# UnivariateLaurentSeriesConstructorCategory(Coef, UTS)¶

laurent.spad line 1 [edit on github]

Coef: Ring

UTS: UnivariateTaylorSeriesCategory Coef

This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair `[n, f(x)]`

, where `n`

is an arbitrary integer and `f(x)`

is a Taylor series. This pair represents the Laurent series `x^n * f(x)`

.

- 0: %
from AbelianMonoid

- 1: %
from MagmaWithUnit

- *: (%, %) -> %
from Magma

- *: (%, Coef) -> %
from RightModule Coef

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

- *: (%, Integer) -> % if UTS has LinearlyExplicitOver Integer and Coef has Field
from RightModule Integer

- *: (%, UTS) -> % if Coef has Field
from RightModule UTS

- *: (Coef, %) -> %
from LeftModule Coef

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

- *: (Integer, %) -> %
from AbelianGroup

- *: (NonNegativeInteger, %) -> %
from AbelianMonoid

- *: (PositiveInteger, %) -> %
from AbelianSemiGroup

- *: (UTS, %) -> % if Coef has Field
from LeftModule UTS

- +: (%, %) -> %
from AbelianSemiGroup

- -: % -> %
from AbelianGroup

- -: (%, %) -> %
from AbelianGroup

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

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

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

- <=: (%, %) -> Boolean if UTS has OrderedSet and Coef has Field
from PartialOrder

- <: (%, %) -> Boolean if UTS has OrderedSet and Coef has Field
from PartialOrder

- >=: (%, %) -> Boolean if UTS has OrderedSet and Coef has Field
from PartialOrder

- >: (%, %) -> Boolean if UTS has OrderedSet and Coef has Field
from PartialOrder

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

- ^: (%, Integer) -> % if Coef has Field
from DivisionRing

- ^: (%, NonNegativeInteger) -> %
from MagmaWithUnit

- ^: (%, PositiveInteger) -> %
from Magma

- abs: % -> % if Coef has Field and UTS has OrderedIntegralDomain
from OrderedRing

- annihilate?: (%, %) -> Boolean
from Rng

- antiCommutator: (%, %) -> %

- approximate: (%, Integer) -> Coef if Coef has coerce: Symbol -> Coef and Coef has ^: (Coef, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)

- associates?: (%, %) -> Boolean if Coef has IntegralDomain
from EntireRing

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

- ceiling: % -> UTS if UTS has IntegerNumberSystem and Coef has Field
from QuotientFieldCategory UTS

- center: % -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)

- characteristic: () -> NonNegativeInteger
from NonAssociativeRing

- charthRoot: % -> Union(%, failed) if Coef has CharacteristicNonZero or Coef has Field

- coefficient: (%, Integer) -> Coef
from AbelianMonoidRing(Coef, Integer)

- coerce: % -> % if Coef has CommutativeRing
from Algebra %

- coerce: % -> OutputForm
from CoercibleTo OutputForm

- coerce: Coef -> % if Coef has CommutativeRing
from Algebra Coef

- coerce: Fraction Integer -> % if Coef has Algebra Fraction Integer
- coerce: Integer -> %
from NonAssociativeRing

- coerce: Symbol -> % if UTS has RetractableTo Symbol and Coef has Field
from CoercibleFrom Symbol

- coerce: UTS -> %
`coerce(f(x))`

converts the Taylor series`f(x)`

to a Laurent series.

- commutator: (%, %) -> %
from NonAssociativeRng

- complete: % -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

- conditionP: Matrix % -> Union(Vector %, failed) if % has CharacteristicNonZero and Coef has Field and UTS has PolynomialFactorizationExplicit

- construct: List Record(k: Integer, c: Coef) -> %
from IndexedProductCategory(Coef, Integer)

- constructOrdered: List Record(k: Integer, c: Coef) -> %
from IndexedProductCategory(Coef, Integer)

- convert: % -> DoubleFloat if UTS has RealConstant and Coef has Field
from ConvertibleTo DoubleFloat

- convert: % -> Float if UTS has RealConstant and Coef has Field
from ConvertibleTo Float

- convert: % -> InputForm if Coef has Field and UTS has ConvertibleTo InputForm
from ConvertibleTo InputForm

- convert: % -> Pattern Float if Coef has Field and UTS has ConvertibleTo Pattern Float
from ConvertibleTo Pattern Float

- convert: % -> Pattern Integer if Coef has Field and UTS has ConvertibleTo Pattern Integer
from ConvertibleTo Pattern Integer

- D: % -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing

- D: (%, List Symbol) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- D: (%, List Symbol, List NonNegativeInteger) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- D: (%, NonNegativeInteger) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing

- D: (%, Symbol) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- D: (%, Symbol, NonNegativeInteger) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- D: (%, UTS -> UTS) -> % if Coef has Field
from DifferentialExtension UTS

- D: (%, UTS -> UTS, NonNegativeInteger) -> % if Coef has Field
from DifferentialExtension UTS

- degree: % -> Integer
`degree(f(x))`

returns the degree of the lowest order term of`f(x)`

, which may have zero as a coefficient.

- denom: % -> UTS if Coef has Field
from QuotientFieldCategory UTS

- denominator: % -> % if Coef has Field
from QuotientFieldCategory UTS

- differentiate: % -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing

- differentiate: (%, List Symbol) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- differentiate: (%, List Symbol, List NonNegativeInteger) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- differentiate: (%, NonNegativeInteger) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing

- differentiate: (%, Symbol) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- differentiate: (%, Symbol, NonNegativeInteger) -> % if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol
- differentiate: (%, UTS -> UTS) -> % if Coef has Field
from DifferentialExtension UTS

- differentiate: (%, UTS -> UTS, NonNegativeInteger) -> % if Coef has Field
from DifferentialExtension UTS

- divide: (%, %) -> Record(quotient: %, remainder: %) if Coef has Field
from EuclideanDomain

- elt: (%, %) -> %
from Eltable(%, %)

- elt: (%, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)

- elt: (%, UTS) -> % if UTS has Eltable(UTS, UTS) and Coef has Field
from Eltable(UTS, %)

- euclideanSize: % -> NonNegativeInteger if Coef has Field
from EuclideanDomain

- eval: (%, Coef) -> Stream Coef if Coef has ^: (Coef, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)

- eval: (%, Equation UTS) -> % if UTS has Evalable UTS and Coef has Field
from Evalable UTS

- eval: (%, List Equation UTS) -> % if UTS has Evalable UTS and Coef has Field
from Evalable UTS

- eval: (%, List Symbol, List UTS) -> % if UTS has InnerEvalable(Symbol, UTS) and Coef has Field
from InnerEvalable(Symbol, UTS)

- eval: (%, List UTS, List UTS) -> % if UTS has Evalable UTS and Coef has Field
from InnerEvalable(UTS, UTS)

- eval: (%, Symbol, UTS) -> % if UTS has InnerEvalable(Symbol, UTS) and Coef has Field
from InnerEvalable(Symbol, UTS)

- eval: (%, UTS, UTS) -> % if UTS has Evalable UTS and Coef has Field
from InnerEvalable(UTS, UTS)

- expressIdealMember: (List %, %) -> Union(List %, failed) if Coef has Field
from PrincipalIdealDomain

- exquo: (%, %) -> Union(%, failed) if Coef has IntegralDomain
from EntireRing

- extend: (%, Integer) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)

- extendedEuclidean: (%, %) -> Record(coef1: %, coef2: %, generator: %) if Coef has Field
from EuclideanDomain

- extendedEuclidean: (%, %, %) -> Union(Record(coef1: %, coef2: %), failed) if Coef has Field
from EuclideanDomain

- factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if Coef has Field and UTS has PolynomialFactorizationExplicit

- factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if Coef has Field and UTS has PolynomialFactorizationExplicit

- floor: % -> UTS if UTS has IntegerNumberSystem and Coef has Field
from QuotientFieldCategory UTS

- fractionPart: % -> % if UTS has EuclideanDomain and Coef has Field
from QuotientFieldCategory UTS

- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has Field
from GcdDomain

- init: % if UTS has StepThrough and Coef has Field
from StepThrough

- integrate: % -> % if Coef has Algebra Fraction Integer
from UnivariateSeriesWithRationalExponents(Coef, Integer)

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

- inv: % -> % if Coef has Field
from DivisionRing

- latex: % -> String
from SetCategory

- laurent: (Integer, Stream Coef) -> %
from UnivariateLaurentSeriesCategory Coef

- laurent: (Integer, UTS) -> %
`laurent(n, f(x))`

returns`x^n * f(x)`

.

- lcmCoef: (%, %) -> Record(llcm_res: %, coeff1: %, coeff2: %) if Coef has Field
from LeftOreRing

- leadingCoefficient: % -> Coef
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

- leadingMonomial: % -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

- leadingSupport: % -> Integer
from IndexedProductCategory(Coef, Integer)

- leadingTerm: % -> Record(k: Integer, c: Coef)
from IndexedProductCategory(Coef, Integer)

- leftPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit

- leftPower: (%, PositiveInteger) -> %
from Magma

- leftRecip: % -> Union(%, failed)
from MagmaWithUnit

- map: (Coef -> Coef, %) -> %
from IndexedProductCategory(Coef, Integer)

- map: (UTS -> UTS, %) -> % if Coef has Field
from FullyEvalableOver UTS

- max: (%, %) -> % if UTS has OrderedSet and Coef has Field
from OrderedSet

- min: (%, %) -> % if UTS has OrderedSet and Coef has Field
from OrderedSet

- monomial?: % -> Boolean
from IndexedProductCategory(Coef, Integer)

- monomial: (Coef, Integer) -> %
from IndexedProductCategory(Coef, Integer)

- multiEuclidean: (List %, %) -> Union(List %, failed) if Coef has Field
from EuclideanDomain

- multiplyCoefficients: (Integer -> Coef, %) -> %
from UnivariateLaurentSeriesCategory Coef

- multiplyExponents: (%, PositiveInteger) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)

- negative?: % -> Boolean if Coef has Field and UTS has OrderedIntegralDomain
from OrderedRing

- nextItem: % -> Union(%, failed) if UTS has StepThrough and Coef has Field
from StepThrough

- numer: % -> UTS if Coef has Field
from QuotientFieldCategory UTS

- numerator: % -> % if Coef has Field
from QuotientFieldCategory UTS

- one?: % -> Boolean
from MagmaWithUnit

- opposite?: (%, %) -> Boolean
from AbelianMonoid

- order: % -> Integer
from UnivariatePowerSeriesCategory(Coef, Integer)

- order: (%, Integer) -> Integer
from UnivariatePowerSeriesCategory(Coef, Integer)

- patternMatch: (%, Pattern Float, PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if UTS has PatternMatchable Float and Coef has Field
from PatternMatchable Float

- patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if UTS has PatternMatchable Integer and Coef has Field
from PatternMatchable Integer

- plenaryPower: (%, PositiveInteger) -> % if Coef has CommutativeRing or Coef has Algebra Fraction Integer
from NonAssociativeAlgebra Coef

- pole?: % -> Boolean
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

- positive?: % -> Boolean if Coef has Field and UTS has OrderedIntegralDomain
from OrderedRing

- principalIdeal: List % -> Record(coef: List %, generator: %) if Coef has Field
from PrincipalIdealDomain

- quo: (%, %) -> % if Coef has Field
from EuclideanDomain

- rationalFunction: (%, Integer) -> Fraction Polynomial Coef if Coef has IntegralDomain
from UnivariateLaurentSeriesCategory Coef

- rationalFunction: (%, Integer, Integer) -> Fraction Polynomial Coef if Coef has IntegralDomain
from UnivariateLaurentSeriesCategory Coef

- recip: % -> Union(%, failed)
from MagmaWithUnit

- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if UTS has LinearlyExplicitOver Integer and Coef has Field
- reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix UTS, vec: Vector UTS) if Coef has Field
from LinearlyExplicitOver UTS

- reducedSystem: Matrix % -> Matrix Integer if UTS has LinearlyExplicitOver Integer and Coef has Field
- reducedSystem: Matrix % -> Matrix UTS if Coef has Field
from LinearlyExplicitOver UTS

- reductum: % -> %
from IndexedProductCategory(Coef, Integer)

- rem: (%, %) -> % if Coef has Field
from EuclideanDomain

- removeZeroes: % -> %
`removeZeroes(f(x))`

removes leading zeroes from the representation of the Laurent series`f(x)`

. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient, the ‘leading zero’ is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note:`removeZeroes(f)`

removes all leading zeroes from`f`

- removeZeroes: (Integer, %) -> %
`removeZeroes(n, f(x))`

removes up to`n`

leading zeroes from the Laurent series`f(x)`

. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient, the ‘leading zero’ is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.

- retract: % -> Fraction Integer if UTS has RetractableTo Integer and Coef has Field
from RetractableTo Fraction Integer

- retract: % -> Integer if UTS has RetractableTo Integer and Coef has Field
from RetractableTo Integer

- retract: % -> Symbol if UTS has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol

- retract: % -> UTS
from RetractableTo UTS

- retractIfCan: % -> Union(Fraction Integer, failed) if UTS has RetractableTo Integer and Coef has Field
from RetractableTo Fraction Integer

- retractIfCan: % -> Union(Integer, failed) if UTS has RetractableTo Integer and Coef has Field
from RetractableTo Integer

- retractIfCan: % -> Union(Symbol, failed) if UTS has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol

- retractIfCan: % -> Union(UTS, failed)
from RetractableTo UTS

- rightPower: (%, NonNegativeInteger) -> %
from MagmaWithUnit

- rightPower: (%, PositiveInteger) -> %
from Magma

- rightRecip: % -> Union(%, failed)
from MagmaWithUnit

- sample: %
from AbelianMonoid

- series: Stream Record(k: Integer, c: Coef) -> %
from UnivariateLaurentSeriesCategory Coef

- sign: % -> Integer if Coef has Field and UTS has OrderedIntegralDomain
from OrderedRing

- sizeLess?: (%, %) -> Boolean if Coef has Field
from EuclideanDomain

- smaller?: (%, %) -> Boolean if UTS has Comparable and Coef has Field
from Comparable

- solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if Coef has Field and UTS has PolynomialFactorizationExplicit

- sqrt: % -> % if Coef has Algebra Fraction Integer
from RadicalCategory

- squareFree: % -> Factored % if Coef has Field

- squareFreePart: % -> % if Coef has Field

- squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if Coef has Field and UTS has PolynomialFactorizationExplicit

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

- taylor: % -> UTS
`taylor(f(x))`

converts the Laurent series`f`

(`x`

) to a Taylor series, if possible. Error: if this is not possible.

- taylorIfCan: % -> Union(UTS, failed)
`taylorIfCan(f(x))`

converts the Laurent series`f(x)`

to a Taylor series, if possible. If this is not possible, “failed” is returned.

- taylorRep: % -> UTS
`taylorRep(f(x))`

returns`g(x)`

, where`f = x^n * g(x)`

is represented by`[n, g(x)]`

.

- terms: % -> Stream Record(k: Integer, c: Coef)
from UnivariatePowerSeriesCategory(Coef, Integer)

- truncate: (%, Integer) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)

- truncate: (%, Integer, Integer) -> %
from UnivariatePowerSeriesCategory(Coef, Integer)

- 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, Integer)

- wholePart: % -> UTS if UTS has EuclideanDomain and Coef has Field
from QuotientFieldCategory UTS

- zero?: % -> Boolean
from AbelianMonoid

AbelianMonoidRing(Coef, Integer)

Algebra % if Coef has CommutativeRing

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer if Coef has Algebra Fraction Integer

ArcHyperbolicFunctionCategory if Coef has Algebra Fraction Integer

ArcTrigonometricFunctionCategory if Coef has Algebra Fraction Integer

BiModule(%, %)

BiModule(Coef, Coef)

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

BiModule(UTS, UTS) if Coef has Field

canonicalsClosed if Coef has Field

canonicalUnitNormal if Coef has Field

CharacteristicNonZero if Coef has Field or Coef has CharacteristicNonZero

CharacteristicZero if Coef has Field or Coef has CharacteristicZero

CoercibleFrom Fraction Integer if UTS has RetractableTo Integer and Coef has Field

CoercibleFrom Integer if UTS has RetractableTo Integer and Coef has Field

CoercibleFrom Symbol if UTS has RetractableTo Symbol and Coef has Field

CoercibleFrom UTS

CommutativeRing if Coef has CommutativeRing

CommutativeStar if Coef has CommutativeRing

Comparable if UTS has Comparable and Coef has Field

ConvertibleTo DoubleFloat if UTS has RealConstant and Coef has Field

ConvertibleTo Float if UTS has RealConstant and Coef has Field

ConvertibleTo InputForm if Coef has Field and UTS has ConvertibleTo InputForm

ConvertibleTo Pattern Float if Coef has Field and UTS has ConvertibleTo Pattern Float

ConvertibleTo Pattern Integer if Coef has Field and UTS has ConvertibleTo Pattern Integer

DifferentialExtension UTS if Coef has Field

DifferentialRing if Coef has Field or Coef has *: (Integer, Coef) -> Coef

DivisionRing if Coef has Field

ElementaryFunctionCategory if Coef has Algebra Fraction Integer

Eltable(%, %)

Eltable(UTS, %) if UTS has Eltable(UTS, UTS) and Coef has Field

EntireRing if Coef has IntegralDomain

EuclideanDomain if Coef has Field

Evalable UTS if UTS has Evalable UTS and Coef has Field

FullyEvalableOver UTS if Coef has Field

FullyLinearlyExplicitOver UTS if Coef has Field

FullyPatternMatchable UTS if Coef has Field

HyperbolicFunctionCategory if Coef has Algebra Fraction Integer

IndexedProductCategory(Coef, Integer)

InnerEvalable(Symbol, UTS) if UTS has InnerEvalable(Symbol, UTS) and Coef has Field

InnerEvalable(UTS, UTS) if UTS has Evalable UTS and Coef has Field

IntegralDomain if Coef has IntegralDomain

LeftModule Coef

LeftModule Fraction Integer if Coef has Algebra Fraction Integer

LeftModule UTS if Coef has Field

LeftOreRing if Coef has Field

LinearlyExplicitOver Integer if UTS has LinearlyExplicitOver Integer and Coef has Field

LinearlyExplicitOver UTS if Coef has Field

Module % if Coef has CommutativeRing

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

NonAssociativeAlgebra % if Coef has CommutativeRing

NonAssociativeAlgebra Coef if Coef has CommutativeRing

NonAssociativeAlgebra Fraction Integer if Coef has Algebra Fraction Integer

NonAssociativeAlgebra UTS if Coef has Field

noZeroDivisors if Coef has IntegralDomain

OrderedAbelianGroup if Coef has Field and UTS has OrderedIntegralDomain

OrderedAbelianMonoid if Coef has Field and UTS has OrderedIntegralDomain

OrderedAbelianSemiGroup if Coef has Field and UTS has OrderedIntegralDomain

OrderedCancellationAbelianMonoid if Coef has Field and UTS has OrderedIntegralDomain

OrderedIntegralDomain if Coef has Field and UTS has OrderedIntegralDomain

OrderedRing if Coef has Field and UTS has OrderedIntegralDomain

OrderedSet if UTS has OrderedSet and Coef has Field

PartialDifferentialRing Symbol if Coef has Field or Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol

PartialOrder if UTS has OrderedSet and Coef has Field

Patternable UTS if Coef has Field

PatternMatchable Float if UTS has PatternMatchable Float and Coef has Field

PatternMatchable Integer if UTS has PatternMatchable Integer and Coef has Field

PolynomialFactorizationExplicit if Coef has Field and UTS has PolynomialFactorizationExplicit

PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

PrincipalIdealDomain if Coef has Field

QuotientFieldCategory UTS if Coef has Field

RadicalCategory if Coef has Algebra Fraction Integer

RealConstant if UTS has RealConstant and Coef has Field

RetractableTo Fraction Integer if UTS has RetractableTo Integer and Coef has Field

RetractableTo Integer if UTS has RetractableTo Integer and Coef has Field

RetractableTo Symbol if UTS has RetractableTo Symbol and Coef has Field

RetractableTo UTS

RightModule Coef

RightModule Fraction Integer if Coef has Algebra Fraction Integer

RightModule Integer if UTS has LinearlyExplicitOver Integer and Coef has Field

RightModule UTS if Coef has Field

StepThrough if UTS has StepThrough and Coef has Field

TranscendentalFunctionCategory if Coef has Algebra Fraction Integer

TrigonometricFunctionCategory if Coef has Algebra Fraction Integer

TwoSidedRecip if Coef has CommutativeRing

UniqueFactorizationDomain if Coef has Field

UnivariateLaurentSeriesCategory Coef

UnivariatePowerSeriesCategory(Coef, Integer)