IntegerΒΆ

integer.spad line 45 [edit on github]

Integer provides the domain of arbitrary precision integers.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (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

mask: % -> %

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?: % -> Boolean

from IntegerNumberSystem

rational: % -> Fraction Integer

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

seedRandom: () -> Void

seedRandom() seeds the pseudo random number generator with a new random seed. Note that internally there is only one (global) pseudo random number generator as a source for random data. All other random objects are derived from that source.

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

Algebra %

BasicType

BiModule(%, %)

CancellationAbelianMonoid

Canonical

canonicalsClosed

canonicalUnitNormal

CharacteristicZero

CoercibleFrom Integer

CoercibleTo OutputForm

CombinatorialFunctionCategory

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Integer

ConvertibleTo Pattern Integer

ConvertibleTo String

DifferentialRing

EntireRing

EuclideanDomain

GcdDomain

IntegerNumberSystem

IntegralDomain

LeftModule %

LeftOreRing

LinearlyExplicitOver Integer

Magma

MagmaWithUnit

Module %

Monoid

multiplicativeValuation

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OpenMath

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedRing

OrderedSet

PartialOrder

PatternMatchable Integer

PolynomialFactorizationExplicit

PrincipalIdealDomain

RealConstant

RetractableTo Integer

RightModule %

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown