IntegerΒΆ

Integer provides the domain of arbitrary precision integers.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (Integer, %) -> %
from AbelianGroup
*: (NonNegativeInteger, %) -> %
from AbelianMonoid
*: (PositiveInteger, %) -> %
from AbelianSemiGroup
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
<: (%, %) -> Boolean
from PartialOrder
<=: (%, %) -> Boolean
from PartialOrder
=: (%, %) -> Boolean
from BasicType
>: (%, %) -> Boolean
from PartialOrder
>=: (%, %) -> Boolean
from PartialOrder
^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
^: (%, PositiveInteger) -> %
from Magma
~=: (%, %) -> Boolean
from BasicType
abs: % -> %
from OrderedRing
addmod: (%, %, %) -> %
from IntegerNumberSystem
annihilate?: (%, %) -> Boolean
from Rng
antiCommutator: (%, %) -> %
from NonAssociativeSemiRng
associates?: (%, %) -> Boolean
from EntireRing
associator: (%, %, %) -> %
from NonAssociativeRng
base: () -> %
from IntegerNumberSystem
binomial: (%, %) -> %
from CombinatorialFunctionCategory
bit?: (%, %) -> Boolean
from IntegerNumberSystem
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
coerce: % -> %
from Algebra %
coerce: % -> OutputForm
from CoercibleTo OutputForm
coerce: Integer -> %
from NonAssociativeRing
commutator: (%, %) -> %
from NonAssociativeRng
convert: % -> DoubleFloat
from ConvertibleTo DoubleFloat
convert: % -> Float
from ConvertibleTo Float
convert: % -> InputForm
from ConvertibleTo InputForm
convert: % -> Integer
from ConvertibleTo Integer
convert: % -> Pattern Integer
from ConvertibleTo Pattern Integer
convert: % -> String
from ConvertibleTo String
copy: % -> %
from IntegerNumberSystem
D: % -> %
from DifferentialRing
D: (%, NonNegativeInteger) -> %
from DifferentialRing
dec: % -> %
from IntegerNumberSystem
differentiate: % -> %
from DifferentialRing
differentiate: (%, NonNegativeInteger) -> %
from DifferentialRing
divide: (%, %) -> Record(quotient: %, remainder: %)
from EuclideanDomain
euclideanSize: % -> NonNegativeInteger
from EuclideanDomain
even?: % -> Boolean
from IntegerNumberSystem
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
factorial: % -> %
from CombinatorialFunctionCategory
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
from PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
from PolynomialFactorizationExplicit
gcd: (%, %) -> %
from GcdDomain
gcd: List % -> %
from GcdDomain
gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
from GcdDomain
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
inc: % -> %
from IntegerNumberSystem
init: %
from StepThrough
invmod: (%, %) -> %
from IntegerNumberSystem
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
length: % -> %
from IntegerNumberSystem
from IntegerNumberSystem
max: (%, %) -> %
from OrderedSet
min: (%, %) -> %
from OrderedSet
mulmod: (%, %, %) -> %
from IntegerNumberSystem
multiEuclidean: (List %, %) -> Union(List %, failed)
from EuclideanDomain
negative?: % -> Boolean
from OrderedRing
nextItem: % -> Union(%, failed)
from StepThrough
odd?: % -> Boolean
from IntegerNumberSystem
OMwrite: % -> String
from OpenMath
OMwrite: (%, Boolean) -> String
from OpenMath
OMwrite: (OpenMathDevice, %) -> Void
from OpenMath
OMwrite: (OpenMathDevice, %, Boolean) -> Void
from OpenMath
one?: % -> Boolean
from MagmaWithUnit
opposite?: (%, %) -> Boolean
from AbelianMonoid
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %)
from PatternMatchable Integer
permutation: (%, %) -> %
from CombinatorialFunctionCategory
positive?: % -> Boolean
from OrderedRing
positiveRemainder: (%, %) -> %
from IntegerNumberSystem
powmod: (%, %, %) -> %
from IntegerNumberSystem
prime?: % -> Boolean
from UniqueFactorizationDomain
principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
quo: (%, %) -> %
from EuclideanDomain
random: % -> %
`random(n)` returns a random integer from 0 to `n-1`.
rational: % -> Fraction Integer
from IntegerNumberSystem
rational?: % -> Boolean
from IntegerNumberSystem
rationalIfCan: % -> Union(Fraction Integer, failed)
from IntegerNumberSystem
recip: % -> Union(%, failed)
from MagmaWithUnit
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer)
from LinearlyExplicitOver Integer
reducedSystem: Matrix % -> Matrix Integer
from LinearlyExplicitOver Integer
rem: (%, %) -> %
from EuclideanDomain
retract: % -> Integer
from RetractableTo Integer
retractIfCan: % -> Union(Integer, failed)
from RetractableTo Integer
rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower: (%, PositiveInteger) -> %
from Magma
rightRecip: % -> Union(%, failed)
from MagmaWithUnit
sample: %
from AbelianMonoid
shift: (%, %) -> %
from IntegerNumberSystem
sign: % -> Integer
from OrderedRing
sizeLess?: (%, %) -> Boolean
from EuclideanDomain
smaller?: (%, %) -> Boolean
from Comparable
solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed)
from PolynomialFactorizationExplicit
squareFree: % -> Factored %
from UniqueFactorizationDomain
squareFreePart: % -> %
from UniqueFactorizationDomain
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial %
from PolynomialFactorizationExplicit
submod: (%, %, %) -> %
from IntegerNumberSystem
subtractIfCan: (%, %) -> Union(%, failed)
from CancellationAbelianMonoid
symmetricRemainder: (%, %) -> %
from IntegerNumberSystem
unit?: % -> Boolean
from EntireRing
unitCanonical: % -> %
from EntireRing
unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

BasicType

BiModule(%, %)

CancellationAbelianMonoid

Canonical

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CombinatorialFunctionCategory

CommutativeRing

CommutativeStar

Comparable

DifferentialRing

EntireRing

EuclideanDomain

GcdDomain

IntegerNumberSystem

IntegralDomain

LeftOreRing

Magma

MagmaWithUnit

Monoid

multiplicativeValuation

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OpenMath

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedRing

OrderedSet

PartialOrder

PolynomialFactorizationExplicit

PrincipalIdealDomain

RealConstant

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown