PAdicInteger p¶
padic.spad line 296 [edit on github]
p: Integer
Stream-based implementation of Zp: p-adic numbers are represented as sum(i = 0.., a[i] * p^i), where the a[i] lie in 0, 1, …, (p - 1).
- 0: %
from AbelianMonoid
- 1: %
from MagmaWithUnit
- *: (%, %) -> %
from LeftModule %
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- approximate: (%, Integer) -> Integer
from PAdicIntegerCategory p
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- characteristic: () -> NonNegativeInteger
from NonAssociativeRing
- coerce: % -> %
from Algebra %
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- coerce: Integer -> %
from NonAssociativeRing
- 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
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
- latex: % -> String
from SetCategory
- 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)
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
BiModule(%, %)
Module %