NMExtendedPadicInteger(p, prec)

jnpadic.spad line 43 [edit on github]

• p: Integer

• prec: Integer

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

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from Magma

*: (%, NMFraction NMInteger) -> %

x * q is the multiplication of a p-adic number and a Julia Nemo Fraction integer.

*: (%, NMInteger) -> %

x * i is the multiplication of an Integer and a p-adic number. For example: example{p := 1 + 2*7 + 4*7^2 + O()$NPADICZ(7)}

*: (Integer, %) -> %

from AbelianGroup

*: (NMFraction NMInteger, %) -> %

q * x is the multiplication of Julia Nemo Fraction integer and a p-adic number.

*: (NMInteger, %) -> %

i * x is the multiplication of a NemoInteger and a p-adic number.

*: (NMInteger, %) -> JLObject

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

+: (%, NMFraction NMInteger) -> %

x + q is the addition of a p-adic number and a Julia Nemo Fraction integer.

+: (%, NMInteger) -> %

x + i is the addition of a p-adic number and a Julia Nemo integer.

+: (NMFraction NMInteger, %) -> %

q + x is the addition of Julia Nemo Fraction integer and a p-adic number.

+: (NMInteger, %) -> %

i + x is the addition of a Julia Nemo Integer and a p-adic number.

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

approximate: (%, Integer) -> Integer

from NMPadicNumberCategory p

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Integer -> %

from NonAssociativeRing

coerce: NMInteger -> %

coerce(x) returns x as the p-adic completion of the Nemo Integer.

commutator: (%, %) -> %

from NonAssociativeRng

complete: % -> %

from NMPadicNumberCategory p

convert: % -> String

from ConvertibleTo String

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

from EuclideanDomain

equal?: (%, %) -> Boolean

from NMRing

euclideanSize: % -> NonNegativeInteger

from EuclideanDomain

exact?: % -> Boolean

from NMRing

exactDivide: (%, %) -> %

from NMRing

exp: % -> %

from ElementaryFunctionCategory

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

from PrincipalIdealDomain

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

from EntireRing

extend: (%, Integer) -> %

from NMPadicNumberCategory 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

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

jlNMRing: () -> String

from NMRing

jlObject: () -> String

from JLObjectType

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlType: % -> String

from JLObjectType

jnpadic: Integer -> %

jnpadic(x) returns x as the p-adic completion of the Nemo Integer.

jnpadic: NMInteger -> %

jnpadic(x) returns x as the p-adic completion of the Nemo Integer.

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

liftQ: % -> NMFraction NMInteger

liftQ(x) lift x to a Nemo Fraction Nemo Integer.

liftZ: % -> NMInteger

liftZ(x) lift x to a Nemo Integer.

log: % -> %

from ElementaryFunctionCategory

moduloP: % -> Integer

from NMPadicNumberCategory p

modulus: () -> Integer

from NMPadicNumberCategory p

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

nothing?: % -> Boolean

from JLObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

O: () -> %

O() returns the default Big-oh from domain parameters.

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> NonNegativeInteger

from NMPadicNumberCategory p

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

precision: % -> Integer

precision(x) returns the precision used for x.

prime: % -> Integer

prime(x) returns the modulus used for x. Convenience function.

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

quotientByP: % -> %

from NMPadicNumberCategory p

recip: % -> Union(%, failed)

from MagmaWithUnit

rem: (%, %) -> %

from EuclideanDomain

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sizeLess?: (%, %) -> Boolean

from EuclideanDomain

sqrt: % -> %

from RadicalCategory

string: % -> String

from JLType

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

from CancellationAbelianMonoid

teichmuller: % -> %

teichmuller(x) computes the Teichmuller lift of x. The valuation of x must be non negative.

unit?: % -> Boolean

from NMRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

valuation: % -> %

valuation(x) is the valuation of x.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

BasicType

BiModule(%, %)

CancellationAbelianMonoid

CharacteristicZero

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

ConvertibleTo String

ElementaryFunctionCategory

EntireRing

EuclideanDomain

GcdDomain

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftOreRing

Magma

MagmaWithUnit

Module %

Monoid

NMCommutativeRing

NMPadicNumberCategory p

NMRing

NMType

NonAssociativeAlgebra %

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PrincipalIdealDomain

RadicalCategory

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

unitsKnown