NemoRealField

jnball.spad line 575 [edit on github]

NemoRealField 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) -> %

*: (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

/: (Integer, %) -> %

<=: (%, %) -> 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 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

addError!: (%, %) -> %

addError!(x, y) adds the values (absolute) of the midpoint and radius of y to the radius of x.

airyAi: % -> %

from SpecialFunctionCategory

airyAiPrime: % -> %

from SpecialFunctionCategory

airyBi: % -> %

from SpecialFunctionCategory

airyBiPrime: % -> %

from SpecialFunctionCategory

angerJ: (%, %) -> %

from SpecialFunctionCategory

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 inverse tangent of x/y.

atanh: % -> %

from ArcHyperbolicFunctionCategory

base: () -> PositiveInteger

from FloatingPointSystem

besselI: (%, %) -> %

from SpecialFunctionCategory

besselJ: (%, %) -> %

from SpecialFunctionCategory

besselK: (%, %) -> %

from SpecialFunctionCategory

besselY: (%, %) -> %

from SpecialFunctionCategory

Beta: (%, %) -> %

from SpecialFunctionCategory

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

from SpecialFunctionCategory

bits: () -> PositiveInteger

from FloatingPointSystem

bits: PositiveInteger -> PositiveInteger

from FloatingPointSystem

ceiling: % -> %

from SpecialFunctionCategory

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from SpecialFunctionCategory

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Float -> %

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JuliaFloat64 -> %

commutator: (%, %) -> %

from NonAssociativeRng

conjugate: % -> %

from SpecialFunctionCategory

contains?: (%, %) -> Boolean

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

contains?: (%, JuliaFloat) -> 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.

containsNegative?: % -> Boolean

containsNegative?(x) cheks whether or not x contains any negative value.

containsNonNegative?: % -> Boolean

containsNonNegative?(x) cheks whether or not x contains any non negative value.

containsNonPositive?: % -> Boolean

containsNonPositive?(x) checks whether or not x contains any non positive value.

containsPositive?: % -> Boolean

containsPositive?(x) cheks whether or not x contains any positive value.

containsZero?: % -> Boolean

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

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> JuliaFloat

convert: % -> NemoRational

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

decreasePrecision: Integer -> PositiveInteger

from FloatingPointSystem

differentiate: % -> %

from DifferentialRing

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

digamma: % -> %

from SpecialFunctionCategory

digits: () -> PositiveInteger

from FloatingPointSystem

digits: PositiveInteger -> PositiveInteger

from FloatingPointSystem

diracDelta: % -> %

from SpecialFunctionCategory

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

from EuclideanDomain

ellipticE: % -> %

from SpecialFunctionCategory

ellipticE: (%, %) -> %

from SpecialFunctionCategory

ellipticF: (%, %) -> %

from SpecialFunctionCategory

ellipticK: % -> %

from SpecialFunctionCategory

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

from SpecialFunctionCategory

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

exact?: % -> Boolean

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

exp1: () -> %

exp() returns the NemoRealField represenation of ℯ (exp(1)).

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

exp() returns the NemoRealField represenation of 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.

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

finite?: % -> Boolean

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

float: (Integer, Integer) -> %

from FloatingPointSystem

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

from FloatingPointSystem

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

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

hermiteH: (%, %) -> %

from SpecialFunctionCategory

hurwitzZeta: (%, %) -> %

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

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

from SpecialFunctionCategory

increasePrecision: Integer -> PositiveInteger

from FloatingPointSystem

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

jnball: (%, %) -> %

jnball(x,r) returns a ball with midpoint x and radius r.

jnrf: Float -> %

jnrf: Fraction Integer -> %

jnrf: Integer -> %

jnrf: 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

log1p: % -> %

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

log: % -> %

from ElementaryFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

mantissa: % -> Integer

from FloatingPointSystem

max: (%, %) -> %

from OrderedSet

max: () -> % if

from FloatingPointSystem

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

midpoint: % -> %

midpoint(x) returns the midpoint of x.

min: (%, %) -> %

from OrderedSet

min: () -> % if

from FloatingPointSystem

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

negative?: % -> Boolean

from OrderedRing

nonNegative?: % -> Boolean

nonnegative(v) checks whether or not x is greater or equal to zero.

nonPositive?: % -> Boolean

nonnegative(v) checks whether or not x is lower or equal to zero.

nonZero?: % -> Boolean

nonZero?(x) returns true if x is equal to 0.

norm: % -> %

from RealNumberSystem

nothing?: % -> Boolean

from JuliaObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> Integer

from FloatingPointSystem

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

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

polygamma: (%, %) -> %

from SpecialFunctionCategory

polylog: (%, %) -> %

from SpecialFunctionCategory

positive?: % -> Boolean

from OrderedRing

precision: () -> PositiveInteger

from FloatingPointSystem

precision: PositiveInteger -> PositiveInteger

from FloatingPointSystem

prime?: % -> Boolean

from UniqueFactorizationDomain

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

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

from SpecialFunctionCategory

radius: % -> %

radius(x) returns the radius of x.

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

retractIfCan: NemoAlgebraicNumber -> Union(%, failed)

riemannZeta: % -> %

from SpecialFunctionCategory

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

setUnion: (%, %) -> %

setUnion(x,y) returns the unions of the intervals x and y.

sign: % -> %

from SpecialFunctionCategory

sign: % -> Integer

from OrderedRing

sin: % -> %

from TrigonometricFunctionCategory

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

struveH: (%, %) -> %

from SpecialFunctionCategory

struveL: (%, %) -> %

from SpecialFunctionCategory

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

from CancellationAbelianMonoid

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

toString: % -> String

from FloatingPointSystem

toString: (%, NonNegativeInteger) -> String

from FloatingPointSystem

trim: % -> %

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

truncate: % -> %

from RealNumberSystem

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

urand01: () -> %

urand01() returns an uniformly distributed random number contained in [0,1].

weberE: (%, %) -> %

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

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

from SpecialFunctionCategory

wholePart: % -> Integer

from RealNumberSystem

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

from SpecialFunctionCategory

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Approximate

arbitraryPrecision

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

LeftModule %

LeftModule Fraction Integer

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Monoid

NemoRing

NemoType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedRing

OrderedSet

PartialOrder

PatternMatchable Float

PrincipalIdealDomain

RadicalCategory

RealConstant

RealNumberSystem

RetractableTo Fraction Integer

RetractableTo Integer

RightModule %

RightModule Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SpecialFunctionCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown