnivariatePolynomial JLFloat32 -> Union(%, failed)

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

reduce: SparseUnivariatePolynomial JLFloat32 -> %

from MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JLFloat32 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix JLFloat32, vec: Vector JLFloat32)

from LinearlyExplicitOver JLFloat32

reducedSystem: Matrix % -> Matrix Integer if JLFloat32 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JLFloat32

from LinearlyExplicitOver JLFloat32

regularRepresentation: % -> Matrix JLFloat32

from FramedAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

regularRepresentation: (%, Vector %) -> Matrix JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

rem: (%, %) -> %

from EuclideanDomain

representationType: () -> Union(prime, polynomial, normal, cyclic) if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

represents: (Vector JLFloat32, Vector %) -> %

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

represents: Vector JLFloat32 -> %

from FramedModule JLFloat32

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JLFloat32

from RetractableTo JLFloat32

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JLFloat32, failed)

from RetractableTo JLFloat32

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 JLFloat32 has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if JLFloat32 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat32 has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

string: % -> String

from JLType

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

from CancellationAbelianMonoid

tableForDiscreteLogarithm: Integer -> Table(PositiveInteger, NonNegativeInteger) if JLFloat32 has FiniteFieldCategory

from FiniteFieldCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

trace: % -> JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

traceMatrix: () -> Matrix JLFloat32

from FramedAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

traceMatrix: Vector % -> Matrix JLFloat32

from FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

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 JLFloat32

arbitraryPrecision if JLFloat32 has arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(JLFloat32, JLFloat32)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if JLFloat32 has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JLFloat32

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory JLFloat32

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm if JLFloat32 has ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if JLFloat32 has ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial JLFloat32

ConvertibleTo String

DifferentialExtension JLFloat32

DifferentialRing

DivisionRing

ElementaryFunctionCategory

Eltable(JLFloat32, %) if JLFloat32 has Eltable(JLFloat32, JLFloat32)

EntireRing

EuclideanDomain

Evalable JLFloat32 if JLFloat32 has Evalable JLFloat32

Field

FieldOfPrimeCharacteristic if JLFloat32 has FiniteFieldCategory

Finite if JLFloat32 has Finite

FiniteFieldCategory if JLFloat32 has FiniteFieldCategory

FiniteRankAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

FramedAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

FramedModule JLFloat32

FullyEvalableOver JLFloat32

FullyLinearlyExplicitOver JLFloat32

FullyPatternMatchable JLFloat32

FullyRetractableTo JLFloat32

GcdDomain

Hashable if JLFloat32 has Hashable

HyperbolicFunctionCategory

InnerEvalable(JLFloat32, JLFloat32) if JLFloat32 has Evalable JLFloat32

InnerEvalable(Symbol, JLFloat32) if JLFloat32 has InnerEvalable(Symbol, JLFloat32)

IntegralDomain

JLType

LeftModule %

LeftModule Fraction Integer

LeftModule JLFloat32

LeftOreRing

LinearlyExplicitOver Integer if JLFloat32 has LinearlyExplicitOver Integer

LinearlyExplicitOver JLFloat32

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module JLFloat32

MonogenicAlgebra(JLFloat32, SparseUnivariatePolynomial JLFloat32)

Monoid

multiplicativeValuation if JLFloat32 has IntegerNumberSystem

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra JLFloat32

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if JLFloat32 has PartialDifferentialRing Symbol

Patternable JLFloat32

PatternMatchable Float

PatternMatchable Integer if JLFloat32 has PatternMatchable Integer

PolynomialFactorizationExplicit if JLFloat32 has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JLFloat32

RightModule %

RightModule Fraction Integer

RightModule Integer if JLFloat32 has LinearlyExplicitOver Integer

RightModule JLFloat32

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if JLFloat32 has FiniteFieldCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown