UnivariateLaurentSeriesConstructor(Coef, UTS)
laurent.spad line 73
[edit on github]
This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are 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)
.
- * : (%, %) -> %
- from Magma
- * : (%, Coef) -> %
- from RightModule(Coef)
- * : (%, UTS) -> % if Coef has Field
- from RightModule(UTS)
- * : (%, Fraction(Integer)) -> % if Coef has Algebra(Fraction(Integer))
- from RightModule(Fraction(Integer))
- * : (%, Integer) -> % if UTS has LinearlyExplicitOver(Integer) and Coef has Field
- from RightModule(Integer)
- * : (Coef, %) -> %
- from LeftModule(Coef)
- * : (UTS, %) -> % if Coef has Field
- from LeftModule(UTS)
- * : (Fraction(Integer), %) -> % if Coef has Algebra(Fraction(Integer))
- from LeftModule(Fraction(Integer))
- * : (Integer, %) -> %
- from AbelianGroup
- * : (NonNegativeInteger, %) -> %
- from AbelianMonoid
- * : (PositiveInteger, %) -> %
- from AbelianSemiGroup
- + : (%, %) -> %
- 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)
- 0 : () -> %
- from AbelianMonoid
- 1 : () -> %
- from MagmaWithUnit
- < : (%, %) -> 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
- 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
- from PartialDifferentialRing(Symbol)
- D : (%, List(Symbol), List(NonNegativeInteger)) -> % if Coef has * : (Integer, Coef) -> Coef and Coef has PartialDifferentialRing(Symbol) or Coef has Field
- from PartialDifferentialRing(Symbol)
- D : (%, Mapping(UTS, UTS)) -> % if Coef has Field
- from DifferentialExtension(UTS)
- D : (%, Mapping(UTS, UTS), NonNegativeInteger) -> % if Coef has Field
- from DifferentialExtension(UTS)
- 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
- from PartialDifferentialRing(Symbol)
- D : (%, Symbol, NonNegativeInteger) -> % if Coef has * : (Integer, Coef) -> Coef and Coef has PartialDifferentialRing(Symbol) or Coef has Field
- from PartialDifferentialRing(Symbol)
- ^ : (%, %) -> % 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
- abs : % -> % if Coef has Field and UTS has OrderedIntegralDomain
- 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 CharacteristicNonZero
- coefficient : (%, Integer) -> Coef
- from AbelianMonoidRing(Coef, Integer)
- coerce : % -> % if Coef has CommutativeRing
- from Algebra(%)
- coerce : Coef -> % if Coef has CommutativeRing
- from Algebra(Coef)
- coerce : UTS -> %
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- coerce : Fraction(Integer) -> % if Coef has Algebra(Fraction(Integer))
- from Algebra(Fraction(Integer))
- coerce : Integer -> %
- from NonAssociativeRing
- coerce : Symbol -> % if UTS has RetractableTo(Symbol) and Coef has Field
- from CoercibleFrom(Symbol)
- coerce : % -> OutputForm
- from CoercibleTo(OutputForm)
- commutator : (%, %) -> %
- from NonAssociativeRng
- complete : % -> %
- from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
- conditionP : Matrix(%) -> Union(Vector(%), "failed") if % has CharacteristicNonZero and Coef has Field and UTS has PolynomialFactorizationExplicit
- from PolynomialFactorizationExplicit
- construct : List(Record(k : Integer, c : Coef)) -> %
- from IndexedProductCategory(Coef, Integer)
- constructOrdered : List(Record(k : Integer, c : Coef)) -> %
- from IndexedProductCategory(Coef, Integer)
- convert : % -> DoubleFloat if UTS has RealConstant and Coef has Field
- from ConvertibleTo(DoubleFloat)
- convert : % -> Float if UTS has RealConstant and Coef has Field
- from ConvertibleTo(Float)
- convert : % -> InputForm if Coef has Field and UTS has ConvertibleTo(InputForm)
- from ConvertibleTo(InputForm)
- convert : % -> Pattern(Float) if Coef has Field and UTS has ConvertibleTo(Pattern(Float))
- from ConvertibleTo(Pattern(Float))
- convert : % -> Pattern(Integer) if Coef has Field and UTS has ConvertibleTo(Pattern(Integer))
- from ConvertibleTo(Pattern(Integer))
- 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
- degree : % -> Integer
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- 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
- from PartialDifferentialRing(Symbol)
- differentiate : (%, List(Symbol), List(NonNegativeInteger)) -> % if Coef has * : (Integer, Coef) -> Coef and Coef has PartialDifferentialRing(Symbol) or Coef has Field
- from PartialDifferentialRing(Symbol)
- differentiate : (%, Mapping(UTS, UTS)) -> % if Coef has Field
- from DifferentialExtension(UTS)
- differentiate : (%, Mapping(UTS, UTS), NonNegativeInteger) -> % if Coef has Field
- from DifferentialExtension(UTS)
- 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
- from PartialDifferentialRing(Symbol)
- differentiate : (%, Symbol, NonNegativeInteger) -> % if Coef has * : (Integer, Coef) -> Coef and Coef has PartialDifferentialRing(Symbol) or Coef has Field
- from PartialDifferentialRing(Symbol)
- divide : (%, %) -> Record(quotient : %, remainder : %) if Coef has Field
- from EuclideanDomain
- elt : (%, %) -> %
- from Eltable(%, %)
- elt : (%, UTS) -> % if UTS has Eltable(UTS, UTS) and Coef has Field
- from Eltable(UTS, %)
- elt : (%, Integer) -> Coef
- from UnivariatePowerSeriesCategory(Coef, Integer)
- euclideanSize : % -> NonNegativeInteger if Coef has Field
- from EuclideanDomain
- eval : (%, UTS, UTS) -> % if UTS has Evalable(UTS) and Coef has Field
- from InnerEvalable(UTS, UTS)
- eval : (%, Equation(UTS)) -> % if UTS has Evalable(UTS) and Coef has Field
- from Evalable(UTS)
- eval : (%, List(UTS), List(UTS)) -> % if UTS has Evalable(UTS) and Coef has Field
- from InnerEvalable(UTS, 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 : (%, Symbol, UTS) -> % if UTS has InnerEvalable(Symbol, UTS) and Coef has Field
- from InnerEvalable(Symbol, UTS)
- eval : (%, Coef) -> Stream(Coef) if Coef has ^ : (Coef, Integer) -> Coef
- from UnivariatePowerSeriesCategory(Coef, Integer)
- 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 Coef has Field and UTS has PolynomialFactorizationExplicit
- from PolynomialFactorizationExplicit
- factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if Coef has Field and UTS has PolynomialFactorizationExplicit
- 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 GcdDomain
- init : () -> % if UTS has StepThrough and Coef has Field
- from StepThrough
- integrate : % -> % if Coef has Algebra(Fraction(Integer))
- from UnivariateSeriesWithRationalExponents(Coef, Integer)
- integrate : (%, Symbol) -> % if Coef has Algebra(Fraction(Integer)) and Coef has integrate : (Coef, Symbol) -> Coef and Coef has variables : Coef -> List(Symbol)
- from UnivariateSeriesWithRationalExponents(Coef, Integer)
- inv : % -> % if Coef has Field
- from DivisionRing
- latex : % -> String
- from SetCategory
- laurent : (Integer, UTS) -> %
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- 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)
- leadingSupport : % -> Integer
- from IndexedProductCategory(Coef, Integer)
- leadingTerm : % -> Record(k : Integer, c : Coef)
- from IndexedProductCategory(Coef, Integer)
- leftPower : (%, NonNegativeInteger) -> %
- from MagmaWithUnit
- leftPower : (%, PositiveInteger) -> %
- from Magma
- leftRecip : % -> Union(%, "failed")
- from MagmaWithUnit
- log : % -> % if Coef has Algebra(Fraction(Integer))
- from ElementaryFunctionCategory
- map : (Mapping(Coef, Coef), %) -> %
- from IndexedProductCategory(Coef, Integer)
- map : (Mapping(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 : (Coef, Integer) -> %
- from IndexedProductCategory(Coef, Integer)
- monomial? : % -> Boolean
- from IndexedProductCategory(Coef, Integer)
- multiEuclidean : (List(%), %) -> Union(List(%), "failed") if Coef has Field
- from EuclideanDomain
- multiplyCoefficients : (Mapping(Coef, Integer), %) -> %
- from UnivariateLaurentSeriesCategory(Coef)
- multiplyExponents : (%, PositiveInteger) -> %
- from UnivariatePowerSeriesCategory(Coef, Integer)
- negative? : % -> Boolean if Coef has Field and UTS has OrderedIntegralDomain
- from OrderedRing
- nextItem : % -> Union(%, "failed") if UTS has StepThrough and Coef has Field
- from StepThrough
- 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
- plenaryPower : (%, PositiveInteger) -> % if Coef has Algebra(Fraction(Integer)) or Coef has CommutativeRing
- from NonAssociativeAlgebra(Coef)
- pole? : % -> Boolean
- from PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
- positive? : % -> Boolean if Coef has Field and UTS has OrderedIntegralDomain
- 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(%) -> Matrix(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(%), Vector(%)) -> Record(mat : Matrix(UTS), vec : Vector(UTS)) if Coef has Field
- from LinearlyExplicitOver(UTS)
- reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(Integer), vec : Vector(Integer)) if UTS has LinearlyExplicitOver(Integer) and Coef has Field
- from LinearlyExplicitOver(Integer)
- reductum : % -> %
- from IndexedProductCategory(Coef, Integer)
- rem : (%, %) -> % if Coef has Field
- from EuclideanDomain
- removeZeroes : % -> %
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- removeZeroes : (Integer, %) -> %
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- retract : % -> UTS
- from RetractableTo(UTS)
- 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)
- retractIfCan : % -> Union(UTS, "failed")
- 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)
- 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 Coef has Field and UTS has OrderedIntegralDomain
- 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 Coef has Field and UTS has PolynomialFactorizationExplicit
- 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 Coef has Field and UTS has PolynomialFactorizationExplicit
- 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
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- taylorIfCan : % -> Union(UTS, "failed")
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- taylorRep : % -> UTS
- from UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
- 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
- ~= : (%, %) -> Boolean
- from BasicType
EntireRing
Ring
Algebra(%)
BiModule(UTS, UTS)
Eltable(%, %)
CancellationAbelianMonoid
CommutativeStar
FullyLinearlyExplicitOver(UTS)
InnerEvalable(Symbol, UTS)
ConvertibleTo(Pattern(Float))
Field
UnivariateSeriesWithRationalExponents(Coef, Integer)
InnerEvalable(UTS, UTS)
LinearlyExplicitOver(Integer)
QuotientFieldCategory(UTS)
SemiGroup
OrderedSet
UnivariateLaurentSeriesCategory(Coef)
ConvertibleTo(Float)
LeftModule(%)
VariablesCommuteWithCoefficients
ConvertibleTo(DoubleFloat)
ArcTrigonometricFunctionCategory
LeftModule(UTS)
PartialOrder
UnivariatePowerSeriesCategory(Coef, Integer)
NonAssociativeAlgebra(Coef)
Monoid
OrderedAbelianSemiGroup
BiModule(Fraction(Integer), Fraction(Integer))
TrigonometricFunctionCategory
Module(%)
Module(UTS)
TranscendentalFunctionCategory
LeftOreRing
NonAssociativeSemiRing
Eltable(UTS, %)
noZeroDivisors
ConvertibleTo(InputForm)
Rng
RightModule(UTS)
SemiRing
NonAssociativeAlgebra(%)
SetCategory
CharacteristicNonZero
IndexedProductCategory(Coef, Integer)
PolynomialFactorizationExplicit
TwoSidedRecip
CoercibleFrom(Fraction(Integer))
NonAssociativeRing
RealConstant
CoercibleFrom(Symbol)
Patternable(UTS)
NonAssociativeRng
Module(Coef)
Algebra(Coef)
Comparable
PrincipalIdealDomain
canonicalsClosed
DivisionRing
LinearlyExplicitOver(UTS)
BiModule(Coef, Coef)
ArcHyperbolicFunctionCategory
ElementaryFunctionCategory
RetractableTo(UTS)
unitsKnown
AbelianSemiGroup
RadicalCategory
canonicalUnitNormal
LeftModule(Fraction(Integer))
PatternMatchable(Float)
Evalable(UTS)
AbelianProductCategory(Coef)
IntegralDomain
RightModule(Integer)
NonAssociativeAlgebra(Fraction(Integer))
NonAssociativeSemiRng
NonAssociativeAlgebra(UTS)
GcdDomain
CharacteristicZero
PowerSeriesCategory(Coef, Integer, SingletonAsOrderedSet)
CommutativeRing
CoercibleFrom(UTS)
EuclideanDomain
HyperbolicFunctionCategory
AbelianGroup
OrderedRing
DifferentialRing
BasicType
DifferentialExtension(UTS)
MagmaWithUnit
LeftModule(Coef)
CoercibleFrom(Integer)
AbelianMonoid
PatternMatchable(Integer)
CoercibleTo(OutputForm)
FullyPatternMatchable(UTS)
BiModule(%, %)
RetractableTo(Fraction(Integer))
Algebra(Fraction(Integer))
StepThrough
OrderedCancellationAbelianMonoid
SemiRng
RetractableTo(Symbol)
RightModule(Coef)
RightModule(Fraction(Integer))
OrderedAbelianMonoid
PartialDifferentialRing(Symbol)
OrderedAbelianGroup
FullyEvalableOver(UTS)
Algebra(UTS)
UniqueFactorizationDomain
OrderedIntegralDomain
UnivariateLaurentSeriesConstructorCategory(Coef, UTS)
ConvertibleTo(Pattern(Integer))
Module(Fraction(Integer))
AbelianMonoidRing(Coef, Integer)
RightModule(%)
RetractableTo(Integer)
Magma