RadixExpansion bbΒΆ

radix.spad line 1 [edit on github]

This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, 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

<=: (%, %) -> Boolean

from PartialOrder

<: (%, %) -> Boolean

from PartialOrder

=: (%, %) -> Boolean

from BasicType

>=: (%, %) -> Boolean

from PartialOrder

>: (%, %) -> Boolean

from PartialOrder

^: (%, Integer) -> %

from DivisionRing

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

abs: % -> %

from OrderedRing

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

associates?: (%, %) -> Boolean

from EntireRing

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

from NonAssociativeRng

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

coerce(rx) converts a radix expansion to a rational number.

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: Symbol -> % if Integer has RetractableTo Symbol

from CoercibleFrom Symbol

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

cycleRagits: % -> List Integer

cycleRagits(rx) returns the cyclic part of the ragits of the fractional part of a radix expansion. For example, if x = 3/28 = 0.10 714285 714285 ..., then cycleRagits(x) = [7, 1, 4, 2, 8, 5].

D: % -> %

from DifferentialRing

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

from DifferentialExtension Integer

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

from DifferentialExtension Integer

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: (%, NonNegativeInteger) -> %

from DifferentialRing

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

from PartialDifferentialRing Symbol

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

from PartialDifferentialRing Symbol

denom: % -> Integer

from QuotientFieldCategory Integer

denominator: % -> %

from QuotientFieldCategory Integer

differentiate: % -> %

from DifferentialRing

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

from DifferentialExtension Integer

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

from DifferentialExtension Integer

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: (%, 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(rx) returns the fractional part of a radix expansion.

fractRadix: (List Integer, List Integer) -> %

fractRadix(pre, cyc) creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example, fractRadix([1], [6]) will return 0.16666666....

fractRagits: % -> Stream Integer

fractRagits(rx) returns the ragits of the fractional part of a radix expansion.

gcd: (%, %) -> %

from GcdDomain

gcd: List % -> %

from GcdDomain

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

from GcdDomain

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

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: (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

positive?: % -> Boolean

from OrderedRing

prefixRagits: % -> List Integer

prefixRagits(rx) returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example, if x = 3/28 = 0.10 714285 714285 ..., then prefixRagits(x)=[1, 0].

prime?: % -> Boolean

from UniqueFactorizationDomain

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

from PrincipalIdealDomain

quo: (%, %) -> %

from EuclideanDomain

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: % -> 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

wholeRadix: List Integer -> %

wholeRadix(l) creates an integral radix expansion from a list of ragits. For example, wholeRadix([1, 3, 4]) will return 134.

wholeRagits: % -> List Integer

wholeRagits(rx) returns the ragits of the integer part of a radix expansion.

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Algebra %

Algebra Fraction Integer

Algebra Integer

BasicType

BiModule(%, %)

BiModule(Fraction Integer, Fraction Integer)

BiModule(Integer, Integer)

CancellationAbelianMonoid

canonicalsClosed

canonicalUnitNormal

CharacteristicNonZero if Integer has CharacteristicNonZero

CharacteristicZero

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom Symbol if Integer has RetractableTo Symbol

CoercibleTo OutputForm

CommutativeRing

CommutativeStar

Comparable

ConvertibleTo DoubleFloat

ConvertibleTo Float

ConvertibleTo InputForm

ConvertibleTo Pattern Float if Integer has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer

DifferentialExtension Integer

DifferentialRing

DivisionRing

Eltable(Integer, %) if Integer has Eltable(Integer, Integer)

EntireRing

EuclideanDomain

Evalable Integer if Integer has Evalable Integer

Field

FullyEvalableOver Integer

FullyLinearlyExplicitOver Integer

FullyPatternMatchable Integer

GcdDomain

InnerEvalable(Integer, Integer) if Integer has Evalable Integer

InnerEvalable(Symbol, Integer) if Integer has InnerEvalable(Symbol, Integer)

IntegralDomain

LeftModule %

LeftModule Fraction Integer

LeftModule Integer

LeftOreRing

LinearlyExplicitOver Integer

Magma

MagmaWithUnit

Module %

Module Fraction Integer

Module Integer

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors

OrderedAbelianGroup

OrderedAbelianMonoid

OrderedAbelianSemiGroup

OrderedCancellationAbelianMonoid

OrderedIntegralDomain

OrderedRing

OrderedSet

PartialDifferentialRing Symbol if Integer has PartialDifferentialRing Symbol

PartialOrder

Patternable Integer

PatternMatchable Float if Integer has PatternMatchable Float

PatternMatchable Integer

PolynomialFactorizationExplicit

PrincipalIdealDomain

QuotientFieldCategory Integer

RealConstant

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo Symbol if Integer has RetractableTo Symbol

RightModule %

RightModule Fraction Integer

RightModule Integer

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough

TwoSidedRecip

UniqueFactorizationDomain

unitsKnown