RealNumberSystem

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The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included DifferentialRing or the elementary functions (see TranscendentalFunctionCategory) in the definition.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean

from EntireRing

associator: (%, %, %) -> %

from NonAssociativeRng

ceiling: % -> %

ceiling x returns the small integer >= x.

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> Pattern Float

from ConvertibleTo Pattern Float

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

from EuclideanDomain

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

floor: % -> %

floor x returns the largest integer <= x.

fractionPart: % -> %

fractionPart x returns the fractional part of x.

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

inv: % -> %

from DivisionRing

latex: % -> String

from SetCategory

lcm: (%, %) -> %

from GcdDomain

lcm: List % -> %

from GcdDomain

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

from LeftOreRing

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

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

from EuclideanDomain

negative?: % -> Boolean

from OrderedRing

norm: % -> %

norm x returns the same as absolute value.

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

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

from PatternMatchable Float

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra Fraction Integer

positive?: % -> Boolean

from OrderedRing

prime?: % -> Boolean

from UniqueFactorizationDomain

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

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: % -> %

round x computes the integer closest to x.

sample: %

from AbelianMonoid

sign: % -> Integer

from OrderedRing

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

sqrt: % -> %

from RadicalCategory

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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

from CancellationAbelianMonoid

truncate: % -> %

truncate x returns the integer between x and 0 closest to x.

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

wholePart: % -> Integer

wholePart x returns the integer part of x.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

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

DivisionRing

EntireRing

EuclideanDomain

Field

GcdDomain

IntegralDomain

LeftModule %

LeftModule Fraction Integer

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Monoid

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedRing

OrderedSet

PartialOrder

PatternMatchable Float

PrincipalIdealDomain

RadicalCategory

RealConstant

RetractableTo Fraction Integer

RetractableTo Integer

RightModule %

RightModule Fraction Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown