NMPadicNumberCategory R

jnpadic.spad line 1 [edit on github]

• R: NMCommutativeRing

This category provides representations of the :code:p-adic numbers using the Nemo Julia package.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

p * q is the product of two p-adic numbers.

*: (%, Fraction Integer) -> % if % has CharacteristicZero

from RightModule Fraction Integer

*: (%, 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.

*: (Fraction Integer, %) -> % if % has CharacteristicZero

from LeftModule Fraction Integer

*: (Integer, %) -> %

from AbelianGroup

*: (NMFraction NMInteger, %) -> %

q * x is the multiplication of a 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

+: (%, %) -> %

p + q is the sum of two p-adic numbers.

+: (%, 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 a 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

-: (%, %) -> %

p - q is the difference of two p-adic numbers.

/: (%, %) -> %

p / q is the division of two p-adic numbers.

=: (%, %) -> 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) -> R

approximate(x, n) returns an integer y such that y = x (mod p^n) when n is positive, and 0 otherwise.

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> %

from Algebra %

coerce: % -> JLObject

from JLObjectType

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> % if % has CharacteristicZero

from Algebra Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

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

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

log: % -> %

from ElementaryFunctionCategory

missing?: % -> Boolean

from JLObjectType

modulus: () -> Integer

modulus() returns the modulus.

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

from EuclideanDomain

mutable?: % -> Boolean

from JLObjectType

nothing?: % -> Boolean

from JLObjectType

nthRoot: (%, Integer) -> %

from RadicalCategory

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> Integer

order(x) returns the exponent of the highest power of p dividing x.

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra %

precision: % -> Integer

precision(x) returns the precision used for x.

prime?: % -> Boolean

from UniqueFactorizationDomain

prime: % -> Integer

prime(x) returns the modulus used for x.

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

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

unit?: % -> Boolean

from NMRing

unitCanonical: % -> %

from EntireRing

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

from EntireRing

valuation: % -> JLObjInt64

valuation(x) is the valuation of x.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer if % has CharacteristicZero

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer) if % has CharacteristicZero

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

ConvertibleTo String

DivisionRing

ElementaryFunctionCategory

EntireRing

EuclideanDomain

Field

GcdDomain

IntegralDomain

JLObjectRing

JLObjectType

JLRing

JLType

LeftModule %

LeftModule Fraction Integer if % has CharacteristicZero

LeftOreRing

Magma

MagmaWithUnit

Module %

Module Fraction Integer if % has CharacteristicZero

Monoid

NMCommutativeRing

NMField

NMRing

NMType

NonAssociativeAlgebra %

NonAssociativeAlgebra Fraction Integer if % has CharacteristicZero

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

PrincipalIdealDomain

RadicalCategory

RightModule %

RightModule Fraction Integer if % has CharacteristicZero

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown