BinaryExpansion

radix.spad line 245 [edit on github]

This domain allows rational numbers to be presented as repeating binary expansions.

* : (%, %) -> %

from Magma

* : (%, Fraction(Integer)) -> %

from RightModule(Fraction(Integer))

* : (%, Integer) -> %

from RightModule(Integer)

* : (Fraction(Integer), %) -> %

from LeftModule(Fraction(Integer))

* : (Integer, %) -> %

from AbelianGroup

* : (NonNegativeInteger, %) -> %

from AbelianMonoid

* : (PositiveInteger, %) -> %

from AbelianSemiGroup

+ : (%, %) -> %

from AbelianSemiGroup

- : % -> %

from AbelianGroup

- : (%, %) -> %

from AbelianGroup

/ : (%, %) -> %

from Field

/ : (Integer, Integer) -> %

from QuotientFieldCategory(Integer)

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 : (%, List(Symbol)) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

D : (%, List(Symbol), List(NonNegativeInteger)) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

D : (%, Mapping(Integer, Integer)) -> %

from DifferentialExtension(Integer)

D : (%, Mapping(Integer, Integer), NonNegativeInteger) -> %

from DifferentialExtension(Integer)

D : (%, NonNegativeInteger) -> %

from DifferentialRing

D : (%, Symbol) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

D : (%, Symbol, NonNegativeInteger) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

^ : (%, Integer) -> %

from DivisionRing

^ : (%, NonNegativeInteger) -> %

from MagmaWithUnit

^ : (%, PositiveInteger) -> %

from Magma

abs : % -> %

from OrderedRing

annihilate? : (%, %) -> Boolean

from Rng

antiCommutator : (%, %) -> %

from NonAssociativeSemiRng

associates? : (%, %) -> Boolean

from EntireRing

associator : (%, %, %) -> %

from NonAssociativeRng

binary : Fraction(Integer) -> %

binary(r) converts a rational number to a binary expansion.

ceiling : % -> Integer

from QuotientFieldCategory(Integer)

characteristic : () -> NonNegativeInteger

from NonAssociativeRing

charthRoot : % -> Union(%, "failed") if Integer has CharacteristicNonZero or % has CharacteristicNonZero

from CharacteristicNonZero

coerce : % -> %

from Algebra(%)

coerce : Fraction(Integer) -> %

from CoercibleFrom(Fraction(Integer))

coerce : Integer -> %

from NonAssociativeRing

coerce : Symbol -> % if Integer has RetractableTo(Symbol)

from CoercibleFrom(Symbol)

coerce : % -> Fraction(Integer)

coerce(b) converts a binary expansion to a rational number.

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

coerce : % -> RadixExpansion(2)

coerce(b) converts a binary expansion to a radix expansion with base 2.

commutator : (%, %) -> %

from NonAssociativeRng

conditionP : Matrix(%) -> Union(Vector(%), "failed") if % has CharacteristicNonZero

from PolynomialFactorizationExplicit

convert : % -> DoubleFloat

from ConvertibleTo(DoubleFloat)

convert : % -> Float

from ConvertibleTo(Float)

convert : % -> InputForm

from ConvertibleTo(InputForm)

convert : % -> Pattern(Float) if Integer has ConvertibleTo(Pattern(Float))

from ConvertibleTo(Pattern(Float))

convert : % -> Pattern(Integer)

from ConvertibleTo(Pattern(Integer))

denom : % -> Integer

from QuotientFieldCategory(Integer)

denominator : % -> %

from QuotientFieldCategory(Integer)

differentiate : % -> %

from DifferentialRing

differentiate : (%, List(Symbol)) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

differentiate : (%, List(Symbol), List(NonNegativeInteger)) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

differentiate : (%, Mapping(Integer, Integer)) -> %

from DifferentialExtension(Integer)

differentiate : (%, Mapping(Integer, Integer), NonNegativeInteger) -> %

from DifferentialExtension(Integer)

differentiate : (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate : (%, Symbol) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

differentiate : (%, Symbol, NonNegativeInteger) -> % if Integer has PartialDifferentialRing(Symbol)

from PartialDifferentialRing(Symbol)

divide : (%, %) -> Record(quotient : %, remainder : %)

from EuclideanDomain

elt : (%, Integer) -> % if Integer has Eltable(Integer, Integer)

from Eltable(Integer, %)

euclideanSize : % -> NonNegativeInteger

from EuclideanDomain

eval : (%, Equation(Integer)) -> % if Integer has Evalable(Integer)

from Evalable(Integer)

eval : (%, Integer, Integer) -> % if Integer has Evalable(Integer)

from InnerEvalable(Integer, Integer)

eval : (%, List(Equation(Integer))) -> % if Integer has Evalable(Integer)

from Evalable(Integer)

eval : (%, List(Integer), List(Integer)) -> % if Integer has Evalable(Integer)

from InnerEvalable(Integer, Integer)

eval : (%, List(Symbol), List(Integer)) -> % if Integer has InnerEvalable(Symbol, Integer)

from InnerEvalable(Symbol, Integer)

eval : (%, Symbol, Integer) -> % if Integer has InnerEvalable(Symbol, Integer)

from InnerEvalable(Symbol, Integer)

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

floor : % -> Integer

from QuotientFieldCategory(Integer)

fractionPart : % -> %

from QuotientFieldCategory(Integer)

fractionPart : % -> Fraction(Integer)

fractionPart(b) returns the fractional part of a binary expansion.

gcd : (%, %) -> %

from GcdDomain

gcd : List(%) -> %

from GcdDomain

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

from PolynomialFactorizationExplicit

init : () -> %

from StepThrough

inv : % -> %

from DivisionRing

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

map : (Mapping(Integer, Integer), %) -> %

from FullyEvalableOver(Integer)

max : (%, %) -> %

from OrderedSet

min : (%, %) -> %

from OrderedSet

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

from EuclideanDomain

negative? : % -> Boolean

from OrderedRing

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

from StepThrough

numer : % -> Integer

from QuotientFieldCategory(Integer)

numerator : % -> %

from QuotientFieldCategory(Integer)

one? : % -> Boolean

from MagmaWithUnit

opposite? : (%, %) -> Boolean

from AbelianMonoid

patternMatch : (%, Pattern(Float), PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if Integer has PatternMatchable(Float)

from PatternMatchable(Float)

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

from PatternMatchable(Integer)

plenaryPower : (%, PositiveInteger) -> %

from NonAssociativeAlgebra(%)

positive? : % -> Boolean

from OrderedRing

prime? : % -> Boolean

from UniqueFactorizationDomain

principalIdeal : List(%) -> Record(coef : List(%), generator : %)

from PrincipalIdealDomain

quo : (%, %) -> %

from EuclideanDomain

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 : % -> Fraction(Integer)

from RetractableTo(Fraction(Integer))

retract : % -> Integer

from RetractableTo(Integer)

retract : % -> Symbol if Integer has RetractableTo(Symbol)

from RetractableTo(Symbol)

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

from RetractableTo(Fraction(Integer))

retractIfCan : % -> Union(Integer, "failed")

from RetractableTo(Integer)

retractIfCan : % -> Union(Symbol, "failed") if Integer has RetractableTo(Symbol)

from RetractableTo(Symbol)

rightPower : (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower : (%, PositiveInteger) -> %

from Magma

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

from MagmaWithUnit

sample : () -> %

from AbelianMonoid

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

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

from CancellationAbelianMonoid

unit? : % -> Boolean

from EntireRing

unitCanonical : % -> %

from EntireRing

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

from EntireRing

wholePart : % -> Integer

from QuotientFieldCategory(Integer)

zero? : % -> Boolean

from AbelianMonoid

~= : (%, %) -> Boolean

from BasicType

FullyLinearlyExplicitOver(Integer)

Module(Fraction(Integer))

ConvertibleTo(Float)

PrincipalIdealDomain

NonAssociativeSemiRing

BiModule(%, %)

ConvertibleTo(InputForm)

Field

canonicalUnitNormal

Rng

CoercibleFrom(Integer)

TwoSidedRecip

OrderedAbelianGroup

FullyEvalableOver(Integer)

SemiRing

EntireRing

Patternable(Integer)

NonAssociativeAlgebra(Fraction(Integer))

CharacteristicNonZero

InnerEvalable(Symbol, Integer)

unitsKnown

PatternMatchable(Float)

Algebra(Integer)

noZeroDivisors

RetractableTo(Fraction(Integer))

UniqueFactorizationDomain

SemiGroup

NonAssociativeAlgebra(Integer)

RightModule(Fraction(Integer))

Magma

RetractableTo(Symbol)

IntegralDomain

LeftModule(%)

NonAssociativeRing

GcdDomain

NonAssociativeAlgebra(%)

PartialDifferentialRing(Symbol)

CharacteristicZero

OrderedIntegralDomain

Algebra(%)

CoercibleFrom(Fraction(Integer))

DifferentialRing

OrderedAbelianMonoid

DivisionRing

CommutativeRing

NonAssociativeRng

PartialOrder

NonAssociativeSemiRng

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

QuotientFieldCategory(Integer)

RetractableTo(Integer)

OrderedCancellationAbelianMonoid

OrderedRing

CommutativeStar

AbelianMonoid

MagmaWithUnit

Comparable

RightModule(%)

Evalable(Integer)

RealConstant

ConvertibleTo(DoubleFloat)

OrderedAbelianSemiGroup

StepThrough

Eltable(Integer, %)

LinearlyExplicitOver(Integer)

BiModule(Integer, Integer)

CoercibleTo(OutputForm)

Module(Integer)

SemiRng

LeftModule(Integer)

CoercibleFrom(Symbol)

Monoid

PolynomialFactorizationExplicit

DifferentialExtension(Integer)

LeftOreRing

OrderedSet

FullyPatternMatchable(Integer)

Algebra(Fraction(Integer))

ConvertibleTo(Pattern(Integer))

BasicType

Ring

RightModule(Integer)

InnerEvalable(Integer, Integer)

AbelianSemiGroup

Module(%)

LeftModule(Fraction(Integer))

SetCategory

PatternMatchable(Integer)

BiModule(Fraction(Integer), Fraction(Integer))

ConvertibleTo(Pattern(Float))

AbelianGroup