SingleInteger

si.spad line 142 [edit on github]

SingleInteger is intended to support machine integer arithmetic.

* : (%, %) -> %

from Magma

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

/\ : (%, %) -> %

n /\ m returns the bit-by-bit logical and of the single integers n and m.

0 : () -> %

from AbelianMonoid

1 : () -> %

from MagmaWithUnit

< : (%, %) -> Boolean

from PartialOrder

<= : (%, %) -> Boolean

from PartialOrder

= : (%, %) -> Boolean

from BasicType

> : (%, %) -> Boolean

from PartialOrder

>= : (%, %) -> Boolean

from PartialOrder

And : (%, %) -> %

And(n, m) returns the bit-by-bit logical and of the single integers n and m.

D : % -> %

from DifferentialRing

D : (%, NonNegativeInteger) -> %

from DifferentialRing

Not : % -> %

Not(n) returns the bit-by-bit logical not of the single integer n.

OMwrite : % -> String

from OpenMath

OMwrite : (%, Boolean) -> String

from OpenMath

OMwrite : (OpenMathDevice, %) -> Void

from OpenMath

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

from OpenMath

Or : (%, %) -> %

Or(n, m) returns the bit-by-bit logical or of the single integers n and m.

T : () -> %

from BoundedMeetSemilattice

\/ : (%, %) -> %

n \/ m returns the bit-by-bit logical or of the single integers n and m.

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

_|_ : () -> %

from BoundedJoinSemilattice

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 CoercibleFrom(Integer)

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

factorial : % -> %

from CombinatorialFunctionCategory

false : () -> %

from Logic

gcd : (%, %) -> %

from GcdDomain

gcd : List(%) -> %

from GcdDomain

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

from GcdDomain

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 : () -> %

max() returns the largest single integer.

max : (%, %) -> %

from OrderedSet

min : () -> %

min() returns the smallest single integer.

min : (%, %) -> %

from OrderedSet

mulmod : (%, %, %) -> %

from IntegerNumberSystem

multiEuclidean : (List(%), %) -> Union(List(%), "failed")

from EuclideanDomain

negative? : % -> Boolean

from OrderedRing

nextItem : % -> Union(%, "failed")

from StepThrough

not : % -> %

not(n) returns the bit-by-bit logical not of the single integer n.

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

qconvert : Integer -> %

qconvert(x) converts x to % trusting that x is in correct range.

quo : (%, %) -> %

from EuclideanDomain

random : % -> %

from IntegerNumberSystem

rational : % -> Fraction(Integer)

from IntegerNumberSystem

rational? : % -> Boolean

from IntegerNumberSystem

rationalIfCan : % -> Union(Fraction(Integer), "failed")

from IntegerNumberSystem

recip : % -> Union(%, "failed")

from MagmaWithUnit

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

squareFree : % -> Factored(%)

from UniqueFactorizationDomain

squareFreePart : % -> %

from UniqueFactorizationDomain

submod : (%, %, %) -> %

from IntegerNumberSystem

subtractIfCan : (%, %) -> Union(%, "failed")

from CancellationAbelianMonoid

symmetricRemainder : (%, %) -> %

from IntegerNumberSystem

true : () -> %

from Logic

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

unitNormal : % -> Record(unit : %, canonical : %, associate : %)

from EntireRing

xor : (%, %) -> %

xor(n, m) returns the bit-by-bit logical xor of the single integers n and m.

zero? : % -> Boolean

from AbelianMonoid

~ : % -> %

~ n returns the bit-by-bit logical not of the single integer n.

~= : (%, %) -> Boolean

from BasicType

ConvertibleTo(Float)

PrincipalIdealDomain

ConvertibleTo(Integer)

NonAssociativeSemiRing

BiModule(%, %)

ConvertibleTo(InputForm)

Logic

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

TwoSidedRecip

OrderedAbelianGroup

SemiRing

EntireRing

JoinSemilattice

unitsKnown

noZeroDivisors

OrderedSet

Magma

SemiGroup

DistributiveLattice

LeftModule(%)

Lattice

NonAssociativeRing

UniqueFactorizationDomain

GcdDomain

NonAssociativeAlgebra(%)

CharacteristicZero

OrderedIntegralDomain

CommutativeRing

Algebra(%)

DifferentialRing

OrderedAbelianMonoid

CombinatorialFunctionCategory

BoundedMeetSemilattice

OpenMath

BoundedDistributiveLattice

MeetSemilattice

NonAssociativeSemiRng

PartialOrder

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

Comparable

RetractableTo(Integer)

OrderedCancellationAbelianMonoid

OrderedRing

CommutativeStar

AbelianMonoid

MagmaWithUnit

RightModule(%)

Hashable

RealConstant

ConvertibleTo(String)

ConvertibleTo(DoubleFloat)

OrderedAbelianSemiGroup

Module(%)

CoercibleTo(OutputForm)

ConvertibleTo(Pattern(Integer))

SemiRng

Monoid

LeftOreRing

BasicType

Ring

Canonical

AbelianSemiGroup

IntegralDomain

SetCategory

BoundedJoinSemilattice

IntegerNumberSystem

multiplicativeValuation

BoundedLattice

NonAssociativeRng

PatternMatchable(Integer)

StepThrough

AbelianGroup