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 RightModule Integer
- *: (Integer, %) -> %
from AbelianGroup
- *: (NonNegativeInteger, %) -> %
from AbelianMonoid
- *: (PositiveInteger, %) -> %
from AbelianSemiGroup
- +: (%, %) -> %
from AbelianSemiGroup
- -: % -> %
from AbelianGroup
- -: (%, %) -> %
from AbelianGroup
- <=: (%, %) -> Boolean
from PartialOrder
- <: (%, %) -> Boolean
from PartialOrder
- >=: (%, %) -> Boolean
from PartialOrder
- >: (%, %) -> Boolean
from PartialOrder
- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
from Magma
- abs: % -> %
from OrderedRing
- addmod: (%, %, %) -> %
from IntegerNumberSystem
- annihilate?: (%, %) -> Boolean
from Rng
- antiCommutator: (%, %) -> %
- associates?: (%, %) -> Boolean
from EntireRing
- associator: (%, %, %) -> %
from NonAssociativeRng
- base: () -> %
from IntegerNumberSystem
- binomial: (%, %) -> %
- 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
- factorial: % -> %
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial %
- hash: % -> SingleInteger
from Hashable
- hashUpdate!: (HashState, %) -> HashState
from Hashable
- inc: % -> %
from IntegerNumberSystem
- init: %
from StepThrough
- invmod: (%, %) -> %
from IntegerNumberSystem
- 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
- 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: (%, %) -> %
- plenaryPower: (%, PositiveInteger) -> %
from NonAssociativeAlgebra %
- positive?: % -> Boolean
from OrderedRing
- positiveRemainder: (%, %) -> %
from IntegerNumberSystem
- powmod: (%, %, %) -> %
from IntegerNumberSystem
- principalIdeal: List % -> Record(coef: List %, generator: %)
from PrincipalIdealDomain
- quo: (%, %) -> %
from EuclideanDomain
- random: % -> %
random(n)returns a random integer from 0 ton-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)
- reducedSystem: Matrix % -> Matrix 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)
- squareFree: % -> Factored %
- squareFreePart: % -> %
- submod: (%, %, %) -> %
from IntegerNumberSystem
- subtractIfCan: (%, %) -> Union(%, failed)
- symmetricRemainder: (%, %) -> %
from IntegerNumberSystem
- unit?: % -> Boolean
from EntireRing
- unitCanonical: % -> %
from EntireRing
- unitNormal: % -> Record(unit: %, canonical: %, associate: %)
from EntireRing
- zero?: % -> Boolean
from AbelianMonoid
Algebra %
BiModule(%, %)
Module %
OrderedCancellationAbelianMonoid