# UnivariateLaurentSeriesConstructorCategory(Coef, UTS)ΒΆ

- 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
- *: (%, 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
- from BasicType
- >: (%, %) -> 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
- from ElementaryFunctionCategory
- ^: (%, Fraction Integer) -> % if Coef has Algebra Fraction Integer
- from RadicalCategory
- ^: (%, Integer) -> % if Coef has Field
- from DivisionRing
- ^: (%, NonNegativeInteger) -> %
- from MagmaWithUnit
- ^: (%, PositiveInteger) -> %
- from Magma
- ~=: (%, %) -> Boolean
- from BasicType
- abs: % -> % if UTS has OrderedIntegralDomain and Coef has Field
- from OrderedRing
- acos: % -> % if Coef has Algebra Fraction Integer
- from ArcTrigonometricFunctionCategory
- acosh: % -> % if Coef has Algebra Fraction Integer
- from ArcHyperbolicFunctionCategory
- acot: % -> % if Coef has Algebra Fraction Integer
- from ArcTrigonometricFunctionCategory
- acoth: % -> % if Coef has Algebra Fraction Integer
- from ArcHyperbolicFunctionCategory
- acsc: % -> % if Coef has Algebra Fraction Integer
- from ArcTrigonometricFunctionCategory
- acsch: % -> % if Coef has Algebra Fraction Integer
- from ArcHyperbolicFunctionCategory
- annihilate?: (%, %) -> Boolean
- from Rng
- antiCommutator: (%, %) -> %
- from NonAssociativeSemiRng
- approximate: (%, Integer) -> Coef if Coef has coerce: Symbol -> Coef and Coef has ^: (Coef, Integer) -> Coef
- from UnivariatePowerSeriesCategory(Coef, Integer)
- asec: % -> % if Coef has Algebra Fraction Integer
- from ArcTrigonometricFunctionCategory
- asech: % -> % if Coef has Algebra Fraction Integer
- from ArcHyperbolicFunctionCategory
- asin: % -> % if Coef has Algebra Fraction Integer
- from ArcTrigonometricFunctionCategory
- asinh: % -> % if Coef has Algebra Fraction Integer
- from ArcHyperbolicFunctionCategory
- associates?: (%, %) -> Boolean if Coef has IntegralDomain
- from EntireRing
- associator: (%, %, %) -> %
- from NonAssociativeRng
- atan: % -> % if Coef has Algebra Fraction Integer
- from ArcTrigonometricFunctionCategory
- atanh: % -> % if Coef has Algebra Fraction Integer
- from ArcHyperbolicFunctionCategory
- 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
- from CharacteristicNonZero
- coefficient: (%, Integer) -> Coef
- from AbelianMonoidRing(Coef, Integer)
- coerce: % -> % if Coef has IntegralDomain
- 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
- from RetractableTo Fraction Integer
- coerce: Integer -> %
- from NonAssociativeRing
- coerce: Symbol -> % if UTS has RetractableTo Symbol and Coef has Field
- from RetractableTo 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)
- 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 UTS has ConvertibleTo InputForm and Coef has Field
- from ConvertibleTo InputForm
- convert: % -> Pattern Float if UTS has ConvertibleTo Pattern Float and Coef has Field
- from ConvertibleTo Pattern Float
- convert: % -> Pattern Integer if UTS has ConvertibleTo Pattern Integer and Coef has Field
- from ConvertibleTo Pattern Integer
- cos: % -> % if Coef has Algebra Fraction Integer
- from TrigonometricFunctionCategory
- cosh: % -> % if Coef has Algebra Fraction Integer
- from HyperbolicFunctionCategory
- cot: % -> % if Coef has Algebra Fraction Integer
- from TrigonometricFunctionCategory
- coth: % -> % if Coef has Algebra Fraction Integer
- from HyperbolicFunctionCategory
- csc: % -> % if Coef has Algebra Fraction Integer
- from TrigonometricFunctionCategory
- csch: % -> % if Coef has Algebra Fraction Integer
- from HyperbolicFunctionCategory
- D: % -> % if Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from DifferentialRing
- D: (%, List Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from PartialDifferentialRing Symbol
- D: (%, List Symbol, List NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from PartialDifferentialRing Symbol
- D: (%, NonNegativeInteger) -> % if Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from DifferentialRing
- D: (%, Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from PartialDifferentialRing Symbol
- D: (%, Symbol, NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from 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 *: (Integer, Coef) -> Coef or Coef has Field
- from DifferentialRing
- differentiate: (%, List Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from PartialDifferentialRing Symbol
- differentiate: (%, List Symbol, List NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from PartialDifferentialRing Symbol
- differentiate: (%, NonNegativeInteger) -> % if Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from DifferentialRing
- differentiate: (%, Symbol) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from PartialDifferentialRing Symbol
- differentiate: (%, Symbol, NonNegativeInteger) -> % if Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef or Coef has Field
- from 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)
- exp: % -> % if Coef has Algebra Fraction Integer
- from ElementaryFunctionCategory
- 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
- factor: % -> Factored % if Coef has Field
- from UniqueFactorizationDomain
- factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UTS has PolynomialFactorizationExplicit and Coef has Field
- from PolynomialFactorizationExplicit
- factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UTS has PolynomialFactorizationExplicit and Coef has Field
- from 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
- gcd: (%, %) -> % if Coef has Field
- from GcdDomain
- gcd: List % -> % if Coef has Field
- from GcdDomain
- gcdPolynomial: (SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % if Coef has Field
- from PolynomialFactorizationExplicit
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- init: % if UTS has StepThrough and Coef has Field
- from StepThrough
- integrate: % -> % if Coef has Algebra Fraction Integer
- from UnivariateLaurentSeriesCategory Coef
- integrate: (%, Symbol) -> % if Coef has Algebra Fraction Integer and Coef has integrate: (Coef, Symbol) -> Coef and Coef has variables: Coef -> List Symbol or Coef has AlgebraicallyClosedFunctionSpace Integer and Coef has Algebra Fraction Integer and Coef has TranscendentalFunctionCategory and Coef has PrimitiveFunctionCategory
- from UnivariateLaurentSeriesCategory Coef
- 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)`

.- lcm: (%, %) -> % if Coef has Field
- from GcdDomain
- lcm: List % -> % if Coef has Field
- from GcdDomain
- 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)
- leftPower: (%, NonNegativeInteger) -> %
- from MagmaWithUnit
- leftPower: (%, PositiveInteger) -> %
- from Magma
- leftRecip: % -> Union(%, failed)
- from MagmaWithUnit
- log: % -> % if Coef has Algebra Fraction Integer
- from ElementaryFunctionCategory
- map: (Coef -> Coef, %) -> %
- from AbelianMonoidRing(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: (%, List SingletonAsOrderedSet, List Integer) -> %
- from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
- monomial: (%, SingletonAsOrderedSet, Integer) -> %
- from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
- monomial: (Coef, Integer) -> %
- from AbelianMonoidRing(Coef, Integer)
- monomial?: % -> Boolean
- from AbelianMonoidRing(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 UTS has OrderedIntegralDomain and Coef has Field
- from OrderedRing
- nextItem: % -> Union(%, failed) if UTS has StepThrough and Coef has Field
- from StepThrough
- nthRoot: (%, Integer) -> % if Coef has Algebra Fraction Integer
- from RadicalCategory
- 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
- pi: () -> % if Coef has Algebra Fraction Integer
- from TranscendentalFunctionCategory
- pole?: % -> Boolean
- from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
- positive?: % -> Boolean if UTS has OrderedIntegralDomain and Coef has Field
- from OrderedRing
- prime?: % -> Boolean if Coef has Field
- from UniqueFactorizationDomain
- 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
- from LinearlyExplicitOver Integer
- 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
- from LinearlyExplicitOver Integer
- reducedSystem: Matrix % -> Matrix UTS if Coef has Field
- from LinearlyExplicitOver UTS
- reductum: % -> %
- from AbelianMonoidRing(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
- sec: % -> % if Coef has Algebra Fraction Integer
- from TrigonometricFunctionCategory
- sech: % -> % if Coef has Algebra Fraction Integer
- from HyperbolicFunctionCategory
- series: Stream Record(k: Integer, c: Coef) -> %
- from UnivariateLaurentSeriesCategory Coef
- sign: % -> Integer if UTS has OrderedIntegralDomain and Coef has Field
- from OrderedRing
- sin: % -> % if Coef has Algebra Fraction Integer
- from TrigonometricFunctionCategory
- sinh: % -> % if Coef has Algebra Fraction Integer
- from HyperbolicFunctionCategory
- 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 UTS has PolynomialFactorizationExplicit and Coef has Field
- from PolynomialFactorizationExplicit
- sqrt: % -> % if Coef has Algebra Fraction Integer
- from RadicalCategory
- squareFree: % -> Factored % if Coef has Field
- from UniqueFactorizationDomain
- squareFreePart: % -> % if Coef has Field
- from UniqueFactorizationDomain
- squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UTS has PolynomialFactorizationExplicit and Coef has Field
- from PolynomialFactorizationExplicit
- subtractIfCan: (%, %) -> Union(%, failed)
- from CancellationAbelianMonoid
- tan: % -> % if Coef has Algebra Fraction Integer
- from TrigonometricFunctionCategory
- tanh: % -> % if Coef has Algebra Fraction Integer
- from HyperbolicFunctionCategory

- 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)
- variables: % -> List SingletonAsOrderedSet
- from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
- wholePart: % -> UTS if UTS has EuclideanDomain and Coef has Field
- from QuotientFieldCategory UTS
- zero?: % -> Boolean
- from AbelianMonoid

AbelianMonoidRing(Coef, Integer)

Algebra % if Coef has IntegralDomain

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 CharacteristicNonZero or Coef has Field

CharacteristicZero if Coef has CharacteristicZero or Coef has Field

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 UTS has ConvertibleTo InputForm and Coef has Field

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

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

DifferentialExtension UTS if Coef has Field

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

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

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 IntegralDomain

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

noZeroDivisors if Coef has IntegralDomain

OrderedAbelianGroup if UTS has OrderedIntegralDomain and Coef has Field

OrderedAbelianMonoid if UTS has OrderedIntegralDomain and Coef has Field

OrderedAbelianSemiGroup if UTS has OrderedIntegralDomain and Coef has Field

OrderedCancellationAbelianMonoid if UTS has OrderedIntegralDomain and Coef has Field

OrderedIntegralDomain if UTS has OrderedIntegralDomain and Coef has Field

OrderedRing if UTS has OrderedIntegralDomain and Coef has Field

OrderedSet if UTS has OrderedSet and Coef has Field

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

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 UTS has PolynomialFactorizationExplicit and Coef has Field

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 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

UniqueFactorizationDomain if Coef has Field

UnivariateLaurentSeriesCategory Coef