# UnivariateLaurentSeriesConstructorCategory(Coef, UTS)¶

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

from RightModule UTS

*: (Coef, %) -> %

from LeftModule Coef

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

^: (%, 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
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: (%, 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
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
ceiling: % -> UTS if UTS has IntegerNumberSystem and Coef has Field

from QuotientFieldCategory UTS

center: % -> Coef

from UnivariatePowerSeriesCategory(Coef, Integer)

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

from AbelianMonoidRing(Coef, Integer)

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

`coerce(f(x))` converts the Taylor series `f(x)` to a Laurent series.

commutator: (%, %) -> %
complete: % -> %

from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

conditionP: Matrix % -> Union(Vector %, failed) if UTS has PolynomialFactorizationExplicit and % has CharacteristicNonZero and Coef has Field
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
convert: % -> Float if UTS has RealConstant and Coef has Field
convert: % -> InputForm if UTS has ConvertibleTo InputForm and Coef has Field
convert: % -> Pattern Float if UTS has ConvertibleTo Pattern Float and Coef has Field
convert: % -> Pattern Integer if UTS has ConvertibleTo Pattern Integer and Coef has Field
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 *: (Integer, Coef) -> Coef or Coef has Field

from DifferentialRing

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

from DifferentialRing

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

from DifferentialRing

differentiate: (%, Symbol) -> % if Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol or Coef has Field
differentiate: (%, Symbol, NonNegativeInteger) -> % if Coef has *: (Integer, Coef) -> Coef and Coef has PartialDifferentialRing Symbol or Coef has Field
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
expressIdealMember: (List %, %) -> Union(List %, failed) if Coef has Field
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
factorPolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UTS has PolynomialFactorizationExplicit and Coef has Field
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UTS has PolynomialFactorizationExplicit and Coef has Field
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 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 variables: Coef -> List Symbol and Coef has integrate: (Coef, Symbol) -> Coef and Coef has Algebra Fraction Integer

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)`.

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

from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

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

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

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
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if UTS has PatternMatchable Integer and Coef has Field
pi: () -> % if Coef has Algebra Fraction Integer
plenaryPower: (%, PositiveInteger) -> % if Coef has Algebra Fraction Integer or Coef has CommutativeRing

from NonAssociativeAlgebra UTS

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
principalIdeal: List % -> Record(coef: List %, generator: %) if Coef has Field
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
retract: % -> Integer if UTS has RetractableTo Integer and Coef has Field
retract: % -> Symbol if UTS has RetractableTo Symbol and Coef has Field
retract: % -> UTS

from RetractableTo UTS

retractIfCan: % -> Union(Fraction Integer, failed) if UTS has RetractableTo Integer and Coef has Field
retractIfCan: % -> Union(Integer, failed) if UTS has RetractableTo Integer and Coef has Field
retractIfCan: % -> Union(Symbol, failed) if UTS has RetractableTo Symbol and Coef has Field
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
sech: % -> % if Coef has Algebra Fraction Integer
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
sinh: % -> % if Coef has Algebra Fraction Integer
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
sqrt: % -> % if Coef has Algebra Fraction Integer

squareFree: % -> Factored % if Coef has Field
squareFreePart: % -> % if Coef has Field
squareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if UTS has PolynomialFactorizationExplicit and Coef has Field
subtractIfCan: (%, %) -> Union(%, failed)
tan: % -> % if Coef has Algebra Fraction Integer
tanh: % -> % if Coef has Algebra Fraction Integer
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

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, Integer)

AbelianSemiGroup

Algebra % if Coef has CommutativeRing

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer if Coef has Algebra Fraction Integer

Algebra UTS if Coef has Field

BasicType

BiModule(%, %)

BiModule(Coef, Coef)

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

BiModule(UTS, UTS) if Coef has Field

CancellationAbelianMonoid

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

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

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

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

Field if Coef has Field

FullyEvalableOver UTS if Coef has Field

FullyLinearlyExplicitOver UTS if Coef has Field

FullyPatternMatchable UTS if Coef has Field

GcdDomain if Coef has Field

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 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

Magma

MagmaWithUnit

Module % if Coef has CommutativeRing

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

Module UTS if Coef has Field

Monoid

NonAssociativeAlgebra % if Coef has CommutativeRing

NonAssociativeAlgebra Coef if Coef has CommutativeRing

NonAssociativeAlgebra UTS if Coef has Field

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

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

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

RightModule Coef

RightModule Integer if UTS has LinearlyExplicitOver Integer and Coef has Field

RightModule UTS if Coef has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if UTS has StepThrough and Coef has Field

TwoSidedRecip if Coef has CommutativeRing

UniqueFactorizationDomain if Coef has Field

unitsKnown

VariablesCommuteWithCoefficients