Stream-based implementation of `Qp:` numbers are represented as sum(`i` = `k`.., a[`i`] * p^i) where the a[`i`] lie in 0, 1, …, (`p` - 1).

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, Fraction Integer) -> %
*: (%, Integer) -> % if PAdicInteger p has LinearlyExplicitOver Integer
*: (%, PAdicInteger p) -> %
*: (Fraction Integer, %) -> %
*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PAdicInteger p, %) -> %
*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

<=: (%, %) -> Boolean if PAdicInteger p has OrderedSet

from PartialOrder

<: (%, %) -> Boolean if PAdicInteger p has OrderedSet

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean if PAdicInteger p has OrderedSet

from PartialOrder

>: (%, %) -> Boolean if PAdicInteger p has OrderedSet

from PartialOrder

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if PAdicInteger p has OrderedIntegralDomain

from OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

approximate: (%, Integer) -> Fraction Integer

associates?: (%, %) -> Boolean

from EntireRing

associator: (%, %, %) -> %
characteristic: () -> NonNegativeInteger
charthRoot: % -> Union(%, failed) if PAdicInteger p has CharacteristicNonZero or % has CharacteristicNonZero and PAdicInteger p has PolynomialFactorizationExplicit
coerce: % -> %

from Algebra %

coerce: % -> OutputForm
coerce: Fraction Integer -> %
coerce: Integer -> %
coerce: Symbol -> % if PAdicInteger p has RetractableTo Symbol
commutator: (%, %) -> %
conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and PAdicInteger p has PolynomialFactorizationExplicit

continuedFraction: % -> ContinuedFraction Fraction Integer

convert: % -> DoubleFloat if PAdicInteger p has RealConstant
convert: % -> Float if PAdicInteger p has RealConstant
convert: % -> InputForm if PAdicInteger p has ConvertibleTo InputForm
convert: % -> Pattern Float if PAdicInteger p has ConvertibleTo Pattern Float
convert: % -> Pattern Integer if PAdicInteger p has ConvertibleTo Pattern Integer
D: % -> % if PAdicInteger p has DifferentialRing

from DifferentialRing

D: (%, List Symbol) -> % if PAdicInteger p has PartialDifferentialRing Symbol
D: (%, List Symbol, List NonNegativeInteger) -> % if PAdicInteger p has PartialDifferentialRing Symbol
D: (%, NonNegativeInteger) -> % if PAdicInteger p has DifferentialRing

from DifferentialRing

D: (%, Symbol) -> % if PAdicInteger p has PartialDifferentialRing Symbol
D: (%, Symbol, NonNegativeInteger) -> % if PAdicInteger p has PartialDifferentialRing Symbol
denominator: % -> %
differentiate: % -> % if PAdicInteger p has DifferentialRing

from DifferentialRing

differentiate: (%, List Symbol) -> % if PAdicInteger p has PartialDifferentialRing Symbol
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if PAdicInteger p has PartialDifferentialRing Symbol
differentiate: (%, NonNegativeInteger) -> % if PAdicInteger p has DifferentialRing

from DifferentialRing

differentiate: (%, Symbol) -> % if PAdicInteger p has PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> % if PAdicInteger p has PartialDifferentialRing Symbol
divide: (%, %) -> Record(quotient: %, remainder: %)

from EuclideanDomain

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

expressIdealMember: (List %, %) -> Union(List %, failed)
exquo: (%, %) -> Union(%, failed)

from EntireRing

extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %)

from EuclideanDomain

extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed)

from EuclideanDomain

factor: % -> Factored %
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PolynomialFactorizationExplicit
fractionPart: % -> %
gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

init: % if PAdicInteger p has StepThrough

from StepThrough

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: (%, %) -> % if PAdicInteger p has OrderedSet

from OrderedSet

min: (%, %) -> % if PAdicInteger p has OrderedSet

from OrderedSet

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

from EuclideanDomain

negative?: % -> Boolean if PAdicInteger p has OrderedIntegralDomain

from OrderedRing

nextItem: % -> Union(%, failed) if PAdicInteger p has StepThrough

from StepThrough

numerator: % -> %
one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if PAdicInteger p has PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if PAdicInteger p has PatternMatchable Integer
plenaryPower: (%, PositiveInteger) -> %
positive?: % -> Boolean if PAdicInteger p has OrderedIntegralDomain

from OrderedRing

prime?: % -> Boolean
principalIdeal: List % -> Record(coef: List %, generator: %)
quo: (%, %) -> %

from EuclideanDomain

recip: % -> Union(%, failed)

from MagmaWithUnit

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

from EuclideanDomain

removeZeroes: % -> %

removeZeroes: (Integer, %) -> %

retract: % -> Fraction Integer if PAdicInteger p has RetractableTo Integer
retract: % -> Integer if PAdicInteger p has RetractableTo Integer
retract: % -> Symbol if PAdicInteger p has RetractableTo Symbol
retractIfCan: % -> Union(Fraction Integer, failed) if PAdicInteger p has RetractableTo Integer
retractIfCan: % -> Union(Integer, failed) if PAdicInteger p has RetractableTo Integer
retractIfCan: % -> Union(PAdicInteger p, failed)
retractIfCan: % -> Union(Symbol, failed) if PAdicInteger p has RetractableTo Symbol
rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer if PAdicInteger p has OrderedIntegralDomain

from OrderedRing

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

smaller?: (%, %) -> Boolean if PAdicInteger p has Comparable

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if PAdicInteger p has PolynomialFactorizationExplicit
squareFree: % -> Factored %
squareFreePart: % -> %
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PAdicInteger p has PolynomialFactorizationExplicit
subtractIfCan: (%, %) -> Union(%, failed)
unit?: % -> Boolean

from EntireRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CommutativeRing

CommutativeStar

DivisionRing

EntireRing

EuclideanDomain

Field

GcdDomain

IntegralDomain

LeftOreRing

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PrincipalIdealDomain

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown