Integer

integer.spad line 45 [edit on github]

Integer provides the domain of arbitrary precision integers.

* : (%, %) -> %

from Magma

* : (%, Integer) -> %

from RightModule(Integer)

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

D : % -> %

from DifferentialRing

D : (%, NonNegativeInteger) -> %

from DifferentialRing

OMwrite : % -> String

from OpenMath

OMwrite : (%, Boolean) -> String

from OpenMath

OMwrite : (OpenMathDevice, %) -> Void

from OpenMath

OMwrite : (OpenMathDevice, %, Boolean) -> Void

from OpenMath

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

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 : Integer -> %

from NonAssociativeRing

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

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

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

factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))

from PolynomialFactorizationExplicit

factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%))

from PolynomialFactorizationExplicit

factorial : % -> %

from CombinatorialFunctionCategory

gcd : (%, %) -> %

from GcdDomain

gcd : List(%) -> %

from GcdDomain

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

from PolynomialFactorizationExplicit

hash : % -> SingleInteger

from Hashable

hashUpdate! : (HashState, %) -> HashState

from Hashable

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

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

patternMatch : (%, Pattern(Integer), PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %)

from PatternMatchable(Integer)

permutation : (%, %) -> %

from CombinatorialFunctionCategory

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

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(%) -> Matrix(Integer)

from LinearlyExplicitOver(Integer)

reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(Integer), vec : Vector(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

~= : (%, %) -> Boolean

from BasicType

ConvertibleTo(Float)

PrincipalIdealDomain

ConvertibleTo(Integer)

NonAssociativeSemiRing

BiModule(%, %)

ConvertibleTo(InputForm)

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

TwoSidedRecip

OrderedAbelianGroup

SemiRing

EntireRing

unitsKnown

NonAssociativeSemiRng

LinearlyExplicitOver(Integer)

noZeroDivisors

OrderedSet

Magma

SemiGroup

GcdDomain

LeftModule(%)

NonAssociativeRing

UniqueFactorizationDomain

CharacteristicZero

OrderedIntegralDomain

Algebra(%)

CommutativeRing

DifferentialRing

CombinatorialFunctionCategory

OpenMath

LeftOreRing

PartialOrder

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

Comparable

RetractableTo(Integer)

OrderedCancellationAbelianMonoid

OrderedAbelianMonoid

OrderedRing

CommutativeStar

AbelianMonoid

MagmaWithUnit

RightModule(%)

Hashable

RealConstant

ConvertibleTo(String)

ConvertibleTo(DoubleFloat)

OrderedAbelianSemiGroup

Module(%)

CoercibleTo(OutputForm)

ConvertibleTo(Pattern(Integer))

SemiRng

Monoid

PolynomialFactorizationExplicit

NonAssociativeAlgebra(%)

BasicType

Ring

RightModule(Integer)

Canonical

AbelianSemiGroup

IntegralDomain

SetCategory

IntegerNumberSystem

multiplicativeValuation

NonAssociativeRng

PatternMatchable(Integer)

StepThrough

AbelianGroup