NemoRational

jnemo.spad line 147 [edit on github]

This domain allows the manipulation of Nemo fraction integers (rationals) using the Nemo package for Julia (FLINT based). https://flintlib.org/

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, Fraction Integer) -> %

from RightModule Fraction Integer

*: (%, Integer) -> %

*: (%, NemoInteger) -> %

from RightModule NemoInteger

*: (Fraction Integer, %) -> %

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NemoInteger, %) -> %

from LeftModule NemoInteger

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

/: (NemoInteger, NemoInteger) -> %

from QuotientFieldCategory NemoInteger

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, 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: % -> NemoInteger

from QuotientFieldCategory NemoInteger

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

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

from PolynomialFactorizationExplicit

coerce: % -> %

from Algebra %

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

coerce: Integer -> %

from NonAssociativeRing

coerce: NemoInteger -> %

coerce: Symbol -> % if NemoInteger has RetractableTo Symbol

from CoercibleFrom Symbol

commutator: (%, %) -> %

from NonAssociativeRng

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

from PolynomialFactorizationExplicit

convert: % -> DoubleFloat

from ConvertibleTo DoubleFloat

convert: % -> Float

from ConvertibleTo Float

convert: % -> InputForm

from ConvertibleTo InputForm

convert: % -> Pattern Float if NemoInteger has ConvertibleTo Pattern Float

from ConvertibleTo Pattern Float

convert: % -> Pattern Integer

from ConvertibleTo Pattern Integer

convert: % -> String

from ConvertibleTo String

D: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from DifferentialExtension NemoInteger

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

from DifferentialExtension NemoInteger

D: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

denom: % -> NemoInteger

from QuotientFieldCategory NemoInteger

denominator: % -> %

from QuotientFieldCategory NemoInteger

differentiate: % -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from DifferentialExtension NemoInteger

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

from DifferentialExtension NemoInteger

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

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

from EuclideanDomain

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

from Eltable(NemoInteger, %)

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

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

from Evalable NemoInteger

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

from Evalable NemoInteger

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

from InnerEvalable(NemoInteger, NemoInteger)

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

from InnerEvalable(Symbol, NemoInteger)

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

from InnerEvalable(NemoInteger, NemoInteger)

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

from InnerEvalable(Symbol, NemoInteger)

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

factorFraction: % -> Fraction Factored NemoInteger

factorFraction(r) factors the numerator and the denominator of the fraction r.

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

from PolynomialFactorizationExplicit

factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NemoInteger has PolynomialFactorizationExplicit

from PolynomialFactorizationExplicit

floor: % -> NemoInteger

from QuotientFieldCategory NemoInteger

fractionPart: % -> %

from QuotientFieldCategory NemoInteger

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

init: %

from StepThrough

inv: % -> %

from DivisionRing

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

jnrat: (NemoInteger, NemoInteger) -> %

jnrat: Fraction Integer -> %

jnrat: Integer -> %

jnrat: NemoInteger -> %

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

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

from FullyEvalableOver NemoInteger

max: (%, %) -> %

from OrderedSet

min: (%, %) -> %

from OrderedSet

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

from EuclideanDomain

mutable?: % -> Boolean

from JuliaObjectType

negative?: % -> Boolean

from OrderedRing

nextItem: % -> Union(%, failed)

from StepThrough

nothing?: % -> Boolean

from JuliaObjectType

numer: % -> NemoInteger

from QuotientFieldCategory NemoInteger

numerator: % -> %

from QuotientFieldCategory NemoInteger

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if NemoInteger has PatternMatchable Float

from PatternMatchable Float

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

from PatternMatchable Integer

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

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

from LinearlyExplicitOver Integer

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

from LinearlyExplicitOver NemoInteger

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

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix NemoInteger

from LinearlyExplicitOver NemoInteger

rem: (%, %) -> %

from EuclideanDomain

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> NemoInteger

from RetractableTo NemoInteger

retract: % -> Symbol if NemoInteger has RetractableTo Symbol

from RetractableTo Symbol

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

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(NemoInteger, failed)

from RetractableTo NemoInteger

retractIfCan: % -> Union(Symbol, failed) if NemoInteger has RetractableTo Symbol

from RetractableTo Symbol

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer

from OrderedRing

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean

from Comparable

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

from PolynomialFactorizationExplicit

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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

from PolynomialFactorizationExplicit

string: % -> String

from JuliaObjectType

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

from CancellationAbelianMonoid

unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

wholePart: % -> NemoInteger

from QuotientFieldCategory NemoInteger

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra NemoInteger

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(NemoInteger, NemoInteger)

CancellationAbelianMonoid

Canonical

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if NemoInteger has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom NemoInteger

CoercibleFrom Symbol if NemoInteger has RetractableTo Symbol

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if NemoInteger has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

ConvertibleTo String

DifferentialExtension NemoInteger

DifferentialRing

DivisionRing

Eltable(NemoInteger, %) if NemoInteger has Eltable(NemoInteger, NemoInteger)

EntireRing

EuclideanDomain

Evalable NemoInteger if NemoInteger has Evalable NemoInteger

Field

FullyEvalableOver NemoInteger

FullyLinearlyExplicitOver NemoInteger

FullyPatternMatchable NemoInteger

GcdDomain

InnerEvalable(NemoInteger, NemoInteger) if NemoInteger has Evalable NemoInteger

InnerEvalable(Symbol, NemoInteger) if NemoInteger has InnerEvalable(Symbol, NemoInteger)

IntegralDomain

JuliaObjectRing

JuliaObjectType

JuliaRing

JuliaType

LeftModule %

LeftModule Fraction Integer

LeftModule NemoInteger

LeftOreRing

LinearlyExplicitOver Integer if NemoInteger has LinearlyExplicitOver Integer

LinearlyExplicitOver NemoInteger

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module NemoInteger

Monoid

NemoRing

NemoType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer

NonAssociativeAlgebra NemoInteger

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedRing

OrderedSet

PartialDifferentialRing Symbol if NemoInteger has PartialDifferentialRing Symbol

PartialOrder

Patternable NemoInteger

PatternMatchable Float if NemoInteger has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit if NemoInteger has PolynomialFactorizationExplicit

PrincipalIdealDomain

QuotientFieldCategory NemoInteger

RealConstant

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo NemoInteger

RetractableTo Symbol if NemoInteger has RetractableTo Symbol

RightModule %

RightModule Fraction Integer

RightModule Integer if NemoInteger has LinearlyExplicitOver Integer

RightModule NemoInteger

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown