NMExtendedPadic(p, prec)

jnpadic.spad line 63 [edit on github]

• p: Integer

• prec: Integer

This domain implements the field of p-adic numbers $mathbb{Q}_p$ using the Nemo Julia package.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from NMPadicNumberCategory NMInteger

*: (%, NMFraction NMInteger) -> %

from NMPadicNumberCategory NMInteger

*: (%, NMInteger) -> %

from NMPadicNumberCategory NMInteger

*: (Integer, %) -> %

from AbelianGroup

*: (NMFraction NMInteger, %) -> %

from NMPadicNumberCategory NMInteger

*: (NMInteger, %) -> %

from NMPadicNumberCategory NMInteger

*: (NMInteger, %) -> JLObject

from JLObjectRing

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from NMPadicNumberCategory NMInteger

+: (%, NMFraction NMInteger) -> %

from NMPadicNumberCategory NMInteger

+: (%, NMInteger) -> %

from NMPadicNumberCategory NMInteger

+: (NMFraction NMInteger, %) -> %

from NMPadicNumberCategory NMInteger

+: (NMInteger, %) -> %

from NMPadicNumberCategory NMInteger

-: % -> %

from AbelianGroup

-: (%, %) -> %

from NMPadicNumberCategory NMInteger

/: (%, %) -> %

from NMPadicNumberCategory NMInteger

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> %

from ElementaryFunctionCategory

^: (%, Fraction Integer) -> %

from RadicalCategory

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

approximate: (%, Integer) -> NMInteger

from NMPadicNumberCategory NMInteger

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) coerces x to a p-adic number.

commutator: (%, %) -> %

from NonAssociativeRng

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

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

from EuclideanDomain

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

from EuclideanDomain

factor: % -> Factored %

from UniqueFactorizationDomain

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

inv: % -> %

from DivisionRing

jlAbout: % -> Void

from JLObjectType

jlApply: (String, %) -> JLObject

from JLObjectType

jlApply: (String, %, %) -> JLObject

from JLObjectType

jlApply: (String, %, %, %) -> JLObject

from JLObjectType

jlApply: (String, %, %, %, %) -> JLObject

from JLObjectType

jlApply: (String, %, %, %, %, %) -> JLObject

from JLObjectType

jlDisplay: % -> Void

from JLObjectType

jlDump: JLObject -> Void

from JLObjectType

jlFieldNames: % -> JLObject

from JLObjectType

jlGetField: (%, JLSymbol) -> JLObject

from JLObjectType

jlGetJuliaIndex: % -> String

from JLObjectType

jlGetProperty: (%, JLSymbol) -> JLObject

from JLObjectType

jlId: % -> JLInt64

from JLObjectType

jlimref: String -> %

from JLObjectType

jlNMRing: () -> String

from NMRing

jlObject: () -> String

from JLObjectType

jlPropertyNames: % -> JLObject

from JLObjectType

jlRef: % -> SExpression

from JLObjectType

jlref: String -> %

from JLObjectType

jlText: (%, String) -> List String

from JLObjectType

jlType: % -> Symbol

from JLObjectType

jnpadic: Integer -> %

jnpadic(x) returns x as a p-adic number.

jnpadic: NMInteger -> %

jnpadic(x) returns x as a p-adic number.

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

missing?: % -> Boolean

from JLObjectType

moduloP: % -> NMInteger

moduloP(x) returns a, where x = a + b p.

modulus: () -> Integer

modulus() returns the value of 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: % -> Integer

from NMPadicNumberCategory NMInteger

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

precision: % -> Integer

from NMPadicNumberCategory NMInteger

prime?: % -> Boolean

from UniqueFactorizationDomain

prime: % -> Integer

from NMPadicNumberCategory NMInteger

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

quotientByP: % -> %

quotientByP(x) returns b, where x = a + b 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

squareFree: % -> Factored %

from UniqueFactorizationDomain

squareFreePart: % -> %

from UniqueFactorizationDomain

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: % -> JLObjInt64

from NMPadicNumberCategory NMInteger

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

BasicType

BiModule(%, %)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

ConvertibleTo String

DivisionRing

ElementaryFunctionCategory

EntireRing

EuclideanDomain

Field

GcdDomain

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftOreRing

Magma

MagmaWithUnit

Module %

Monoid

NMCommutativeRing

NMField

NMPadicNumberCategory NMInteger

NMRing

NMType

NonAssociativeAlgebra %

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PrincipalIdealDomain

RadicalCategory

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown