UnivariateLaurentSeriesConstructorCategory(Coef, UTS)ΒΆ

laurent.spad line 1

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

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

ArcHyperbolicFunctionCategory if Coef has Algebra Fraction Integer

ArcTrigonometricFunctionCategory if Coef has Algebra Fraction Integer

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

CoercibleTo OutputForm

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

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

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 %

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

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

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 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 %

RightModule Coef

RightModule Fraction Integer if Coef has Algebra Fraction Integer

RightModule UTS if Coef has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

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

unitsKnown

UnivariateLaurentSeriesCategory Coef

UnivariatePowerSeriesCategory(Coef, Integer)

VariablesCommuteWithCoefficients