NMComplexField

jnball.spad line 885 [edit on github]

NMComplexField implements arbitrary precision ball arithmetic using the Nemo Julia package.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> %

• undocumented

*: (%, NMRealField) -> %

from RightModule NMRealField

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NMInteger, %) -> %

from JLObjectRing

*: (NMRealField, %) -> %

from LeftModule NMRealField

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (%, Integer) -> %

/ undocumented

/: (Integer, %) -> %

/ undocumented

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from SpecialFunctionCategory

accuracyBits: % -> JLInt64

accuracyBits(x) returns the relative accuracy of x in bits.

acos: % -> %

from ArcTrigonometricFunctionCategory

acosh: % -> %

from ArcHyperbolicFunctionCategory

acot: % -> %

from ArcTrigonometricFunctionCategory

acoth: % -> %

from ArcHyperbolicFunctionCategory

acsc: % -> %

from ArcTrigonometricFunctionCategory

acsch: % -> %

from ArcHyperbolicFunctionCategory

airyAi: % -> %

from SpecialFunctionCategory

airyAiPrime: % -> %

from SpecialFunctionCategory

airyBi: % -> %

from SpecialFunctionCategory

airyBiPrime: % -> %

from SpecialFunctionCategory

angerJ: (%, %) -> %

from SpecialFunctionCategory

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

argument: % -> NMRealField

from ComplexCategory NMRealField

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 NMRealField

besselI: (%, %) -> %

from SpecialFunctionCategory

besselJ: (%, %) -> %

from SpecialFunctionCategory

besselK: (%, %) -> %

from SpecialFunctionCategory

besselY: (%, %) -> %

from SpecialFunctionCategory

Beta: (%, %) -> %

from SpecialFunctionCategory

Beta: (%, %, %) -> %

from SpecialFunctionCategory

ceiling: % -> %

from SpecialFunctionCategory

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial NMRealField

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

charlierC: (%, %, %) -> %

from SpecialFunctionCategory

charthRoot: % -> % if NMRealField has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Complex Integer -> %

coerce(z) coerces z. Convenience function.

coerce: Float -> %

``coerce ``undocumented

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JLFloat64 -> %

``coerce ``undocumented

coerce: NMAlgebraicNumber -> %

``coerce ``undocumented

coerce: NMRealField -> %

from CoercibleFrom NMRealField

coerce: String -> %

``coerce ``undocumented

commutator: (%, %) -> %

from NonAssociativeRng

complex: (NMRealField, NMRealField) -> %

from ComplexCategory NMRealField

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from SpecialFunctionCategory

contains?: (%, %) -> Boolean

contains?(x,y) checks whether or not y is contained in x.

contains?: (%, NMFraction NMInteger) -> Boolean

contains?(x,y) checks whether or not y is contained in x.

contains?: (%, NMInteger) -> Boolean

contains?(x,y) checks whether or not y is contained in x.

containsZero?: % -> Boolean

containsZero?(x) checks whether or not 0 is contained in x.

convert: % -> Complex DoubleFloat

from ConvertibleTo Complex DoubleFloat

convert: % -> Complex Float

from ConvertibleTo Complex Float

convert: % -> InputForm if NMRealField has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

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

from ConvertibleTo Pattern Integer

convert: % -> SparseUnivariatePolynomial NMRealField

from ConvertibleTo SparseUnivariatePolynomial NMRealField

convert: % -> String

from ConvertibleTo String

convert: % -> Vector NMRealField

from FramedModule NMRealField

convert: SparseUnivariatePolynomial NMRealField -> %

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

convert: Vector NMRealField -> %

from FramedModule NMRealField

coordinates: % -> Vector NMRealField

from FramedModule NMRealField

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

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

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

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

coordinates: Vector % -> Matrix NMRealField

from FramedModule NMRealField

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if NMRealField has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from DifferentialExtension NMRealField

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

from DifferentialExtension NMRealField

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

definingPolynomial: () -> SparseUnivariatePolynomial NMRealField

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

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

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

differentiate: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from DifferentialExtension NMRealField

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

from DifferentialExtension NMRealField

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

digamma: % -> %

from SpecialFunctionCategory

diracDelta: % -> %

from SpecialFunctionCategory

discreteLog: % -> NonNegativeInteger if NMRealField has FiniteFieldCategory

from FiniteFieldCategory

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

from FieldOfPrimeCharacteristic

discriminant: () -> NMRealField

from FramedAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

discriminant: Vector % -> NMRealField

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

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

from EuclideanDomain

ellipticE: % -> %

from SpecialFunctionCategory

ellipticE: (%, %) -> %

from SpecialFunctionCategory

ellipticF: (%, %) -> %

from SpecialFunctionCategory

ellipticK: % -> %

from SpecialFunctionCategory

ellipticPi: (%, %, %) -> %

from SpecialFunctionCategory

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

from Eltable(NMRealField, %)

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

from Finite

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable NMRealField

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

from Evalable NMRealField

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

from InnerEvalable(NMRealField, NMRealField)

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

from InnerEvalable(Symbol, NMRealField)

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

from InnerEvalable(NMRealField, NMRealField)

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

from InnerEvalable(Symbol, NMRealField)

exact?: % -> Boolean

exact?(x) checks whether x is exact i.e. with 0 radius.

exp1: () -> %

exp() returns the NMComplexField ℯ (exp(1)).

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the NMComplexField ℯ (exp(1)).

expm1: % -> %

expm1(x) computes accurately e^x-1. It avoids the loss of precision involved in the direct evaluation of exp(x)-1 for small values of x.

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

from PrincipalIdealDomain

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

from EntireRing

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

from ComplexCategory NMRealField

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

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

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

finite?: % -> Boolean

finite?(x) checks whether or not x is finite, not an infinity for example.

floor: % -> %

from SpecialFunctionCategory

fractionPart: % -> %

from SpecialFunctionCategory

Gamma: % -> %

from SpecialFunctionCategory

Gamma: (%, %) -> %

from SpecialFunctionCategory

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

generator: () -> %

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

guess: (%, NonNegativeInteger) -> NMAlgebraicNumber

guess(a, deg) returns the reconstructed algebraic number found if it succeeds. Up to degree deg.

hahn_p: (%, %, %, %, %) -> %

from SpecialFunctionCategory

hahnQ: (%, %, %, %, %) -> %

from SpecialFunctionCategory

hahnR: (%, %, %, %, %) -> %

from SpecialFunctionCategory

hahnS: (%, %, %, %, %) -> %

from SpecialFunctionCategory

hankelH1: (%, %) -> %

from SpecialFunctionCategory

hankelH2: (%, %) -> %

from SpecialFunctionCategory

hash: % -> SingleInteger if NMRealField has Hashable

from Hashable

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

from Hashable

hermiteH: (%, %) -> %

from SpecialFunctionCategory

hurwitzZeta: (%, %) -> %

hurwitzZeta(s,a) returns the Hurwitz zeta function of s and a.

hypergeometric1F1: (%, %, %) -> %

hypergeometric1F1(a,b,z) is the confluent hypergeometric function 1F1.

hypergeometric1F1Regularized: (%, %, %) -> %

hypergeometric1F1Regularized(a,b,z) is the regularized confluent hypergeometric function 1F1.

hypergeometricF: (List %, List %, %) -> %

from SpecialFunctionCategory

hypergeometricU: (%, %, %) -> %

hypergeometricU(a,b,x) is the confluent hypergeometric function U.

imag: % -> NMRealField

from ComplexCategory NMRealField

imaginary: () -> %

from ComplexCategory NMRealField

index: PositiveInteger -> % if NMRealField has Finite

from Finite

init: % if NMRealField has FiniteFieldCategory

from StepThrough

integer?: % -> Boolean

integer?(x) checks whether or not x is an integer.

inv: % -> %

from DivisionRing

jacobiCn: (%, %) -> %

from SpecialFunctionCategory

jacobiDn: (%, %) -> %

from SpecialFunctionCategory

jacobiP: (%, %, %, %) -> %

from SpecialFunctionCategory

jacobiSn: (%, %) -> %

from SpecialFunctionCategory

jacobiTheta: (%, %) -> %

from SpecialFunctionCategory

jacobiZeta: (%, %) -> %

from SpecialFunctionCategory

jlAbout: % -> Void

from JLObjectType

jlApply: (String, %) -> %

from JLObjectType

jlApply: (String, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %) -> %

from JLObjectType

jlApply: (String, %, %, %, %, %) -> %

from JLObjectType

jlDisplay: % -> Void

from JLObjectType

jlId: % -> JLInt64

from JLObjectType

jlNMRing: () -> String

from NMRing

jlObject: () -> String

from NMRing

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlType: % -> String

from JLObjectType

jncf: (Float, Float) -> %

``jncf ``undocumented

jncf: (Integer, Integer) -> %

``jncf ``undocumented

jncf: (String, String) -> %

``jncf ``undocumented

jncf: Float -> %

``jncf ``undocumented

jncf: Integer -> %

``jncf ``undocumented

jncf: String -> %

``jncf ``undocumented

kelvinBei: (%, %) -> %

from SpecialFunctionCategory

kelvinBer: (%, %) -> %

from SpecialFunctionCategory

kelvinKei: (%, %) -> %

from SpecialFunctionCategory

kelvinKer: (%, %) -> %

from SpecialFunctionCategory

krawtchoukK: (%, %, %, %) -> %

from SpecialFunctionCategory

kummerM: (%, %, %) -> %

from SpecialFunctionCategory

kummerU: (%, %, %) -> %

from SpecialFunctionCategory

laguerreL: (%, %, %) -> %

from SpecialFunctionCategory

lambertW: % -> %

from SpecialFunctionCategory

latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)

from LeftOreRing

ldexp: (%, NMInteger) -> %

ldexp(x, n) returns x * 2^n.

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

legendreP: (%, %, %) -> %

from SpecialFunctionCategory

legendreQ: (%, %, %) -> %

from SpecialFunctionCategory

lerchPhi: (%, %, %) -> %

from SpecialFunctionCategory

lift: % -> SparseUnivariatePolynomial NMRealField

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

log1p: % -> %

log1p(x) logarithm of 1+x computed accurately.

log: % -> %

from ElementaryFunctionCategory

lommelS1: (%, %, %) -> %

from SpecialFunctionCategory

lommelS2: (%, %, %) -> %

from SpecialFunctionCategory

lookup: % -> PositiveInteger if NMRealField has Finite

from Finite

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

from FullyEvalableOver NMRealField

meijerG: (List %, List %, List %, List %, %) -> %

from SpecialFunctionCategory

meixnerM: (%, %, %, %) -> %

from SpecialFunctionCategory

meixnerP: (%, %, %, %) -> %

from SpecialFunctionCategory

minimalPolynomial: % -> SparseUnivariatePolynomial NMRealField

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

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

from StepThrough

norm: % -> NMRealField

from ComplexCategory NMRealField

nothing?: % -> Boolean

from JLObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if NMRealField has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if NMRealField has FiniteFieldCategory

from FiniteFieldCategory

overlaps?: (%, %) -> Boolean

overlaps?(x,y) checks whether or not any part of x and y balls overlaps.

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

from PatternMatchable Float

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

from PatternMatchable Integer

pi: () -> %

pi() returns the JLFloat representation of π.

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

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

from ComplexCategory NMRealField

polygamma: (%, %) -> %

from SpecialFunctionCategory

polylog: (%, %) -> %

from SpecialFunctionCategory

precision: () -> PositiveInteger

``precision ``undocumented

precision: PositiveInteger -> PositiveInteger

precisionundocumented

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if NMRealField has FiniteFieldCategory

from FieldOfPrimeCharacteristic

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

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if NMRealField has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if NMRealField has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

racahR: (%, %, %, %, %, %) -> %

from SpecialFunctionCategory

random: () -> % if NMRealField has Finite

from Finite

rank: () -> PositiveInteger

from FramedModule NMRealField

rational?: % -> Boolean if NMRealField has IntegerNumberSystem

from ComplexCategory NMRealField

rational: % -> Fraction Integer if NMRealField has IntegerNumberSystem

from ComplexCategory NMRealField

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

from ComplexCategory NMRealField

real: % -> NMRealField

from ComplexCategory NMRealField

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

reduce: SparseUnivariatePolynomial NMRealField -> %

from MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

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

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver NMRealField

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

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix NMRealField

from LinearlyExplicitOver NMRealField

regularRepresentation: % -> Matrix NMRealField

from FramedAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

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

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

rem: (%, %) -> %

from EuclideanDomain

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

from FiniteFieldCategory

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

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

represents: Vector NMRealField -> %

from FramedModule NMRealField

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> NMRealField

from RetractableTo NMRealField

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(NMRealField, failed)

from RetractableTo NMRealField

riemannZeta: % -> %

from SpecialFunctionCategory

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

rootOfUnity: (NonNegativeInteger, Integer) -> %

rootOfUnity(n,k)Return the root of unity exp(2*%pi*%i*k/n).

rootOfUnity: NonNegativeInteger -> %

rootOfUnity(n)Return the root of unity exp(2*%pi*%i/n).

sample: %

from AbelianMonoid

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

sign: % -> %

from SpecialFunctionCategory

sin: % -> %

from TrigonometricFunctionCategory

sinh: % -> %

from HyperbolicFunctionCategory

size: () -> NonNegativeInteger if NMRealField has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

string: % -> String

from JLType

struveH: (%, %) -> %

from SpecialFunctionCategory

struveL: (%, %) -> %

from SpecialFunctionCategory

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

from CancellationAbelianMonoid

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

from FiniteFieldCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

trace: % -> NMRealField

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

traceMatrix: () -> Matrix NMRealField

from FramedAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

traceMatrix: Vector % -> Matrix NMRealField

from FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

trim: % -> %

trim(x) rounds off insignificant bits from the midpoint.

uniqueInteger: % -> Union(NMInteger, failed)

uniqueInteger(x) returns a NMInteger if there is a unique integer in the interval x, “failed” otherwise.

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

unitStep: % -> %

from SpecialFunctionCategory

weberE: (%, %) -> %

from SpecialFunctionCategory

weierstrassP: (%, %, %) -> %

from SpecialFunctionCategory

weierstrassPInverse: (%, %, %) -> %

from SpecialFunctionCategory

weierstrassPPrime: (%, %, %) -> %

from SpecialFunctionCategory

weierstrassSigma: (%, %, %) -> %

from SpecialFunctionCategory

weierstrassZeta: (%, %, %) -> %

from SpecialFunctionCategory

whittakerM: (%, %, %) -> %

from SpecialFunctionCategory

whittakerW: (%, %, %) -> %

from SpecialFunctionCategory

wilsonW: (%, %, %, %, %, %) -> %

from SpecialFunctionCategory

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra NMRealField

arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(NMRealField, NMRealField)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if NMRealField has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom NMRealField

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory NMRealField

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm if NMRealField has ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if NMRealField has ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial NMRealField

ConvertibleTo String

DifferentialExtension NMRealField

DifferentialRing

DivisionRing

ElementaryFunctionCategory

Eltable(NMRealField, %) if NMRealField has Eltable(NMRealField, NMRealField)

EntireRing

EuclideanDomain

Evalable NMRealField if NMRealField has Evalable NMRealField

Field

FieldOfPrimeCharacteristic if NMRealField has FiniteFieldCategory

Finite if NMRealField has Finite

FiniteFieldCategory if NMRealField has FiniteFieldCategory

FiniteRankAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

FramedAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

FramedModule NMRealField

FullyEvalableOver NMRealField

FullyLinearlyExplicitOver NMRealField

FullyPatternMatchable NMRealField

FullyRetractableTo NMRealField

GcdDomain

Hashable if NMRealField has Hashable

HyperbolicFunctionCategory

InnerEvalable(NMRealField, NMRealField) if NMRealField has Evalable NMRealField

InnerEvalable(Symbol, NMRealField) if NMRealField has InnerEvalable(Symbol, NMRealField)

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftModule Fraction Integer

LeftModule NMRealField

LeftOreRing

LinearlyExplicitOver Integer if NMRealField has LinearlyExplicitOver Integer

LinearlyExplicitOver NMRealField

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module NMRealField

MonogenicAlgebra(NMRealField, SparseUnivariatePolynomial NMRealField)

Monoid

multiplicativeValuation if NMRealField has IntegerNumberSystem

NMRing

NMType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra NMRealField

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if NMRealField has PartialDifferentialRing Symbol

Patternable NMRealField

PatternMatchable Float

PatternMatchable Integer if NMRealField has PatternMatchable Integer

PolynomialFactorizationExplicit if NMRealField has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo NMRealField

RightModule %

RightModule Fraction Integer

RightModule Integer if NMRealField has LinearlyExplicitOver Integer

RightModule NMRealField

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SpecialFunctionCategory

StepThrough if NMRealField has FiniteFieldCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown