NemoAcbField p

jnball.spad line 313 [edit on github]

• p: PositiveInteger

NemoAcbField implements fixed precision complex ball arbitrary precision ball arithmetic using the Julia Nemo package - based on the Arb library.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> %

• undocumented

*: (%, NemoArbField p) -> %

from RightModule NemoArbField p

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NemoArbField p, %) -> %

from LeftModule NemoArbField p

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (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: % -> 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: % -> NemoArbField p

from ComplexCategory NemoArbField p

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 NemoArbField p

besselI: (%, %) -> %

from SpecialFunctionCategory

besselJ: (%, %) -> %

from SpecialFunctionCategory

besselK: (%, %) -> %

from SpecialFunctionCategory

besselY: (%, %) -> %

from SpecialFunctionCategory

Beta: (%, %) -> %

from SpecialFunctionCategory

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

from SpecialFunctionCategory

bits: % -> JuliaInt64

bits(x) returns the bit length of the mantissa of x. For a result computed at prec bits of precision this can be anywhere in the range 0 <= b <= prec. For example 0 has 0 bits, 0.75 has 2 bits, and 3.7 has 126 bits after rounding to prec = 128 (with the default rounding mode) because the two least significant bits are zero and thus get discarded. Source of documentation: flint-devel@googlegroups.com

ceiling: % -> %

from SpecialFunctionCategory

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

characteristicPolynomial: % -> SparseUnivariatePolynomial NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

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

from SpecialFunctionCategory

charthRoot: % -> % if NemoArbField p has FiniteFieldCategory

from FiniteFieldCategory

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Complex Integer -> %

coerce(z) coerces z. Convenience function.

coerce: Float -> %

coerce(r) coerce the floating point number r.

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: NemoArbField p -> %

from Algebra NemoArbField p

commutator: (%, %) -> %

from NonAssociativeRng

complex: (NemoArbField p, NemoArbField p) -> %

from ComplexCategory NemoArbField p

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

from PolynomialFactorizationExplicit

conjugate: % -> %

from SpecialFunctionCategory

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 NemoArbField p has ConvertibleTo InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer if NemoArbField p has ConvertibleTo Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> SparseUnivariatePolynomial NemoArbField p

from ConvertibleTo SparseUnivariatePolynomial NemoArbField p

convert: % -> String

from ConvertibleTo String

convert: % -> Vector NemoArbField p

from FramedModule NemoArbField p

convert: SparseUnivariatePolynomial NemoArbField p -> %

from MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

convert: Vector NemoArbField p -> %

from FramedModule NemoArbField p

coordinates: % -> Vector NemoArbField p

from FramedModule NemoArbField p

coordinates: (%, Vector %) -> Vector NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

coordinates: (Vector %, Vector %) -> Matrix NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

coordinates: Vector % -> Matrix NemoArbField p

from FramedModule NemoArbField p

cos: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

createPrimitiveElement: () -> % if NemoArbField p has FiniteFieldCategory

from FiniteFieldCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

D: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

D: (%, NemoArbField p -> NemoArbField p) -> %

from DifferentialExtension NemoArbField p

D: (%, NemoArbField p -> NemoArbField p, NonNegativeInteger) -> %

from DifferentialExtension NemoArbField p

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

definingPolynomial: () -> SparseUnivariatePolynomial NemoArbField p

from MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

derivationCoordinates: (Vector %, NemoArbField p -> NemoArbField p) -> Matrix NemoArbField p

from MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

differentiate: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

differentiate: (%, NemoArbField p -> NemoArbField p) -> %

from DifferentialExtension NemoArbField p

differentiate: (%, NemoArbField p -> NemoArbField p, NonNegativeInteger) -> %

from DifferentialExtension NemoArbField p

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

digamma: % -> %

from SpecialFunctionCategory

diracDelta: % -> %

from SpecialFunctionCategory

discreteLog: % -> NonNegativeInteger if NemoArbField p has FiniteFieldCategory

from FiniteFieldCategory

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

from FieldOfPrimeCharacteristic

discriminant: () -> NemoArbField p

from FramedAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

discriminant: Vector % -> NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

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

from EuclideanDomain

ellipticE: % -> %

from SpecialFunctionCategory

ellipticE: (%, %) -> %

from SpecialFunctionCategory

ellipticF: (%, %) -> %

from SpecialFunctionCategory

ellipticK: % -> %

from SpecialFunctionCategory

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

from SpecialFunctionCategory

elt: (%, NemoArbField p) -> % if NemoArbField p has Eltable(NemoArbField p, NemoArbField p)

from Eltable(NemoArbField p, %)

enumerate: () -> List % if NemoArbField p has Finite

from Finite

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable NemoArbField p

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

from Evalable NemoArbField p

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

from InnerEvalable(NemoArbField p, NemoArbField p)

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

from InnerEvalable(Symbol, NemoArbField p)

eval: (%, NemoArbField p, NemoArbField p) -> % if NemoArbField p has Evalable NemoArbField p

from InnerEvalable(NemoArbField p, NemoArbField p)

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

from InnerEvalable(Symbol, NemoArbField p)

exact?: % -> Boolean

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

exp1: () -> %

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

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the NemoAcbField 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: (%, NemoArbField p) -> Union(%, failed)

from ComplexCategory NemoArbField p

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NemoArbField p has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

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

from FiniteFieldCategory

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NemoArbField p 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(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

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 NemoArbField p has Hashable

from Hashable

hashUpdate!: (HashState, %) -> HashState if NemoArbField p 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: % -> NemoArbField p

from ComplexCategory NemoArbField p

imaginary: () -> %

from ComplexCategory NemoArbField p

index: PositiveInteger -> % if NemoArbField p has Finite

from Finite

init: % if NemoArbField p 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

jncb: (Float, Float) -> %

jncb(r,i) returns r and i as a complex Arb ball using real and imaginary part.

jncb: (Integer, Integer) -> %

jncb(r,i) returns r and i as a complex Arb ball using real and imaginary part.

jncb: (String, String) -> %

jncb(strr, stri) evaluates strr and stri to a complex Arb field. using real and imaginary part.

jncb: Float -> %

jncb(r) returns r as a complex complex Arb ball.

jncb: Integer -> %

jncb(r) returns r as a complex complex Arb ball.

jncb: NemoAlgebraicNumber -> %

jncb(an) evaluates numerically an by converting it to a complex Arb field.

jncb: NemoExactComplexField -> %

jncb(necf) evaluates numerically necf by converting it to a complex Arb field.

jncb: String -> %

jncb(str) evaluates str to a complex Arb field.

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 NemoArbField p

from MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

log1p: % -> %

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

log: % -> %

from ElementaryFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

lookup: % -> PositiveInteger if NemoArbField p has Finite

from Finite

map: (NemoArbField p -> NemoArbField p, %) -> %

from FullyEvalableOver NemoArbField p

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

minimalPolynomial: % -> SparseUnivariatePolynomial NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

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

from StepThrough

norm: % -> NemoArbField p

from ComplexCategory NemoArbField p

nothing?: % -> Boolean

from JuliaObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> OnePointCompletion PositiveInteger if NemoArbField p has FiniteFieldCategory

from FieldOfPrimeCharacteristic

order: % -> PositiveInteger if NemoArbField p 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 NemoArbField p has PatternMatchable Integer

from PatternMatchable Integer

pi: () -> %

pi() returns the JuliaFloat representation of π.

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

polarCoordinates: % -> Record(r: NemoArbField p, phi: NemoArbField p)

from ComplexCategory NemoArbField p

polygamma: (%, %) -> %

from SpecialFunctionCategory

polylog: (%, %) -> %

from SpecialFunctionCategory

precision: () -> PositiveInteger

precision() returns precision in bits used.

prime?: % -> Boolean

from UniqueFactorizationDomain

primeFrobenius: % -> % if NemoArbField p has FiniteFieldCategory

from FieldOfPrimeCharacteristic

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

from FieldOfPrimeCharacteristic

primitive?: % -> Boolean if NemoArbField p has FiniteFieldCategory

from FiniteFieldCategory

primitiveElement: () -> % if NemoArbField p has FiniteFieldCategory

from FiniteFieldCategory

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

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

from SpecialFunctionCategory

random: () -> % if NemoArbField p has Finite

from Finite

rank: () -> PositiveInteger

from FramedModule NemoArbField p

rational?: % -> Boolean if NemoArbField p has IntegerNumberSystem

from ComplexCategory NemoArbField p

rational: % -> Fraction Integer if NemoArbField p has IntegerNumberSystem

from ComplexCategory NemoArbField p

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

from ComplexCategory NemoArbField p

real: % -> NemoArbField p

from ComplexCategory NemoArbField p

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

reduce: SparseUnivariatePolynomial NemoArbField p -> %

from MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

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

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver NemoArbField p

reducedSystem: Matrix % -> Matrix Integer if NemoArbField p has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix NemoArbField p

from LinearlyExplicitOver NemoArbField p

regularRepresentation: % -> Matrix NemoArbField p

from FramedAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

regularRepresentation: (%, Vector %) -> Matrix NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

rem: (%, %) -> %

from EuclideanDomain

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

from FiniteFieldCategory

represents: (Vector NemoArbField p, Vector %) -> %

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

represents: Vector NemoArbField p -> %

from FramedModule NemoArbField p

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> NemoArbField p

from RetractableTo NemoArbField p

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(NemoArbField p, failed)

from RetractableTo NemoArbField p

riemannZeta: % -> %

from SpecialFunctionCategory

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

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 NemoArbField p has Finite

from Finite

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NemoArbField p 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 NemoArbField p has FiniteFieldCategory

from FiniteFieldCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

trace: % -> NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

traceMatrix: () -> Matrix NemoArbField p

from FramedAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

traceMatrix: Vector % -> Matrix NemoArbField p

from FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

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 NemoArbField p

Approximate

arbitraryPrecision

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(NemoArbField p, NemoArbField p)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if NemoArbField p has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom NemoArbField p

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ComplexCategory NemoArbField p

ConvertibleTo Complex DoubleFloat

ConvertibleTo Complex Float

ConvertibleTo InputForm if NemoArbField p has ConvertibleTo InputForm

ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if NemoArbField p has ConvertibleTo Pattern Integer

ConvertibleTo SparseUnivariatePolynomial NemoArbField p

ConvertibleTo String

DifferentialExtension NemoArbField p

DifferentialRing

DivisionRing

ElementaryFunctionCategory

Eltable(NemoArbField p, %) if NemoArbField p has Eltable(NemoArbField p, NemoArbField p)

EntireRing

EuclideanDomain

Evalable NemoArbField p if NemoArbField p has Evalable NemoArbField p

Field

FieldOfPrimeCharacteristic if NemoArbField p has FiniteFieldCategory

Finite if NemoArbField p has Finite

FiniteFieldCategory if NemoArbField p has FiniteFieldCategory

FiniteRankAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

FramedAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

FramedModule NemoArbField p

FullyEvalableOver NemoArbField p

FullyLinearlyExplicitOver NemoArbField p

FullyPatternMatchable NemoArbField p

FullyRetractableTo NemoArbField p

GcdDomain

Hashable if NemoArbField p has Hashable

HyperbolicFunctionCategory

InnerEvalable(NemoArbField p, NemoArbField p) if NemoArbField p has Evalable NemoArbField p

InnerEvalable(Symbol, NemoArbField p) if NemoArbField p has InnerEvalable(Symbol, NemoArbField p)

IntegralDomain

JuliaArbitraryPrecision

JuliaObjectRing

JuliaObjectType

JuliaRing

JuliaType

LeftModule %

LeftModule Fraction Integer

LeftModule NemoArbField p

LeftOreRing

LinearlyExplicitOver Integer if NemoArbField p has LinearlyExplicitOver Integer

LinearlyExplicitOver NemoArbField p

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module NemoArbField p

MonogenicAlgebra(NemoArbField p, SparseUnivariatePolynomial NemoArbField p)

Monoid

multiplicativeValuation if NemoArbField p has IntegerNumberSystem

NemoRing

NemoType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra NemoArbField p

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PartialDifferentialRing Symbol if NemoArbField p has PartialDifferentialRing Symbol

Patternable NemoArbField p

PatternMatchable Float

PatternMatchable Integer if NemoArbField p has PatternMatchable Integer

PolynomialFactorizationExplicit if NemoArbField p has PolynomialFactorizationExplicit

PrincipalIdealDomain

RadicalCategory

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo NemoArbField p

RightModule %

RightModule Fraction Integer

RightModule Integer if NemoArbField p has LinearlyExplicitOver Integer

RightModule NemoArbField p

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SpecialFunctionCategory

StepThrough if NemoArbField p has FiniteFieldCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown