NMRealBallΒΆ

jnball.spad line 315 [edit on github]

convenience domain to reflect Nemo ArbField(256), i.e. without parameters.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> %

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NMInteger, %) -> JLObject

from JLObjectRing

*: (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 OrderedAbelianGroup

accuracyBits: % -> JLInt64

acos: % -> %

from ArcTrigonometricFunctionCategory

acosh: % -> %

from ArcHyperbolicFunctionCategory

acot: % -> %

from ArcTrigonometricFunctionCategory

acoth: % -> %

from ArcHyperbolicFunctionCategory

acsc: % -> %

from ArcTrigonometricFunctionCategory

acsch: % -> %

from ArcHyperbolicFunctionCategory

addError!: (%, %) -> %

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: (%, %) -> %

atanh: % -> %

from ArcHyperbolicFunctionCategory

base: () -> PositiveInteger

from FloatingPointSystem

bits: % -> JLInt64

bits: () -> PositiveInteger

from FloatingPointSystem

bits: PositiveInteger -> PositiveInteger

from FloatingPointSystem

ceiling: % -> %

from RealNumberSystem

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Float -> %

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JLFloat64 -> %

commutator: (%, %) -> %

from NonAssociativeRng

contains?: (%, %) -> Boolean

contains?: (%, JLFloat) -> Boolean

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

contains?: (%, NMInteger) -> Boolean

containsNegative?: % -> Boolean

containsNonNegative?: % -> Boolean

containsNonPositive?: % -> Boolean

containsPositive?: % -> Boolean

containsZero?: % -> Boolean

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> JLFloat

convert: % -> NMFraction NMInteger

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

digits: () -> PositiveInteger

from FloatingPointSystem

digits: PositiveInteger -> PositiveInteger

from FloatingPointSystem

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

from EuclideanDomain

equal?: (%, %) -> Boolean

from NMRing

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

exact?: % -> Boolean

exactDivide: (%, %) -> %

from NMRing

exp1: () -> %

exp: % -> %

from ElementaryFunctionCategory

exp: () -> %

expm1: % -> %

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

float: (Integer, Integer) -> %

from FloatingPointSystem

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

from FloatingPointSystem

floor: % -> %

from RealNumberSystem

fractionPart: % -> %

from RealNumberSystem

Gamma: % -> %

Gamma: (%, %) -> %

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

guess: (%, NonNegativeInteger) -> NMAlgebraicNumber

hurwitzZeta: (%, %) -> %

increasePrecision: Integer -> PositiveInteger

from FloatingPointSystem

integer?: % -> Boolean

inv: % -> %

from DivisionRing

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

jlDump: JLObject -> Void

from JLObjectType

jlId: % -> JLInt64

from JLObjectType

jlNMRing: () -> String

from NMRing

jlObject: () -> String

from JLObjectType

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlType: % -> String

from JLObjectType

jnball: (%, %) -> %

jnrb: Float -> %

jnrb: Fraction Integer -> %

jnrb: Integer -> %

jnrb: NMAlgebraicNumber -> %

jnrb: NMExactCalciumField -> %

jnrb: String -> %

latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

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

from LeftOreRing

ldexp: (%, NMInteger) -> %

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log1p: % -> %

log: % -> %

from ElementaryFunctionCategory

mantissa: % -> Integer

from FloatingPointSystem

max: (%, %) -> %

from OrderedSet

max: () -> % if

from FloatingPointSystem

midpoint: % -> %

min: (%, %) -> %

from OrderedSet

min: () -> % if

from FloatingPointSystem

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

negative?: % -> Boolean

from OrderedAbelianGroup

nonNegative?: % -> Boolean

nonPositive?: % -> Boolean

nonZero?: % -> Boolean

norm: % -> %

from RealNumberSystem

nothing?: % -> Boolean

from JLObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> Integer

from FloatingPointSystem

overlaps?: (%, %) -> Boolean

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

from PatternMatchable Float

pi: () -> %

from TranscendentalFunctionCategory

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

polyLog: (%, %) -> %

positive?: % -> Boolean

from OrderedAbelianGroup

precision: () -> PositiveInteger

from FloatingPointSystem

precision: PositiveInteger -> PositiveInteger

from FloatingPointSystem

prime?: % -> Boolean

from UniqueFactorizationDomain

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

radius: % -> %

recip: % -> Union(%, failed)

from MagmaWithUnit

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

round: % -> %

from RealNumberSystem

sample: %

from AbelianMonoid

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

setUnion: (%, %) -> %

sign: % -> Integer

from OrderedAbelianGroup

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 JLType

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

from CancellationAbelianMonoid

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

toString: % -> String

from FloatingPointSystem

toString: (%, NonNegativeInteger) -> String

from FloatingPointSystem

trim: % -> %

truncate: % -> %

from RealNumberSystem

uniqueInteger: % -> Union(NMInteger, failed)

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

urand01: () -> %

wholePart: % -> Integer

from RealNumberSystem

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

JLArbitraryPrecision

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftModule Fraction Integer

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Monoid

NMRing

NMType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedMonoid

OrderedRing

OrderedSemiGroup

OrderedSet

PartialOrder

PatternMatchable Float

PrincipalIdealDomain

RadicalCategory

RealConstant

RealNumberSystem

RetractableTo Fraction Integer

RetractableTo Integer

RightModule %

RightModule Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown