JLComplexFloatΒΆ
jobject.spad line 1176 [edit on github]
JLFComplexloat implements arbitrary precision floating point arithmetic for complex numbers using Julia BigFloats (MPFR based). https://www.mpfr.org/
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
*: (%, Integer) -> %
- *: (%, JLFloat) -> %
from RightModule JLFloat
- *: (Fraction Integer, %) -> %
from LeftModule Fraction Integer
- *: (Integer, %) -> %
from AbelianGroup
- *: (JLFloat, %) -> %
from LeftModule JLFloat
- *: (NMInteger, %) -> %
from JLObjectRing
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
/: (%, Integer) -> %
/: (Integer, %) -> %
- ^: (%, %) -> %
- ^: (%, Fraction Integer) -> %
from RadicalCategory
- ^: (%, Integer) -> %
from DivisionRing
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> %
from ComplexCategory JLFloat
- acos: % -> %
- acosh: % -> %
- acot: % -> %
- acoth: % -> %
- acsc: % -> %
- acsch: % -> %
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- argument: % -> JLFloat
from ComplexCategory JLFloat
- asec: % -> %
- asech: % -> %
- asin: % -> %
- asinh: % -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- atan: % -> %
atan(x)
computes the inverse tangent ofx
.
- atan: (%, %) -> %
atan(x, y)
computes the inverse tangent of x/y.
- atanh: % -> %
- basis: () -> Vector %
from FramedModule JLFloat
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- characteristicPolynomial: % -> SparseUnivariatePolynomial JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- charthRoot: % -> % if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- charthRoot: % -> Union(%, failed) if JLFloat has CharacteristicNonZero or % has CharacteristicNonZero and JLFloat has PolynomialFactorizationExplicit
- cis: % -> %
cis(x)
returns exp(%i*x) computed efficiently.
- cispi: % -> %
cispi(x)
returns cis(%pi*x) computed efficiently.
- coerce: % -> %
from Algebra %
- coerce: % -> JLObject
from JLObjectType
- coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Float -> %
- coerce: Fraction Integer -> %
- coerce: Integer -> %
from NonAssociativeRing
- coerce: JLFloat -> %
from CoercibleFrom JLFloat
coerce: JLFloat64 -> %
- commutator: (%, %) -> %
from NonAssociativeRng
- complex: (JLFloat, JLFloat) -> %
from ComplexCategory JLFloat
- conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and JLFloat has PolynomialFactorizationExplicit or JLFloat has FiniteFieldCategory
- conjugate: % -> %
from ComplexCategory JLFloat
- convert: % -> Complex DoubleFloat
- convert: % -> Complex Float
from ConvertibleTo Complex Float
- convert: % -> InputForm if JLFloat has ConvertibleTo InputForm
from ConvertibleTo InputForm
- convert: % -> Pattern Float
from ConvertibleTo Pattern Float
- convert: % -> Pattern Integer if JLFloat has ConvertibleTo Pattern Integer
from ConvertibleTo Pattern Integer
- convert: % -> SparseUnivariatePolynomial JLFloat
- convert: % -> String
from ConvertibleTo String
- convert: % -> Vector JLFloat
from FramedModule JLFloat
- convert: SparseUnivariatePolynomial JLFloat -> %
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- convert: Vector JLFloat -> %
from FramedModule JLFloat
- coordinates: % -> Vector JLFloat
from FramedModule JLFloat
- coordinates: (%, Vector %) -> Vector JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- coordinates: (Vector %, Vector %) -> Matrix JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- coordinates: Vector % -> Matrix JLFloat
from FramedModule JLFloat
- cos: % -> %
- cosh: % -> %
- cot: % -> %
- coth: % -> %
- createPrimitiveElement: () -> % if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- csc: % -> %
- csch: % -> %
- D: % -> %
from DifferentialRing
- D: (%, JLFloat -> JLFloat) -> %
- D: (%, JLFloat -> JLFloat, NonNegativeInteger) -> %
- D: (%, List Symbol) -> % if JLFloat has PartialDifferentialRing Symbol
- D: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat has PartialDifferentialRing Symbol
- D: (%, NonNegativeInteger) -> %
from DifferentialRing
- D: (%, Symbol) -> % if JLFloat has PartialDifferentialRing Symbol
- D: (%, Symbol, NonNegativeInteger) -> % if JLFloat has PartialDifferentialRing Symbol
- definingPolynomial: () -> SparseUnivariatePolynomial JLFloat
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- derivationCoordinates: (Vector %, JLFloat -> JLFloat) -> Matrix JLFloat
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- differentiate: % -> %
from DifferentialRing
- differentiate: (%, JLFloat -> JLFloat) -> %
- differentiate: (%, JLFloat -> JLFloat, NonNegativeInteger) -> %
- differentiate: (%, List Symbol) -> % if JLFloat has PartialDifferentialRing Symbol
- differentiate: (%, List Symbol, List NonNegativeInteger) -> % if JLFloat has PartialDifferentialRing Symbol
- differentiate: (%, NonNegativeInteger) -> %
from DifferentialRing
- differentiate: (%, Symbol) -> % if JLFloat has PartialDifferentialRing Symbol
- differentiate: (%, Symbol, NonNegativeInteger) -> % if JLFloat has PartialDifferentialRing Symbol
- discreteLog: % -> NonNegativeInteger if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- discreteLog: (%, %) -> Union(NonNegativeInteger, failed) if JLFloat has FiniteFieldCategory
- discriminant: () -> JLFloat
from FramedAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- discriminant: Vector % -> JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
- euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
- eval: (%, Equation JLFloat) -> % if JLFloat has Evalable JLFloat
- eval: (%, JLFloat, JLFloat) -> % if JLFloat has Evalable JLFloat
from InnerEvalable(JLFloat, JLFloat)
- eval: (%, List Equation JLFloat) -> % if JLFloat has Evalable JLFloat
- eval: (%, List JLFloat, List JLFloat) -> % if JLFloat has Evalable JLFloat
from InnerEvalable(JLFloat, JLFloat)
- eval: (%, List Symbol, List JLFloat) -> % if JLFloat has InnerEvalable(Symbol, JLFloat)
from InnerEvalable(Symbol, JLFloat)
- eval: (%, Symbol, JLFloat) -> % if JLFloat has InnerEvalable(Symbol, JLFloat)
from InnerEvalable(Symbol, JLFloat)
- exp10: % -> %
exp10(x)
computes the base 10 exponential ofx
.
- exp1: () -> %
exp1()
returns the JLComplexFloatβ―
(%e
or exp(1)).
- exp2: % -> %
exp2(x)
computes the base 2 exponential ofx
.
- exp: % -> %
- exp: () -> %
exp()
returns the JLComplexFloatβ―
(%e
or exp(1)).
- expm1: % -> %
expm1(x)
computes accuratelyβ―^x
-1. It avoids the loss of precision involved in the direct evaluation of exp(x
)-1
for small values ofx
.
- expressIdealMember: (List %, %) -> Union(List %, failed)
from PrincipalIdealDomain
- exquo: (%, %) -> Union(%, failed)
from EntireRing
- exquo: (%, JLFloat) -> Union(%, failed)
from ComplexCategory JLFloat
- extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)
from EuclideanDomain
- extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)
from EuclideanDomain
- factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat has PolynomialFactorizationExplicit
- factorsOfCyclicGroupSize: () -> List Record(factor: Integer, exponent: NonNegativeInteger) if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat has PolynomialFactorizationExplicit
- finite?: % -> Boolean
finite?(x)
tests whether or notx
is finite.
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
- generator: () -> %
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- hash: % -> SingleInteger if JLFloat has Hashable
from Hashable
- imag: % -> JLFloat
from ComplexCategory JLFloat
- imaginary: () -> %
from ComplexCategory JLFloat
- index: PositiveInteger -> % if JLFloat has Finite
from Finite
- init: % if JLFloat has FiniteFieldCategory
from StepThrough
- integer?: % -> Boolean
integer?(x)
tests whether or notx
is an integer.
- inv: % -> %
from DivisionRing
jcfloat: Float -> %
jcfloat: Fraction Integer -> %
jcfloat: Integer -> %
- jlAbout: % -> Void
from JLObjectType
- jlApply: (String, %) -> %
jlApply(func, x)
applies the functionfunc
withx
as parameter.
- jlApply: (String, %, %) -> %
jlApply(func, x, y)
applies the functionfunc
tox
andy
.
- jlApply: (String, %, %, %) -> %
jlApply(func, x, y, z)
applies the functionfunc
tox
,y
andz
.- jlApply: (String, %, %, %, %) -> %
from JLObjectType
- jlApply: (String, %, %, %, %, %) -> %
from JLObjectType
- 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.
- jlApprox?: (%, %, %) -> Boolean
jlApprox?(x,y,atol)
computes inexact equality comparison with absolute toleranceatol
. Two numbers compare equal if their relative distance or their absolute distance is within tolerance bounds.
- jlDisplay: % -> Void
from JLObjectType
- jlDump: JLObject -> Void
from JLObjectType
- jlId: % -> JLInt64
from JLObjectType
- jlObject: () -> String
from JLObjectType
- jlRef: % -> SExpression
from JLObjectType
- jlref: String -> %
from JLObjectType
- jlType: % -> String
from JLObjectType
- latex: % -> String
from SetCategory
- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)
from LeftOreRing
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
- lift: % -> SparseUnivariatePolynomial JLFloat
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- log10: % -> %
log10(x)
computes the base 10 logarithm ofx
.
- log1p: % -> %
log1p(x)
computes accurately log(1+x)
- log2: % -> %
log2(x)
computes the base 2 logarithm ofx
.
- log: % -> %
- lookup: % -> PositiveInteger if JLFloat has Finite
from Finite
- map: (JLFloat -> JLFloat, %) -> %
from FullyEvalableOver JLFloat
- minimalPolynomial: % -> SparseUnivariatePolynomial JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
- mutable?: % -> Boolean
from JLObjectType
- nextItem: % -> Union(%, failed) if JLFloat has FiniteFieldCategory
from StepThrough
- norm: % -> JLFloat
from ComplexCategory JLFloat
- nothing?: % -> Boolean
from JLObjectType
- nrand: () -> %
nrand()
returns an normally distributed random number.
- nthRoot: (%, Integer) -> %
from RadicalCategory
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- order: % -> OnePointCompletion PositiveInteger if JLFloat has FiniteFieldCategory
- order: % -> PositiveInteger if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %)
from PatternMatchable Float
- patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if JLFloat has PatternMatchable Integer
from PatternMatchable Integer
- pi: () -> %
- plenaryPower: (%, PositiveInteger) -> %
- polarCoordinates: % -> Record(r: JLFloat, phi: JLFloat)
from ComplexCategory JLFloat
- precision: % -> PositiveInteger
precision(x)
returns the precision ofx
.
- precision: (%, PositiveInteger) -> %
precision(x, p)
returns a copy ofx
with precisionp
.
- primeFrobenius: % -> % if JLFloat has FiniteFieldCategory
- primeFrobenius: (%, NonNegativeInteger) -> % if JLFloat has FiniteFieldCategory
- primitive?: % -> Boolean if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- primitiveElement: () -> % if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
- quo: (%, %) -> %
from EuclideanDomain
- rational?: % -> Boolean if JLFloat has IntegerNumberSystem
from ComplexCategory JLFloat
- rational: % -> Fraction Integer if JLFloat has IntegerNumberSystem
from ComplexCategory JLFloat
- rationalIfCan: % -> Union(Fraction Integer, failed) if JLFloat has IntegerNumberSystem
from ComplexCategory JLFloat
- real?: % -> Boolean
real?(x)
tests whether or notx
is real.
- real: % -> JLFloat
from ComplexCategory JLFloat
- recip: % -> Union(%, failed)
from MagmaWithUnit
- reduce: Fraction SparseUnivariatePolynomial JLFloat -> Union(%, failed)
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- reduce: SparseUnivariatePolynomial JLFloat -> %
from MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JLFloat has LinearlyExplicitOver Integer
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix JLFloat, vec: Vector JLFloat)
- reducedSystem: Matrix % -> Matrix Integer if JLFloat has LinearlyExplicitOver Integer
- reducedSystem: Matrix % -> Matrix JLFloat
- regularRepresentation: % -> Matrix JLFloat
from FramedAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- regularRepresentation: (%, Vector %) -> Matrix JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- rem: (%, %) -> %
from EuclideanDomain
- representationType: () -> Union(prime, polynomial, normal, cyclic) if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- represents: (Vector JLFloat, Vector %) -> %
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- represents: Vector JLFloat -> %
from FramedModule JLFloat
- retract: % -> Fraction Integer
from RetractableTo Fraction Integer
- retract: % -> Integer
from RetractableTo Integer
- retract: % -> JLFloat
from RetractableTo JLFloat
- retractIfCan: % -> Union(Fraction Integer, failed)
from RetractableTo Fraction Integer
- retractIfCan: % -> Union(Integer, failed)
from RetractableTo Integer
- retractIfCan: % -> Union(JLFloat, failed)
from RetractableTo JLFloat
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from AbelianMonoid
- sec: % -> %
- sech: % -> %
- sin: % -> %
- sinh: % -> %
- size: () -> NonNegativeInteger if JLFloat has Finite
from Finite
- sizeLess?: (%, %) -> Boolean
from EuclideanDomain
- smaller?: (%, %) -> Boolean
from Comparable
- solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if JLFloat has PolynomialFactorizationExplicit
- sqrt: % -> %
from RadicalCategory
- squareFree: % -> Factored %
- squareFreePart: % -> %
- squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if JLFloat has PolynomialFactorizationExplicit
- subtractIfCan: (%, %) -> Union(%, failed)
- tableForDiscreteLogarithm: Integer -> Table(PositiveInteger, NonNegativeInteger) if JLFloat has FiniteFieldCategory
from FiniteFieldCategory
- tan: % -> %
- tanh: % -> %
- traceMatrix: () -> Matrix JLFloat
from FramedAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- traceMatrix: Vector % -> Matrix JLFloat
from FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- urand01: () -> %
urand01()
returns an uniformly distributed random number contained in [0,1].
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
ArcTrigonometricFunctionCategory
BiModule(%, %)
BiModule(Fraction Integer, Fraction Integer)
CharacteristicNonZero if JLFloat has CharacteristicNonZero
CoercibleFrom Fraction Integer
ConvertibleTo Complex DoubleFloat
ConvertibleTo InputForm if JLFloat has ConvertibleTo InputForm
ConvertibleTo Pattern Integer if JLFloat has ConvertibleTo Pattern Integer
ConvertibleTo SparseUnivariatePolynomial JLFloat
Eltable(JLFloat, %) if JLFloat has Eltable(JLFloat, JLFloat)
Evalable JLFloat if JLFloat has Evalable JLFloat
FieldOfPrimeCharacteristic if JLFloat has FiniteFieldCategory
FiniteFieldCategory if JLFloat has FiniteFieldCategory
FiniteRankAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
FramedAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
FullyLinearlyExplicitOver JLFloat
Hashable if JLFloat has Hashable
InnerEvalable(JLFloat, JLFloat) if JLFloat has Evalable JLFloat
InnerEvalable(Symbol, JLFloat) if JLFloat has InnerEvalable(Symbol, JLFloat)
LinearlyExplicitOver Integer if JLFloat has LinearlyExplicitOver Integer
Module %
MonogenicAlgebra(JLFloat, SparseUnivariatePolynomial JLFloat)
multiplicativeValuation if JLFloat has IntegerNumberSystem
NonAssociativeAlgebra Fraction Integer
PartialDifferentialRing Symbol if JLFloat has PartialDifferentialRing Symbol
PatternMatchable Integer if JLFloat has PatternMatchable Integer
PolynomialFactorizationExplicit if JLFloat has PolynomialFactorizationExplicit
RetractableTo Fraction Integer
RightModule Integer if JLFloat has LinearlyExplicitOver Integer
StepThrough if JLFloat has FiniteFieldCategory