This is the category of stream-based representations of Qp.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, Fraction Integer) -> %

*: (Fraction Integer, %) -> %
*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, %) -> %

from Field

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

from PartialOrder

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

from PartialOrder

=: (%, %) -> Boolean

from BasicType

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

from PartialOrder

>: (%, %) -> Boolean if PADIC has OrderedSet

from PartialOrder

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> % if PADIC has OrderedIntegralDomain

from OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
approximate: (%, Integer) -> Fraction Integer

approximate(x, n) returns a rational number y such that y = x (mod p^n).

associates?: (%, %) -> Boolean

from EntireRing

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

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

from Algebra %

coerce: % -> OutputForm
coerce: Fraction Integer -> %
coerce: Integer -> %

coerce: Symbol -> % if PADIC has RetractableTo Symbol
commutator: (%, %) -> %
conditionP: Matrix % -> Union(Vector %, failed) if PADIC has PolynomialFactorizationExplicit and % has CharacteristicNonZero
continuedFraction: % -> ContinuedFraction Fraction Integer

continuedFraction(x) converts the p-adic rational number x to a continued fraction.

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

from DifferentialRing

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

from DifferentialRing

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

denominator: % -> %

differentiate: % -> % if PADIC has DifferentialRing

from DifferentialRing

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

from DifferentialRing

differentiate: (%, Symbol) -> % if PADIC has PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> % if PADIC 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 PADIC has PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC has PolynomialFactorizationExplicit

fractionPart: % -> %

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

init: % if PADIC 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 PADIC has OrderedSet

from OrderedSet

min: (%, %) -> % if PADIC has OrderedSet

from OrderedSet

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

from EuclideanDomain

negative?: % -> Boolean if PADIC has OrderedIntegralDomain

from OrderedRing

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

from StepThrough

numerator: % -> %

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if PADIC has PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if PADIC has PatternMatchable Integer
positive?: % -> Boolean if PADIC 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 PADIC has LinearlyExplicitOver Integer
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix PADIC, vec: Vector PADIC)

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

rem: (%, %) -> %

from EuclideanDomain

removeZeroes: % -> %

removeZeroes: (Integer, %) -> %

removeZeroes(n, x) removes up to n leading zeroes from the p-adic rational x.

retract: % -> Fraction Integer if PADIC has RetractableTo Integer
retract: % -> Integer if PADIC has RetractableTo Integer

retract: % -> Symbol if PADIC has RetractableTo Symbol
retractIfCan: % -> Union(Fraction Integer, failed) if PADIC has RetractableTo Integer
retractIfCan: % -> Union(Integer, failed) if PADIC has RetractableTo Integer

retractIfCan: % -> Union(Symbol, failed) if PADIC has RetractableTo Symbol
rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sign: % -> Integer if PADIC has OrderedIntegralDomain

from OrderedRing

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

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

from Comparable

solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if PADIC has PolynomialFactorizationExplicit
squareFree: % -> Factored %
squareFreePart: % -> %
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if PADIC 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

CoercibleFrom Fraction Integer if PADIC has RetractableTo Integer

CoercibleFrom Integer if PADIC has RetractableTo Integer

CoercibleFrom Symbol if PADIC has RetractableTo Symbol

CommutativeRing

CommutativeStar

ConvertibleTo DoubleFloat if PADIC has RealConstant

ConvertibleTo Float if PADIC has RealConstant

ConvertibleTo InputForm if PADIC has ConvertibleTo InputForm

DivisionRing

EntireRing

EuclideanDomain

Field

GcdDomain

IntegralDomain

LeftOreRing

Magma

MagmaWithUnit

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PatternMatchable Float if PADIC has PatternMatchable Float

PatternMatchable Integer if PADIC has PatternMatchable Integer

PrincipalIdealDomain

RetractableTo Fraction Integer if PADIC has RetractableTo Integer

RetractableTo Integer if PADIC has RetractableTo Integer

RetractableTo Symbol if PADIC has RetractableTo Symbol

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory