NemoComplexField

jnball.spad line 857 [edit on github]

NemoComplexField 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) -> %

*: (%, NemoRealField) -> %

from RightModule NemoRealField

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NemoRealField, %) -> %

from LeftModule NemoRealField

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (%, Integer) -> %

/: (Integer, %) -> %

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from ComplexCategory NemoRealField

accuracyBits: % -> JuliaInt64

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: % -> NemoRealField

from ComplexCategory NemoRealField

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 NemoRealField

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 NemoRealField

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from SpecialFunctionCategory

charthRoot: % -> % if NemoRealField has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Complex Integer -> %

coerce(z) coerces z. Convenience function.

coerce: Float -> %

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JuliaFloat64 -> %

coerce: NemoAlgebraicNumber -> %

coerce: NemoRealField -> %

from CoercibleFrom NemoRealField

coerce: String -> %

commutator: (%, %) -> %

from NonAssociativeRng

complex: (NemoRealField, NemoRealField) -> %

from ComplexCategory NemoRealField

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from ComplexCategory NemoRealField

contains?: (%, %) -> Boolean

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

contains?: (%, NemoInteger) -> Boolean

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

contains?: (%, NemoRational) -> 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 NemoRealField has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

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

from ConvertibleTo Pattern Integer

convert: % -> SparseUnivariatePolynomial NemoRealField

from ConvertibleTo SparseUnivariatePolynomial NemoRealField

convert: % -> String

from ConvertibleTo String

convert: % -> Vector NemoRealField

from FramedModule NemoRealField

convert: SparseUnivariatePolynomial NemoRealField -> %

from MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

convert: Vector NemoRealField -> %

from FramedModule NemoRealField

coordinates: % -> Vector NemoRealField

from FramedModule NemoRealField

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

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

coordinates: Vector % -> Matrix NemoRealField

from FramedModule NemoRealField

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if NemoRealField has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from DifferentialExtension NemoRealField

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

from DifferentialExtension NemoRealField

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

definingPolynomial: () -> SparseUnivariatePolynomial NemoRealField

from MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

differentiate: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from DifferentialExtension NemoRealField

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

from DifferentialExtension NemoRealField

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

digamma: % -> %

from SpecialFunctionCategory

diracDelta: % -> %

from SpecialFunctionCategory

discreteLog: % -> NonNegativeInteger if NemoRealField has FiniteFieldCategory

from FiniteFieldCategory

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

from FieldOfPrimeCharacteristic

discriminant: () -> NemoRealField

from FramedAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

discriminant: Vector % -> NemoRealField

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from EuclideanDomain

ellipticE: % -> %

from SpecialFunctionCategory

ellipticE: (%, %) -> %

from SpecialFunctionCategory

ellipticF: (%, %) -> %

from SpecialFunctionCategory

ellipticK: % -> %

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from Eltable(NemoRealField, %)

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

from Finite

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable NemoRealField

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

from Evalable NemoRealField

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

from InnerEvalable(NemoRealField, NemoRealField)

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

from InnerEvalable(Symbol, NemoRealField)

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

from InnerEvalable(NemoRealField, NemoRealField)

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

from InnerEvalable(Symbol, NemoRealField)

exact?: % -> Boolean

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

exp1: () -> %

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

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the NemoComplexField 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: (%, NemoRealField) -> Union(%, failed)

from ComplexCategory NemoRealField

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

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

from FiniteFieldCategory

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NemoRealField 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(NemoRealField, SparseUnivariatePolynomial NemoRealField)

guess: (%, NonNegativeInteger) -> NemoAlgebraicNumber

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 NemoRealField has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if NemoRealField 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: % -> NemoRealField

from ComplexCategory NemoRealField

imaginary: () -> %

from ComplexCategory NemoRealField

index: PositiveInteger -> % if NemoRealField has Finite

from Finite

init: % if NemoRealField 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 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

jlId: % -> String

from JuliaObjectType

jlRef: % -> SExpression

from JuliaObjectType

jlref: String -> %

from JuliaObjectType

jlType: % -> String

from JuliaObjectType

jncf: (Float, Float) -> %

jncf: (Integer, Integer) -> %

jncf: (String, String) -> %

jncf: Float -> %

jncf: Integer -> %

jncf: String -> %

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: (%, NemoInteger) -> %

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 NemoRealField

from MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

log1p: % -> %

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

log: % -> %

from ElementaryFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

lookup: % -> PositiveInteger if NemoRealField has Finite

from Finite

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

from FullyEvalableOver NemoRealField

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

minimalPolynomial: % -> SparseUnivariatePolynomial NemoRealField

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

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

from StepThrough

norm: % -> NemoRealField

from ComplexCategory NemoRealField

nothing?: % -> Boolean

from JuliaObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if NemoRealField has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if NemoRealField 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 NemoRealField has PatternMatchable Integer

from PatternMatchable Integer

pi: () -> %

pi() returns the JuliaFloat representation of π.

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

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

from ComplexCategory NemoRealField

polygamma: (%, %) -> %

from SpecialFunctionCategory

polylog: (%, %) -> %

from SpecialFunctionCategory

precision: () -> PositiveInteger

precision: PositiveInteger -> PositiveInteger

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if NemoRealField has FiniteFieldCategory

from FieldOfPrimeCharacteristic

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

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if NemoRealField has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if NemoRealField has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

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

from SpecialFunctionCategory

random: () -> % if NemoRealField has Finite

from Finite

rank: () -> PositiveInteger

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

rational?: % -> Boolean if NemoRealField has IntegerNumberSystem

from ComplexCategory NemoRealField

rational: % -> Fraction Integer if NemoRealField has IntegerNumberSystem

from ComplexCategory NemoRealField

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

from ComplexCategory NemoRealField

real: % -> NemoRealField

from ComplexCategory NemoRealField

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

reduce: SparseUnivariatePolynomial NemoRealField -> %

from MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver NemoRealField

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

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix NemoRealField

from LinearlyExplicitOver NemoRealField

regularRepresentation: % -> Matrix NemoRealField

from FramedAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

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

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

rem: (%, %) -> %

from EuclideanDomain

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

from FiniteFieldCategory

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

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

represents: Vector NemoRealField -> %

from FramedModule NemoRealField

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> NemoRealField

from RetractableTo NemoRealField

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(NemoRealField, failed)

from RetractableTo NemoRealField

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 NemoRealField has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

string: % -> String

from JuliaObjectType

struveH: (%, %) -> %

from SpecialFunctionCategory

struveL: (%, %) -> %

from SpecialFunctionCategory

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

from CancellationAbelianMonoid

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

from FiniteFieldCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

trace: % -> NemoRealField

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

traceMatrix: () -> Matrix NemoRealField

from FramedAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

traceMatrix: Vector % -> Matrix NemoRealField

from FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

trim: % -> %

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

uniqueInteger: % -> Union(NemoInteger, failed)

uniqueInteger(x) returns a NemoInteger 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 NemoRealField

arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(NemoRealField, NemoRealField)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if NemoRealField has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom NemoRealField

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory NemoRealField

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm if NemoRealField has ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if NemoRealField has ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial NemoRealField

ConvertibleTo String

DifferentialExtension NemoRealField

DifferentialRing

DivisionRing

ElementaryFunctionCategory

Eltable(NemoRealField, %) if NemoRealField has Eltable(NemoRealField, NemoRealField)

EntireRing

EuclideanDomain

Evalable NemoRealField if NemoRealField has Evalable NemoRealField

Field

FieldOfPrimeCharacteristic if NemoRealField has FiniteFieldCategory

Finite if NemoRealField has Finite

FiniteFieldCategory if NemoRealField has FiniteFieldCategory

FiniteRankAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

FramedAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

FramedModule NemoRealField

FullyEvalableOver NemoRealField

FullyLinearlyExplicitOver NemoRealField

FullyPatternMatchable NemoRealField

FullyRetractableTo NemoRealField

GcdDomain

Hashable if NemoRealField has Hashable

HyperbolicFunctionCategory

InnerEvalable(NemoRealField, NemoRealField) if NemoRealField has Evalable NemoRealField

InnerEvalable(Symbol, NemoRealField) if NemoRealField has InnerEvalable(Symbol, NemoRealField)

IntegralDomain

JuliaObjectRing

JuliaObjectType

JuliaRing

JuliaType

LeftModule %

LeftModule Fraction Integer

LeftModule NemoRealField

LeftOreRing

LinearlyExplicitOver Integer if NemoRealField has LinearlyExplicitOver Integer

LinearlyExplicitOver NemoRealField

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module NemoRealField

MonogenicAlgebra(NemoRealField, SparseUnivariatePolynomial NemoRealField)

Monoid

multiplicativeValuation if NemoRealField has IntegerNumberSystem

NemoRing

NemoType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra NemoRealField

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if NemoRealField has PartialDifferentialRing Symbol

Patternable NemoRealField

PatternMatchable Float

PatternMatchable Integer if NemoRealField has PatternMatchable Integer

PolynomialFactorizationExplicit if NemoRealField has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo NemoRealField

RightModule %

RightModule Fraction Integer

RightModule Integer if NemoRealField has LinearlyExplicitOver Integer

RightModule NemoRealField

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SpecialFunctionCategory

StepThrough if NemoRealField has FiniteFieldCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown