InnerPAdicInteger(p, unBalanced?)

padic.spad line 47 [edit on github]

• p : Integer
• unBalanced? : Boolean

This domain implements Zp, the p-adic completion of the integers. This is an internal domain.

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

= : (%, %) -> Boolean

from BasicType

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

approximate : (%, Integer) -> Integer

from PAdicIntegerCategory(p)

associates? : (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

coerce : % -> %

from Algebra(%)

coerce : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

commutator : (%, %) -> %

from NonAssociativeRng

complete : % -> %

from PAdicIntegerCategory(p)

digits : % -> Stream(Integer)

from PAdicIntegerCategory(p)

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

from EuclideanDomain

euclideanSize : % -> NonNegativeInteger

from EuclideanDomain

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

from PrincipalIdealDomain

exquo : (%, %) -> Union(%, "failed")

from EntireRing

extend : (%, Integer) -> %

from PAdicIntegerCategory(p)

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

from EuclideanDomain

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

from EuclideanDomain

gcd : (%, %) -> %

from GcdDomain

gcd : List(%) -> %

from GcdDomain

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

from GcdDomain

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

moduloP : % -> Integer

from PAdicIntegerCategory(p)

modulus : () -> Integer

from PAdicIntegerCategory(p)

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

from EuclideanDomain

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

order : % -> NonNegativeInteger

from PAdicIntegerCategory(p)

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

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

from PrincipalIdealDomain

quo : (%, %) -> %

from EuclideanDomain

quotientByP : % -> %

from PAdicIntegerCategory(p)

recip : % -> Union(%, "failed")

from MagmaWithUnit

rem : (%, %) -> %

from EuclideanDomain

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

rightRecip : % -> Union(%, "failed")

from MagmaWithUnit

root : (SparseUnivariatePolynomial(Integer), Integer) -> %

from PAdicIntegerCategory(p)

sample : () -> %

from AbelianMonoid

sizeLess? : (%, %) -> Boolean

from EuclideanDomain

sqrt : (%, Integer) -> %

from PAdicIntegerCategory(p)

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

from CancellationAbelianMonoid

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

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

from EntireRing

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

IntegralDomain

noZeroDivisors

Algebra(%)

RightModule(%)

Monoid

GcdDomain

AbelianMonoid

PAdicIntegerCategory(p)

EuclideanDomain

EntireRing

CancellationAbelianMonoid

MagmaWithUnit

NonAssociativeRing

AbelianGroup

LeftModule(%)

CommutativeStar

Module(%)

SetCategory

LeftOreRing

Rng

CommutativeRing

TwoSidedRecip

Magma

SemiGroup

BiModule(%, %)

CoercibleTo(OutputForm)

AbelianSemiGroup

NonAssociativeSemiRing

NonAssociativeAlgebra(%)

PrincipalIdealDomain

NonAssociativeRng

unitsKnown

Ring

SemiRng

NonAssociativeSemiRng

CharacteristicZero

BasicType

SemiRing