JuliaWSReal

jws.spad line 411 [edit on github]

Julia Wolfram Symbolic real numbers using Wolfram Symbolic Transport Protocol. Precision is determined during coercion. Machine precision will be used for jWSReal("3.14”) whereas jWSReal("3.14159265358979323846264338327950288419716939937510”) will have arbitrary precision of about 50 digits.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (%, Integer) -> %

from FloatingPointSystem

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from OrderedRing

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

asec: % -> %

from ArcTrigonometricFunctionCategory

asech: % -> %

from ArcHyperbolicFunctionCategory

asin: % -> %

from ArcTrigonometricFunctionCategory

asinh: % -> %

from ArcHyperbolicFunctionCategory

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

atan: % -> %

from ArcTrigonometricFunctionCategory

atan: (%, %) -> %

atan(x,y) computes the arc tangent of y/x.

atanh: % -> %

from ArcHyperbolicFunctionCategory

base: () -> PositiveInteger

from FloatingPointSystem

bits: () -> PositiveInteger

from FloatingPointSystem

ceiling: % -> %

from RealNumberSystem

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

Chi: % -> %

from LiouvillianFunctionCategory

Ci: % -> %

from LiouvillianFunctionCategory

coerce: % -> %

from Algebra %

coerce: % -> DoubleFloat

coerce(r) coerces r to a DoubleFloat.

coerce: % -> JuliaFloat

coerce(x) converts x as a JuliaFloat.

coerce: % -> JuliaFloat64

coerce(r) coerce r to a JuliaFloat64.

coerce: % -> JuliaWSExpression

coerce(x) coerce x to a JuliaWSExpression.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: DoubleFloat -> %

coerce(x) converts x as a JuliaWSReal.

coerce: Float -> %

coerce(x) converts x as a JuliaWSReal.

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JuliaFloat -> %

coerce(x) converts x as a JuliaWSReal.

coerce: JuliaFloat64 -> %

coerce(x) converts x as a JuliaWSReal.

coerce: String -> %

coerce(str) construct str as a JuliaWSReal.

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

convert: % -> String

from ConvertibleTo String

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

D: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: % -> %

from DifferentialRing

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

digits: () -> PositiveInteger

from FloatingPointSystem

dilog: % -> %

from LiouvillianFunctionCategory

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

from EuclideanDomain

Ei: % -> %

from LiouvillianFunctionCategory

erf: % -> %

from LiouvillianFunctionCategory

erf: (%, %) -> %

erf(x) computes the error function of x.

erfc: % -> %

erfc(x) computes the complementary error function of x.

erfi: % -> %

from LiouvillianFunctionCategory

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

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

exponent: % -> Integer

from FloatingPointSystem

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

from PrincipalIdealDomain

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

from EntireRing

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

float: (Integer, Integer) -> %

from FloatingPointSystem

float: (Integer, Integer, PositiveInteger) -> %

from FloatingPointSystem

floor: % -> %

from RealNumberSystem

fractionPart: % -> %

from RealNumberSystem

fresnelC: % -> %

from LiouvillianFunctionCategory

fresnelS: % -> %

from LiouvillianFunctionCategory

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

integerPart: % -> JuliaWSInteger

integerPart(x) returns the integer part of x.

integral: (%, SegmentBinding %) -> %

from PrimitiveFunctionCategory

integral: (%, Symbol) -> %

from PrimitiveFunctionCategory

inv: % -> %

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

jlApprox?: (%, %) -> Boolean

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

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

jWSInterpret: (String, String) -> %

from JuliaWSObject

jWSReal: DoubleFloat -> %

jWSReal(z) coerces the integer z to a JuliaWSReal.

jWSReal: Float -> %

jWSReal(z) coerces the integer z to a JuliaWSReal.

jWSReal: Integer -> %

jWSReal(z) coerces the integer z to a JuliaWSReal.

jWSReal: JuliaFloat64 -> %

jWSReal(z) coerces the integer z to a JuliaWSReal.

jWSReal: String -> %

jWSReal(str) constructs str as a JuliaWSReal.

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

log10: % -> %

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

log2: % -> %

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

log: % -> %

from ElementaryFunctionCategory

mantissa: % -> Integer

from FloatingPointSystem

max: (%, %) -> %

from OrderedSet

max: () -> % if % hasn’t arbitraryExponent and % hasn’t arbitraryPrecision

from FloatingPointSystem

min: (%, %) -> %

from OrderedSet

min: () -> % if % hasn’t arbitraryExponent and % hasn’t arbitraryPrecision

from FloatingPointSystem

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

negative?: % -> Boolean

from OrderedRing

norm: % -> %

from RealNumberSystem

nothing?: % -> Boolean

from JuliaObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from JuliaRing

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> Integer

from FloatingPointSystem

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

from PatternMatchable Float

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

positive?: % -> Boolean

from OrderedRing

precision: () -> PositiveInteger

from FloatingPointSystem

prime?: % -> Boolean

from UniqueFactorizationDomain

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

rationalApproximation: % -> JuliaWSRational

rationalApproximation(x) try to find a rational approximation of x. Error if x can not be retracted.

rationalApproximation: (%, %) -> JuliaWSRational

rationalApproximation(x, dx) returns a rational approximation of x within tolerance dx. If dx = 0, converts it anyway.

recip: % -> Union(%, failed)

from MagmaWithUnit

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

round: % -> %

from RealNumberSystem

sample: %

from AbelianMonoid

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

Shi: % -> %

from LiouvillianFunctionCategory

Si: % -> %

from LiouvillianFunctionCategory

sign: % -> Integer

from OrderedRing

sin: % -> %

from TrigonometricFunctionCategory

sinc: % -> %

sinc(x) compues the unormalized sinc of x, sin(x)/x.

sinh: % -> %

from HyperbolicFunctionCategory

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

string: % -> String

from JuliaObjectType

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

from CancellationAbelianMonoid

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

toString: % -> String

from JuliaWSObject

toString: (%, NonNegativeInteger) -> String

from FloatingPointSystem

truncate: % -> %

from RealNumberSystem

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

urand01: () -> %

urand01() returns a uniformly distributed random number in the range 0..1.

wholePart: % -> Integer

from RealNumberSystem

zero?: % -> Boolean

from JuliaRing

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Approximate

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo Pattern Float

ConvertibleTo String

DifferentialRing

DivisionRing

ElementaryFunctionCategory

EntireRing

EuclideanDomain

Field

FloatingPointSystem

GcdDomain

HyperbolicFunctionCategory

IntegralDomain

JuliaObjectRing

JuliaObjectType

JuliaRing

JuliaType

JuliaWSNumber

JuliaWSObject

JuliaWSRing

LeftModule %

LeftModule Fraction Integer

LeftOreRing

LiouvillianFunctionCategory

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedRing

OrderedSet

PartialOrder

PatternMatchable Float

PrimitiveFunctionCategory

PrincipalIdealDomain

RadicalCategory

RealConstant

RealNumberSystem

RetractableTo Fraction Integer

RetractableTo Integer

RightModule %

RightModule Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown