SparseUnivariateLaurentSeries(Coef, var, cen)ΒΆ

sups.spad line 1459

Sparse Laurent series in one variable SparseUnivariateLaurentSeries is a domain representing Laurent series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring, the power series variable, and the center of the power series expansion. For example, SparseUnivariateLaurentSeries(Integer, x, 3) represents Laurent series in (x - 3) with integer coefficients.

0: %
from AbelianMonoid
1: %
from MagmaWithUnit
*: (%, %) -> %
from Magma
*: (%, Coef) -> %
from RightModule Coef
*: (%, Fraction Integer) -> % if Coef has Algebra Fraction Integer
from RightModule Fraction Integer
*: (%, SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from RightModule SparseUnivariateTaylorSeries(Coef, var, cen)
*: (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
*: (SparseUnivariateTaylorSeries(Coef, var, cen), %) -> % if Coef has Field
from LeftModule SparseUnivariateTaylorSeries(Coef, var, cen)
+: (%, %) -> %
from AbelianSemiGroup
-: % -> %
from AbelianGroup
-: (%, %) -> %
from AbelianGroup
/: (%, %) -> % if Coef has Field
from Field
/: (%, Coef) -> % if Coef has Field
from AbelianMonoidRing(Coef, Integer)
/: (SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
<: (%, %) -> Boolean if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
<=: (%, %) -> Boolean if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
=: (%, %) -> Boolean
from BasicType
>: (%, %) -> Boolean if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from PartialOrder
>=: (%, %) -> Boolean if SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) 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: % -> SparseUnivariateTaylorSeries(Coef, var, cen) if SparseUnivariateTaylorSeries(Coef, var, cen) has IntegerNumberSystem and Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
center: % -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
characteristic: () -> NonNegativeInteger
from NonAssociativeRing
charthRoot: % -> Union(%, failed) if SparseUnivariateTaylorSeries(Coef, var, cen) has CharacteristicNonZero and Coef has Field or Coef has CharacteristicNonZero
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: SparseUnivariateTaylorSeries(Coef, var, cen) -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
coerce: Symbol -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol
coerce: Variable var -> %
coerce(var) converts the series variable var into a Laurent series.
commutator: (%, %) -> %
from NonAssociativeRng
complete: % -> %
from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
convert: % -> DoubleFloat if SparseUnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field
from ConvertibleTo DoubleFloat
convert: % -> Float if SparseUnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field
from ConvertibleTo Float
convert: % -> InputForm if SparseUnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo InputForm and Coef has Field
from ConvertibleTo InputForm
convert: % -> Pattern Float if SparseUnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Float and Coef has Field
from ConvertibleTo Pattern Float
convert: % -> Pattern Integer if SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing
D: (%, List Symbol) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
D: (%, List Symbol, List NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
D: (%, NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing
D: (%, SparseUnivariateTaylorSeries(Coef, var, cen) -> SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from DifferentialExtension SparseUnivariateTaylorSeries(Coef, var, cen)
D: (%, SparseUnivariateTaylorSeries(Coef, var, cen) -> SparseUnivariateTaylorSeries(Coef, var, cen), NonNegativeInteger) -> % if Coef has Field
from DifferentialExtension SparseUnivariateTaylorSeries(Coef, var, cen)
D: (%, Symbol) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
D: (%, Symbol, NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
degree: % -> Integer
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
denom: % -> SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
denominator: % -> % if Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
differentiate: % -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing
differentiate: (%, List Symbol) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
differentiate: (%, List Symbol, List NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
differentiate: (%, NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field or Coef has *: (Integer, Coef) -> Coef
from DifferentialRing
differentiate: (%, SparseUnivariateTaylorSeries(Coef, var, cen) -> SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if Coef has Field
from DifferentialExtension SparseUnivariateTaylorSeries(Coef, var, cen)
differentiate: (%, SparseUnivariateTaylorSeries(Coef, var, cen) -> SparseUnivariateTaylorSeries(Coef, var, cen), NonNegativeInteger) -> % if Coef has Field
from DifferentialExtension SparseUnivariateTaylorSeries(Coef, var, cen)
differentiate: (%, Symbol) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
differentiate: (%, Symbol, NonNegativeInteger) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has PartialDifferentialRing Symbol and Coef has Field or Coef has PartialDifferentialRing Symbol and Coef has *: (Integer, Coef) -> Coef
from PartialDifferentialRing Symbol
differentiate: (%, Variable var) -> %
differentiate(f(x), x) returns the derivative of f(x) with respect to x.
divide: (%, %) -> Record(quotient: %, remainder: %) if Coef has Field
from EuclideanDomain
elt: (%, %) -> %
from Eltable(%, %)
elt: (%, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
elt: (%, SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has Eltable(SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen)) and Coef has Field
from Eltable(SparseUnivariateTaylorSeries(Coef, var, cen), %)
euclideanSize: % -> NonNegativeInteger if Coef has Field
from EuclideanDomain
eval: (%, Coef) -> Stream Coef if Coef has ^: (Coef, Integer) -> Coef
from UnivariatePowerSeriesCategory(Coef, Integer)
eval: (%, Equation SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has Evalable SparseUnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from Evalable SparseUnivariateTaylorSeries(Coef, var, cen)
eval: (%, List Equation SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has Evalable SparseUnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from Evalable SparseUnivariateTaylorSeries(Coef, var, cen)
eval: (%, List SparseUnivariateTaylorSeries(Coef, var, cen), List SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has Evalable SparseUnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from InnerEvalable(SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen))
eval: (%, List Symbol, List SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has InnerEvalable(Symbol, SparseUnivariateTaylorSeries(Coef, var, cen)) and Coef has Field
from InnerEvalable(Symbol, SparseUnivariateTaylorSeries(Coef, var, cen))
eval: (%, SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has Evalable SparseUnivariateTaylorSeries(Coef, var, cen) and Coef has Field
from InnerEvalable(SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen))
eval: (%, Symbol, SparseUnivariateTaylorSeries(Coef, var, cen)) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has InnerEvalable(Symbol, SparseUnivariateTaylorSeries(Coef, var, cen)) and Coef has Field
from InnerEvalable(Symbol, SparseUnivariateTaylorSeries(Coef, var, cen))
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 SparseUnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
factorSquareFreePolynomial: SparseUnivariatePolynomial % -> Factored SparseUnivariatePolynomial % if SparseUnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field
from PolynomialFactorizationExplicit
floor: % -> SparseUnivariateTaylorSeries(Coef, var, cen) if SparseUnivariateTaylorSeries(Coef, var, cen) has IntegerNumberSystem and Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
fractionPart: % -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has EuclideanDomain and Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
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 SparseUnivariateTaylorSeries(Coef, var, cen) has StepThrough and Coef has Field
from StepThrough
integrate: % -> % if Coef has Algebra Fraction Integer
from UnivariateLaurentSeriesCategory Coef
integrate: (%, Symbol) -> % if Coef has AlgebraicallyClosedFunctionSpace Integer and Coef has Algebra Fraction Integer and Coef has TranscendentalFunctionCategory and Coef has PrimitiveFunctionCategory or Coef has Algebra Fraction Integer and Coef has integrate: (Coef, Symbol) -> Coef and Coef has variables: Coef -> List Symbol
from UnivariateLaurentSeriesCategory Coef
integrate: (%, Variable var) -> % if Coef has Algebra Fraction Integer
integrate(f(x)) returns an anti-derivative of the power series f(x) with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.
inv: % -> % if Coef has Field
from DivisionRing
latex: % -> String
from SetCategory
laurent: (Integer, SparseUnivariateTaylorSeries(Coef, var, cen)) -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
laurent: (Integer, Stream Coef) -> %
from UnivariateLaurentSeriesCategory Coef
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: (SparseUnivariateTaylorSeries(Coef, var, cen) -> SparseUnivariateTaylorSeries(Coef, var, cen), %) -> % if Coef has Field
from FullyEvalableOver SparseUnivariateTaylorSeries(Coef, var, cen)
max: (%, %) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field
from OrderedSet
min: (%, %) -> % if SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field
from OrderedRing
nextItem: % -> Union(%, failed) if SparseUnivariateTaylorSeries(Coef, var, cen) has StepThrough and Coef has Field
from StepThrough
nthRoot: (%, Integer) -> % if Coef has Algebra Fraction Integer
from RadicalCategory
numer: % -> SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
numerator: % -> % if Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
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 SparseUnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Float and Coef has Field
from PatternMatchable Float
patternMatch: (%, Pattern Integer, PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) has LinearlyExplicitOver Integer and Coef has Field
from LinearlyExplicitOver Integer
reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix SparseUnivariateTaylorSeries(Coef, var, cen), vec: Vector SparseUnivariateTaylorSeries(Coef, var, cen)) if Coef has Field
from LinearlyExplicitOver SparseUnivariateTaylorSeries(Coef, var, cen)
reducedSystem: Matrix % -> Matrix Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has LinearlyExplicitOver Integer and Coef has Field
from LinearlyExplicitOver Integer
reducedSystem: Matrix % -> Matrix SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field
from LinearlyExplicitOver SparseUnivariateTaylorSeries(Coef, var, cen)
reductum: % -> %
from AbelianMonoidRing(Coef, Integer)
rem: (%, %) -> % if Coef has Field
from EuclideanDomain
removeZeroes: % -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
removeZeroes: (Integer, %) -> %
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
retract: % -> Fraction Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Fraction Integer
retract: % -> Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Integer
retract: % -> SparseUnivariateTaylorSeries(Coef, var, cen)
from RetractableTo SparseUnivariateTaylorSeries(Coef, var, cen)
retract: % -> Symbol if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol
retractIfCan: % -> Union(Fraction Integer, failed) if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Fraction Integer
retractIfCan: % -> Union(Integer, failed) if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field
from RetractableTo Integer
retractIfCan: % -> Union(SparseUnivariateTaylorSeries(Coef, var, cen), failed)
from RetractableTo SparseUnivariateTaylorSeries(Coef, var, cen)
retractIfCan: % -> Union(Symbol, failed) if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field
from RetractableTo Symbol
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 SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) has Comparable and Coef has Field
from Comparable
solveLinearPolynomialEquation: (List SparseUnivariatePolynomial %, SparseUnivariatePolynomial %) -> Union(List SparseUnivariatePolynomial %, failed) if SparseUnivariateTaylorSeries(Coef, var, cen) 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 SparseUnivariateTaylorSeries(Coef, var, cen) 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: % -> SparseUnivariateTaylorSeries(Coef, var, cen)
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
taylorIfCan: % -> Union(SparseUnivariateTaylorSeries(Coef, var, cen), failed)
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
taylorRep: % -> SparseUnivariateTaylorSeries(Coef, var, cen)
from UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))
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: % -> SparseUnivariateTaylorSeries(Coef, var, cen) if SparseUnivariateTaylorSeries(Coef, var, cen) has EuclideanDomain and Coef has Field
from QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen)
zero?: % -> Boolean
from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianMonoidRing(Coef, Integer)

AbelianSemiGroup

Algebra % if Coef has IntegralDomain

Algebra Coef if Coef has CommutativeRing

Algebra Fraction Integer if Coef has Algebra Fraction Integer

Algebra SparseUnivariateTaylorSeries(Coef, var, cen) 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(SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen)) if Coef has Field

CancellationAbelianMonoid

canonicalsClosed if Coef has Field

canonicalUnitNormal if Coef has Field

CharacteristicNonZero if SparseUnivariateTaylorSeries(Coef, var, cen) has CharacteristicNonZero and Coef has Field or Coef has CharacteristicNonZero

CharacteristicZero if SparseUnivariateTaylorSeries(Coef, var, cen) has CharacteristicZero and Coef has Field or Coef has CharacteristicZero

CoercibleTo OutputForm

CommutativeRing if Coef has CommutativeRing

CommutativeStar if Coef has CommutativeRing

Comparable if SparseUnivariateTaylorSeries(Coef, var, cen) has Comparable and Coef has Field

ConvertibleTo DoubleFloat if SparseUnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field

ConvertibleTo Float if SparseUnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field

ConvertibleTo InputForm if SparseUnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo InputForm and Coef has Field

ConvertibleTo Pattern Float if SparseUnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Float and Coef has Field

ConvertibleTo Pattern Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has ConvertibleTo Pattern Integer and Coef has Field

DifferentialExtension SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

DifferentialRing if SparseUnivariateTaylorSeries(Coef, var, cen) has DifferentialRing and Coef has Field or Coef has *: (Integer, Coef) -> Coef

DivisionRing if Coef has Field

ElementaryFunctionCategory if Coef has Algebra Fraction Integer

Eltable(%, %)

Eltable(SparseUnivariateTaylorSeries(Coef, var, cen), %) if SparseUnivariateTaylorSeries(Coef, var, cen) has Eltable(SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen)) and Coef has Field

EntireRing if Coef has IntegralDomain

EuclideanDomain if Coef has Field

Evalable SparseUnivariateTaylorSeries(Coef, var, cen) if SparseUnivariateTaylorSeries(Coef, var, cen) has Evalable SparseUnivariateTaylorSeries(Coef, var, cen) and Coef has Field

Field if Coef has Field

FullyEvalableOver SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

FullyLinearlyExplicitOver SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

FullyPatternMatchable SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

GcdDomain if Coef has Field

HyperbolicFunctionCategory if Coef has Algebra Fraction Integer

InnerEvalable(SparseUnivariateTaylorSeries(Coef, var, cen), SparseUnivariateTaylorSeries(Coef, var, cen)) if SparseUnivariateTaylorSeries(Coef, var, cen) has Evalable SparseUnivariateTaylorSeries(Coef, var, cen) and Coef has Field

InnerEvalable(Symbol, SparseUnivariateTaylorSeries(Coef, var, cen)) if SparseUnivariateTaylorSeries(Coef, var, cen) has InnerEvalable(Symbol, SparseUnivariateTaylorSeries(Coef, var, cen)) and Coef has Field

IntegralDomain if Coef has IntegralDomain

LeftModule %

LeftModule Coef

LeftModule Fraction Integer if Coef has Algebra Fraction Integer

LeftModule SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

LeftOreRing if Coef has Field

LinearlyExplicitOver Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has LinearlyExplicitOver Integer and Coef has Field

LinearlyExplicitOver SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

Magma

MagmaWithUnit

Module % if Coef has IntegralDomain

Module Coef if Coef has CommutativeRing

Module Fraction Integer if Coef has Algebra Fraction Integer

Module SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

Monoid

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

noZeroDivisors if Coef has IntegralDomain

OrderedAbelianGroup if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedAbelianMonoid if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedAbelianSemiGroup if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedCancellationAbelianMonoid if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedIntegralDomain if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedRing if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedIntegralDomain and Coef has Field

OrderedSet if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field

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

PartialOrder if SparseUnivariateTaylorSeries(Coef, var, cen) has OrderedSet and Coef has Field

Patternable SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

PatternMatchable Float if SparseUnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Float and Coef has Field

PatternMatchable Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has PatternMatchable Integer and Coef has Field

PolynomialFactorizationExplicit if SparseUnivariateTaylorSeries(Coef, var, cen) has PolynomialFactorizationExplicit and Coef has Field

PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)

PrincipalIdealDomain if Coef has Field

QuotientFieldCategory SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

RadicalCategory if Coef has Algebra Fraction Integer

RealConstant if SparseUnivariateTaylorSeries(Coef, var, cen) has RealConstant and Coef has Field

RetractableTo Fraction Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field

RetractableTo Integer if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Integer and Coef has Field

RetractableTo SparseUnivariateTaylorSeries(Coef, var, cen)

RetractableTo Symbol if SparseUnivariateTaylorSeries(Coef, var, cen) has RetractableTo Symbol and Coef has Field

RightModule %

RightModule Coef

RightModule Fraction Integer if Coef has Algebra Fraction Integer

RightModule SparseUnivariateTaylorSeries(Coef, var, cen) if Coef has Field

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

StepThrough if SparseUnivariateTaylorSeries(Coef, var, cen) 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

UnivariateLaurentSeriesConstructorCategory(Coef, SparseUnivariateTaylorSeries(Coef, var, cen))

UnivariatePowerSeriesCategory(Coef, Integer)

VariablesCommuteWithCoefficients