# UnivariateSeriesWithRationalExponents(Coef, Expon)ΒΆ

undocumented

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

*: (%, %) -> %

from LeftModule %

*: (%, Coef) -> %

from RightModule Coef

*: (%, Fraction Integer) -> % if Coef has Algebra Fraction Integer
*: (Coef, %) -> %

from LeftModule Coef

*: (Fraction Integer, %) -> % if Coef has Algebra Fraction Integer
*: (Integer, %) -> %

from AbelianGroup

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, Coef) -> % if Coef has Field

from AbelianMonoidRing(Coef, Expon)

=: (%, %) -> Boolean

from BasicType

^: (%, %) -> % if Coef has Algebra Fraction Integer
^: (%, Fraction Integer) -> % if Coef has Algebra Fraction Integer

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

acos: % -> % if Coef has Algebra Fraction Integer
acosh: % -> % if Coef has Algebra Fraction Integer
acot: % -> % if Coef has Algebra Fraction Integer
acoth: % -> % if Coef has Algebra Fraction Integer
acsc: % -> % if Coef has Algebra Fraction Integer
acsch: % -> % if Coef has Algebra Fraction Integer
annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %
approximate: (%, Expon) -> Coef if Coef has coerce: Symbol -> Coef and Coef has ^: (Coef, Expon) -> Coef

from UnivariatePowerSeriesCategory(Coef, Expon)

asec: % -> % if Coef has Algebra Fraction Integer
asech: % -> % if Coef has Algebra Fraction Integer
asin: % -> % if Coef has Algebra Fraction Integer
asinh: % -> % if Coef has Algebra Fraction Integer
associates?: (%, %) -> Boolean if Coef has IntegralDomain

from EntireRing

associator: (%, %, %) -> %
atan: % -> % if Coef has Algebra Fraction Integer
atanh: % -> % if Coef has Algebra Fraction Integer
center: % -> Coef

from UnivariatePowerSeriesCategory(Coef, Expon)

characteristic: () -> NonNegativeInteger
charthRoot: % -> Union(%, failed) if Coef has CharacteristicNonZero
coefficient: (%, Expon) -> Coef

from AbelianMonoidRing(Coef, Expon)

coerce: % -> % if Coef has CommutativeRing

from Algebra %

coerce: % -> OutputForm
coerce: Coef -> % if Coef has CommutativeRing

from Algebra Coef

coerce: Fraction Integer -> % if Coef has Algebra Fraction Integer
coerce: Integer -> %
commutator: (%, %) -> %
complete: % -> %

from PowerSeriesCategory(Coef, Expon, SingletonAsOrderedSet)

construct: List Record(k: Expon, c: Coef) -> %

from IndexedProductCategory(Coef, Expon)

constructOrdered: List Record(k: Expon, c: Coef) -> %

from IndexedProductCategory(Coef, Expon)

cos: % -> % if Coef has Algebra Fraction Integer
cosh: % -> % if Coef has Algebra Fraction Integer
cot: % -> % if Coef has Algebra Fraction Integer
coth: % -> % if Coef has Algebra Fraction Integer
csc: % -> % if Coef has Algebra Fraction Integer
csch: % -> % if Coef has Algebra Fraction Integer
D: % -> % if Coef has *: (Expon, Coef) -> Coef

from DifferentialRing

D: (%, List Symbol) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
D: (%, List Symbol, List NonNegativeInteger) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
D: (%, NonNegativeInteger) -> % if Coef has *: (Expon, Coef) -> Coef

from DifferentialRing

D: (%, Symbol) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
D: (%, Symbol, NonNegativeInteger) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
degree: % -> Expon

from PowerSeriesCategory(Coef, Expon, SingletonAsOrderedSet)

differentiate: % -> % if Coef has *: (Expon, Coef) -> Coef

from DifferentialRing

differentiate: (%, List Symbol) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
differentiate: (%, NonNegativeInteger) -> % if Coef has *: (Expon, Coef) -> Coef

from DifferentialRing

differentiate: (%, Symbol) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> % if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
elt: (%, %) -> % if Expon has SemiGroup

from Eltable(%, %)

elt: (%, Expon) -> Coef

from UnivariatePowerSeriesCategory(Coef, Expon)

eval: (%, Coef) -> Stream Coef if Coef has ^: (Coef, Expon) -> Coef

from UnivariatePowerSeriesCategory(Coef, Expon)

exp: % -> % if Coef has Algebra Fraction Integer
exquo: (%, %) -> Union(%, failed) if Coef has IntegralDomain

from EntireRing

extend: (%, Expon) -> %

from UnivariatePowerSeriesCategory(Coef, Expon)

integrate: % -> % if Coef has Algebra Fraction Integer

`integrate(f(x))` returns an anti-derivative of the power series `f(x)` with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.

integrate: (%, Symbol) -> % if Coef has variables: Coef -> List Symbol and Coef has integrate: (Coef, Symbol) -> Coef and Coef has Algebra Fraction Integer

`integrate(f(x), y)` returns an anti-derivative of the power series `f(x)` with respect to the variable `y`.

latex: % -> String

from SetCategory

from PowerSeriesCategory(Coef, Expon, SingletonAsOrderedSet)

from PowerSeriesCategory(Coef, Expon, SingletonAsOrderedSet)

from IndexedProductCategory(Coef, Expon)

leadingTerm: % -> Record(k: Expon, c: Coef)

from IndexedProductCategory(Coef, Expon)

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

log: % -> % if Coef has Algebra Fraction Integer
map: (Coef -> Coef, %) -> %

from IndexedProductCategory(Coef, Expon)

monomial?: % -> Boolean

from IndexedProductCategory(Coef, Expon)

monomial: (Coef, Expon) -> %

from IndexedProductCategory(Coef, Expon)

multiplyExponents: (%, PositiveInteger) -> %

from UnivariatePowerSeriesCategory(Coef, Expon)

nthRoot: (%, Integer) -> % if Coef has Algebra Fraction Integer

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

order: % -> Expon

from UnivariatePowerSeriesCategory(Coef, Expon)

order: (%, Expon) -> Expon

from UnivariatePowerSeriesCategory(Coef, Expon)

pi: () -> % if Coef has Algebra Fraction Integer
plenaryPower: (%, PositiveInteger) -> % if Coef has CommutativeRing or Coef has Algebra Fraction Integer
pole?: % -> Boolean

from PowerSeriesCategory(Coef, Expon, SingletonAsOrderedSet)

recip: % -> Union(%, failed)

from MagmaWithUnit

reductum: % -> %

from IndexedProductCategory(Coef, Expon)

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

sample: %

from AbelianMonoid

sec: % -> % if Coef has Algebra Fraction Integer
sech: % -> % if Coef has Algebra Fraction Integer
sin: % -> % if Coef has Algebra Fraction Integer
sinh: % -> % if Coef has Algebra Fraction Integer
sqrt: % -> % if Coef has Algebra Fraction Integer

subtractIfCan: (%, %) -> Union(%, failed)
tan: % -> % if Coef has Algebra Fraction Integer
tanh: % -> % if Coef has Algebra Fraction Integer
terms: % -> Stream Record(k: Expon, c: Coef)

from UnivariatePowerSeriesCategory(Coef, Expon)

truncate: (%, Expon) -> %

from UnivariatePowerSeriesCategory(Coef, Expon)

truncate: (%, Expon, Expon) -> %

from UnivariatePowerSeriesCategory(Coef, Expon)

unit?: % -> Boolean if Coef has IntegralDomain

from EntireRing

unitCanonical: % -> % if Coef has IntegralDomain

from EntireRing

unitNormal: % -> Record(unit: %, canonical: %, associate: %) if Coef has IntegralDomain

from EntireRing

variable: % -> Symbol

from UnivariatePowerSeriesCategory(Coef, Expon)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, Expon)

AbelianSemiGroup

Algebra % if Coef has CommutativeRing

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer if Coef has Algebra Fraction Integer

BasicType

BiModule(%, %)

BiModule(Coef, Coef)

BiModule(Fraction Integer, Fraction Integer) if Coef has Algebra Fraction Integer

CancellationAbelianMonoid

CharacteristicNonZero if Coef has CharacteristicNonZero

CharacteristicZero if Coef has CharacteristicZero

CommutativeRing if Coef has CommutativeRing

CommutativeStar if Coef has CommutativeRing

DifferentialRing if Coef has *: (Expon, Coef) -> Coef

Eltable(%, %) if Expon has SemiGroup

EntireRing if Coef has IntegralDomain

IndexedProductCategory(Coef, Expon)

IntegralDomain if Coef has IntegralDomain

LeftModule Coef

Magma

MagmaWithUnit

Module % if Coef has CommutativeRing

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

Monoid

NonAssociativeAlgebra % if Coef has CommutativeRing

NonAssociativeAlgebra Coef if Coef has CommutativeRing

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

PartialDifferentialRing Symbol if Coef has *: (Expon, Coef) -> Coef and Coef has PartialDifferentialRing Symbol

PowerSeriesCategory(Coef, Expon, SingletonAsOrderedSet)

RadicalCategory if Coef has Algebra Fraction Integer

RightModule Coef

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

TwoSidedRecip if Coef has CommutativeRing

unitsKnown

UnivariatePowerSeriesCategory(Coef, Expon)

VariablesCommuteWithCoefficients