NMPadicRational pΒΆ
jnpadic.spad line 439 [edit on github]
p: Integer
This is a domain of Qp
.
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from Magma
- *: (%, Fraction Integer) -> %
from RightModule Fraction Integer
- *: (%, Integer) -> % if NMExtendedPadicInteger(p, 64) has LinearlyExplicitOver Integer
from RightModule Integer
- *: (%, NMExtendedPadicInteger(p, 64)) -> %
from RightModule NMExtendedPadicInteger(p, 64)
*: (%, NMFraction NMInteger) -> %
*: (%, NMInteger) -> %
- *: (Fraction Integer, %) -> %
from LeftModule Fraction Integer
- *: (Integer, %) -> %
from AbelianGroup
- *: (NMExtendedPadicInteger(p, 64), %) -> %
from LeftModule NMExtendedPadicInteger(p, 64)
*: (NMFraction NMInteger, %) -> %
*: (NMInteger, %) -> %
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
+: (%, NMFraction NMInteger) -> %
+: (%, NMInteger) -> %
+: (NMFraction NMInteger, %) -> %
+: (NMInteger, %) -> %
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- /: (%, %) -> %
from Field
- /: (NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64)) -> %
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- <=: (%, %) -> Boolean if NMExtendedPadicInteger(p, 64) has OrderedSet
from PartialOrder
- <: (%, %) -> Boolean if NMExtendedPadicInteger(p, 64) has OrderedSet
from PartialOrder
- >=: (%, %) -> Boolean if NMExtendedPadicInteger(p, 64) has OrderedSet
from PartialOrder
- >: (%, %) -> Boolean if NMExtendedPadicInteger(p, 64) has OrderedSet
from PartialOrder
- ^: (%, %) -> %
- ^: (%, Fraction Integer) -> %
from RadicalCategory
- ^: (%, Integer) -> %
from DivisionRing
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> % if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
from OrderedRing
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- ceiling: % -> NMExtendedPadicInteger(p, 64) if NMExtendedPadicInteger(p, 64) has IntegerNumberSystem
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- characteristic: % -> NonNegativeInteger
from NMRing
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- charthRoot: % -> Union(%, failed) if % has CharacteristicNonZero and NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit or NMExtendedPadicInteger(p, 64) has CharacteristicNonZero
- coerce: % -> %
from Algebra %
- coerce: % -> JLObject
from JLObjectType
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: Fraction Integer -> %
from CoercibleFrom Fraction Integer
- coerce: Integer -> %
from NonAssociativeRing
- coerce: NMExtendedPadicInteger(p, 64) -> %
from Algebra NMExtendedPadicInteger(p, 64)
coerce: NMInteger -> %
- coerce: Symbol -> % if NMExtendedPadicInteger(p, 64) has RetractableTo Symbol
from CoercibleFrom Symbol
- commutator: (%, %) -> %
from NonAssociativeRng
- conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit
- convert: % -> DoubleFloat if NMExtendedPadicInteger(p, 64) has RealConstant
from ConvertibleTo DoubleFloat
- convert: % -> Float if NMExtendedPadicInteger(p, 64) has RealConstant
from ConvertibleTo Float
- convert: % -> InputForm if NMExtendedPadicInteger(p, 64) has ConvertibleTo InputForm
from ConvertibleTo InputForm
- convert: % -> Pattern Float if NMExtendedPadicInteger(p, 64) has ConvertibleTo Pattern Float
from ConvertibleTo Pattern Float
- convert: % -> Pattern Integer if NMExtendedPadicInteger(p, 64) has ConvertibleTo Pattern Integer
from ConvertibleTo Pattern Integer
- convert: % -> String
from ConvertibleTo String
- D: % -> % if NMExtendedPadicInteger(p, 64) has DifferentialRing
from DifferentialRing
- D: (%, List Symbol) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- D: (%, List Symbol, List NonNegativeInteger) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- D: (%, NMExtendedPadicInteger(p, 64) -> NMExtendedPadicInteger(p, 64)) -> %
from DifferentialExtension NMExtendedPadicInteger(p, 64)
- D: (%, NMExtendedPadicInteger(p, 64) -> NMExtendedPadicInteger(p, 64), NonNegativeInteger) -> %
from DifferentialExtension NMExtendedPadicInteger(p, 64)
- D: (%, NonNegativeInteger) -> % if NMExtendedPadicInteger(p, 64) has DifferentialRing
from DifferentialRing
- D: (%, Symbol) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- D: (%, Symbol, NonNegativeInteger) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- denom: % -> NMExtendedPadicInteger(p, 64)
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- denominator: % -> %
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- differentiate: % -> % if NMExtendedPadicInteger(p, 64) has DifferentialRing
from DifferentialRing
- differentiate: (%, List Symbol) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- differentiate: (%, List Symbol, List NonNegativeInteger) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- differentiate: (%, NMExtendedPadicInteger(p, 64) -> NMExtendedPadicInteger(p, 64)) -> %
from DifferentialExtension NMExtendedPadicInteger(p, 64)
- differentiate: (%, NMExtendedPadicInteger(p, 64) -> NMExtendedPadicInteger(p, 64), NonNegativeInteger) -> %
from DifferentialExtension NMExtendedPadicInteger(p, 64)
- differentiate: (%, NonNegativeInteger) -> % if NMExtendedPadicInteger(p, 64) has DifferentialRing
from DifferentialRing
- differentiate: (%, Symbol) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- differentiate: (%, Symbol, NonNegativeInteger) -> % if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
- divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
- elt: (%, NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has Eltable(NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64))
from Eltable(NMExtendedPadicInteger(p, 64), %)
- euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
- eval: (%, Equation NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has Evalable NMExtendedPadicInteger(p, 64)
from Evalable NMExtendedPadicInteger(p, 64)
- eval: (%, List Equation NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has Evalable NMExtendedPadicInteger(p, 64)
from Evalable NMExtendedPadicInteger(p, 64)
- eval: (%, List NMExtendedPadicInteger(p, 64), List NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has Evalable NMExtendedPadicInteger(p, 64)
from InnerEvalable(NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64))
- eval: (%, List Symbol, List NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has InnerEvalable(Symbol, NMExtendedPadicInteger(p, 64))
from InnerEvalable(Symbol, NMExtendedPadicInteger(p, 64))
- eval: (%, NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has Evalable NMExtendedPadicInteger(p, 64)
from InnerEvalable(NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64))
- eval: (%, Symbol, NMExtendedPadicInteger(p, 64)) -> % if NMExtendedPadicInteger(p, 64) has InnerEvalable(Symbol, NMExtendedPadicInteger(p, 64))
from InnerEvalable(Symbol, NMExtendedPadicInteger(p, 64))
- exactDivide: (%, %) -> %
from NMRing
- exp: % -> %
- 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
- factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit
- factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit
- floor: % -> NMExtendedPadicInteger(p, 64) if NMExtendedPadicInteger(p, 64) has IntegerNumberSystem
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- fractionPart: % -> %
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
frobenius: (%, Integer) -> %
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
- init: % if NMExtendedPadicInteger(p, 64) has StepThrough
from StepThrough
- 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
- jlRef: % -> SExpression
from JLObjectType
- jlref: String -> %
from JLObjectType
- jlType: % -> String
from JLObjectType
jnpadic: Integer -> %
jnpadic: NMInteger -> %
- latex: % -> String
from SetCategory
- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %)
from LeftOreRing
- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
from Magma
- leftRecip: % -> Union(%, failed)
from MagmaWithUnit
liftQ: % -> NMFraction NMInteger
liftZ: % -> NMInteger
- log: % -> %
- map: (NMExtendedPadicInteger(p, 64) -> NMExtendedPadicInteger(p, 64), %) -> %
from FullyEvalableOver NMExtendedPadicInteger(p, 64)
- max: (%, %) -> % if NMExtendedPadicInteger(p, 64) has OrderedSet
from OrderedSet
- min: (%, %) -> % if NMExtendedPadicInteger(p, 64) has OrderedSet
from OrderedSet
modulus: () -> Integer
- multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
- mutable?: % -> Boolean
from JLObjectType
- negative?: % -> Boolean if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
from OrderedRing
- nextItem: % -> Union(%, failed) if NMExtendedPadicInteger(p, 64) has StepThrough
from StepThrough
- nothing?: % -> Boolean
from JLObjectType
- nthRoot: (%, Integer) -> %
from RadicalCategory
- numer: % -> NMExtendedPadicInteger(p, 64)
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- numerator: % -> %
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
O: () -> %
- one?: % -> Boolean
from MagmaWithUnit
- opposite?: (%, %) -> Boolean
from AbelianMonoid
- patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if NMExtendedPadicInteger(p, 64) has PatternMatchable Float
from PatternMatchable Float
- patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if NMExtendedPadicInteger(p, 64) has PatternMatchable Integer
from PatternMatchable Integer
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra %
- positive?: % -> Boolean if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
from OrderedRing
precision: % -> Integer
prime: % -> Integer
- 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 NMExtendedPadicInteger(p, 64) has LinearlyExplicitOver Integer
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix NMExtendedPadicInteger(p, 64), vec: Vector NMExtendedPadicInteger(p, 64))
from LinearlyExplicitOver NMExtendedPadicInteger(p, 64)
- reducedSystem: Matrix % -> Matrix Integer if NMExtendedPadicInteger(p, 64) has LinearlyExplicitOver Integer
- reducedSystem: Matrix % -> Matrix NMExtendedPadicInteger(p, 64)
from LinearlyExplicitOver NMExtendedPadicInteger(p, 64)
- rem: (%, %) -> %
from EuclideanDomain
- retract: % -> Fraction Integer if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
from RetractableTo Fraction Integer
- retract: % -> Integer if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
from RetractableTo Integer
- retract: % -> NMExtendedPadicInteger(p, 64)
from RetractableTo NMExtendedPadicInteger(p, 64)
- retract: % -> Symbol if NMExtendedPadicInteger(p, 64) has RetractableTo Symbol
from RetractableTo Symbol
- retractIfCan: % -> Union(Fraction Integer, failed) if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
from RetractableTo Fraction Integer
- retractIfCan: % -> Union(Integer, failed) if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
from RetractableTo Integer
- retractIfCan: % -> Union(NMExtendedPadicInteger(p, 64), failed)
from RetractableTo NMExtendedPadicInteger(p, 64)
- retractIfCan: % -> Union(Symbol, failed) if NMExtendedPadicInteger(p, 64) has RetractableTo Symbol
from RetractableTo Symbol
- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- rightPower: (%, PositiveInteger) -> %
from Magma
- rightRecip: % -> Union(%, failed)
from MagmaWithUnit
- sample: %
from AbelianMonoid
- sign: % -> Integer if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
from OrderedRing
- sizeLess?: (%, %) -> Boolean
from EuclideanDomain
- smaller?: (%, %) -> Boolean if NMExtendedPadicInteger(p, 64) has Comparable
from Comparable
- solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit
- sqrt: % -> %
from RadicalCategory
- squareFree: % -> Factored %
- squareFreePart: % -> %
- squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit
- subtractIfCan: (%, %) -> Union(%, failed)
teichmuller: % -> %
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
valuation: % -> %
- wholePart: % -> NMExtendedPadicInteger(p, 64)
from QuotientFieldCategory NMExtendedPadicInteger(p, 64)
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
Algebra NMExtendedPadicInteger(p, 64)
BiModule(%, %)
BiModule(Fraction Integer, Fraction Integer)
BiModule(NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64))
CharacteristicNonZero if NMExtendedPadicInteger(p, 64) has CharacteristicNonZero
CoercibleFrom Fraction Integer if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
CoercibleFrom Integer if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
CoercibleFrom NMExtendedPadicInteger(p, 64)
CoercibleFrom Symbol if NMExtendedPadicInteger(p, 64) has RetractableTo Symbol
Comparable if NMExtendedPadicInteger(p, 64) has Comparable
ConvertibleTo DoubleFloat if NMExtendedPadicInteger(p, 64) has RealConstant
ConvertibleTo Float if NMExtendedPadicInteger(p, 64) has RealConstant
ConvertibleTo InputForm if NMExtendedPadicInteger(p, 64) has ConvertibleTo InputForm
ConvertibleTo Pattern Float if NMExtendedPadicInteger(p, 64) has ConvertibleTo Pattern Float
ConvertibleTo Pattern Integer if NMExtendedPadicInteger(p, 64) has ConvertibleTo Pattern Integer
DifferentialExtension NMExtendedPadicInteger(p, 64)
DifferentialRing if NMExtendedPadicInteger(p, 64) has DifferentialRing
Eltable(NMExtendedPadicInteger(p, 64), %) if NMExtendedPadicInteger(p, 64) has Eltable(NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64))
Evalable NMExtendedPadicInteger(p, 64) if NMExtendedPadicInteger(p, 64) has Evalable NMExtendedPadicInteger(p, 64)
FullyEvalableOver NMExtendedPadicInteger(p, 64)
FullyLinearlyExplicitOver NMExtendedPadicInteger(p, 64)
FullyPatternMatchable NMExtendedPadicInteger(p, 64)
InnerEvalable(NMExtendedPadicInteger(p, 64), NMExtendedPadicInteger(p, 64)) if NMExtendedPadicInteger(p, 64) has Evalable NMExtendedPadicInteger(p, 64)
InnerEvalable(Symbol, NMExtendedPadicInteger(p, 64)) if NMExtendedPadicInteger(p, 64) has InnerEvalable(Symbol, NMExtendedPadicInteger(p, 64))
LeftModule NMExtendedPadicInteger(p, 64)
LinearlyExplicitOver Integer if NMExtendedPadicInteger(p, 64) has LinearlyExplicitOver Integer
LinearlyExplicitOver NMExtendedPadicInteger(p, 64)
Module %
Module NMExtendedPadicInteger(p, 64)
NonAssociativeAlgebra Fraction Integer
NonAssociativeAlgebra NMExtendedPadicInteger(p, 64)
OrderedAbelianGroup if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
OrderedAbelianMonoid if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
OrderedAbelianSemiGroup if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
OrderedCancellationAbelianMonoid if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
OrderedIntegralDomain if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
OrderedRing if NMExtendedPadicInteger(p, 64) has OrderedIntegralDomain
OrderedSet if NMExtendedPadicInteger(p, 64) has OrderedSet
PartialDifferentialRing Symbol if NMExtendedPadicInteger(p, 64) has PartialDifferentialRing Symbol
PartialOrder if NMExtendedPadicInteger(p, 64) has OrderedSet
Patternable NMExtendedPadicInteger(p, 64)
PatternMatchable Float if NMExtendedPadicInteger(p, 64) has PatternMatchable Float
PatternMatchable Integer if NMExtendedPadicInteger(p, 64) has PatternMatchable Integer
PolynomialFactorizationExplicit if NMExtendedPadicInteger(p, 64) has PolynomialFactorizationExplicit
QuotientFieldCategory NMExtendedPadicInteger(p, 64)
RealConstant if NMExtendedPadicInteger(p, 64) has RealConstant
RetractableTo Fraction Integer if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
RetractableTo Integer if NMExtendedPadicInteger(p, 64) has RetractableTo Integer
RetractableTo NMExtendedPadicInteger(p, 64)
RetractableTo Symbol if NMExtendedPadicInteger(p, 64) has RetractableTo Symbol
RightModule Integer if NMExtendedPadicInteger(p, 64) has LinearlyExplicitOver Integer
RightModule NMExtendedPadicInteger(p, 64)
StepThrough if NMExtendedPadicInteger(p, 64) has StepThrough