Complex(R)

gaussian.spad line 543 [edit on github]

Complex(R) creates the domain of elements of the form a + b * i where a and b come from the ring R, and i is a new element such that i^2 = -1.

* : (%, %) -> %
from Magma
* : (%, R) -> %
from RightModule(R)
* : (%, Fraction(Integer)) -> % if R has Field
from RightModule(Fraction(Integer))
* : (%, Integer) -> % if R has LinearlyExplicitOver(Integer)
from RightModule(Integer)
* : (R, %) -> %
from LeftModule(R)
* : (Fraction(Integer), %) -> % if R has Field
from LeftModule(Fraction(Integer))
* : (Integer, %) -> %
from AbelianGroup
* : (NonNegativeInteger, %) -> %
from AbelianMonoid
* : (PositiveInteger, %) -> %
from AbelianSemiGroup
+ : (%, %) -> %
from AbelianSemiGroup
- : % -> %
from AbelianGroup
- : (%, %) -> %
from AbelianGroup
/ : (%, %) -> % if R has Field
from Field
0 : () -> %
from AbelianMonoid
1 : () -> %
from MagmaWithUnit
= : (%, %) -> Boolean
from BasicType
D : % -> % if R has DifferentialRing
from DifferentialRing
D : (%, List(Symbol)) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
D : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
D : (%, Mapping(R, R)) -> %
from DifferentialExtension(R)
D : (%, Mapping(R, R), NonNegativeInteger) -> %
from DifferentialExtension(R)
D : (%, NonNegativeInteger) -> % if R has DifferentialRing
from DifferentialRing
D : (%, Symbol) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
D : (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
OMwrite : % -> String if R has OpenMath
from OpenMath
OMwrite : (%, Boolean) -> String if R has OpenMath
from OpenMath
OMwrite : (OpenMathDevice, %) -> Void if R has OpenMath
from OpenMath
OMwrite : (OpenMathDevice, %, Boolean) -> Void if R has OpenMath
from OpenMath
^ : (%, %) -> % if R has TranscendentalFunctionCategory
from ElementaryFunctionCategory
^ : (%, Fraction(Integer)) -> % if R has RadicalCategory and R has TranscendentalFunctionCategory
from RadicalCategory
^ : (%, Integer) -> % if R has Field
from DivisionRing
^ : (%, NonNegativeInteger) -> %
from MagmaWithUnit
^ : (%, PositiveInteger) -> %
from Magma
abs : % -> % if R has RealNumberSystem
from ComplexCategory(R)
acos : % -> % if R has TranscendentalFunctionCategory
from ArcTrigonometricFunctionCategory
acosh : % -> % if R has TranscendentalFunctionCategory
from ArcHyperbolicFunctionCategory
acot : % -> % if R has TranscendentalFunctionCategory
from ArcTrigonometricFunctionCategory
acoth : % -> % if R has TranscendentalFunctionCategory
from ArcHyperbolicFunctionCategory
acsc : % -> % if R has TranscendentalFunctionCategory
from ArcTrigonometricFunctionCategory
acsch : % -> % if R has TranscendentalFunctionCategory
from ArcHyperbolicFunctionCategory
annihilate? : (%, %) -> Boolean
from Rng
antiCommutator : (%, %) -> %
from NonAssociativeSemiRng
argument : % -> R if R has TranscendentalFunctionCategory
from ComplexCategory(R)
asec : % -> % if R has TranscendentalFunctionCategory
from ArcTrigonometricFunctionCategory
asech : % -> % if R has TranscendentalFunctionCategory
from ArcHyperbolicFunctionCategory
asin : % -> % if R has TranscendentalFunctionCategory
from ArcTrigonometricFunctionCategory
asinh : % -> % if R has TranscendentalFunctionCategory
from ArcHyperbolicFunctionCategory
associates? : (%, %) -> Boolean if R has IntegralDomain
from EntireRing
associator : (%, %, %) -> %
from NonAssociativeRng
atan : % -> % if R has TranscendentalFunctionCategory
from ArcTrigonometricFunctionCategory
atanh : % -> % if R has TranscendentalFunctionCategory
from ArcHyperbolicFunctionCategory
basis : () -> Vector(%)
from FramedModule(R)
characteristic : () -> NonNegativeInteger
from NonAssociativeRing
characteristicPolynomial : % -> SparseUnivariatePolynomial(R)
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
charthRoot : % -> % if R has FiniteFieldCategory
from FiniteFieldCategory
charthRoot : % -> Union(%, "failed") if % has CharacteristicNonZero and R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has CharacteristicNonZero
from CharacteristicNonZero
coerce : % -> %
from Algebra(%)
coerce : R -> %
from CoercibleFrom(R)
coerce : Fraction(Integer) -> % if R has Field or R has RetractableTo(Fraction(Integer))
from Algebra(Fraction(Integer))
coerce : Integer -> %
from NonAssociativeRing
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
commutator : (%, %) -> %
from NonAssociativeRng
complex : (R, R) -> %
from ComplexCategory(R)
conditionP : Matrix(%) -> Union(Vector(%), "failed") if % has CharacteristicNonZero and R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has FiniteFieldCategory
from PolynomialFactorizationExplicit
conjugate : % -> %
from ComplexCategory(R)
convert : SparseUnivariatePolynomial(R) -> %
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
convert : Vector(R) -> %
from FramedModule(R)
convert : % -> Complex(DoubleFloat) if R has RealConstant
from ConvertibleTo(Complex(DoubleFloat))
convert : % -> Complex(Float) if R has RealConstant
from ConvertibleTo(Complex(Float))
convert : % -> InputForm if R has ConvertibleTo(InputForm)
from ConvertibleTo(InputForm)
convert : % -> Pattern(Float) if R has ConvertibleTo(Pattern(Float))
from ConvertibleTo(Pattern(Float))
convert : % -> Pattern(Integer) if R has ConvertibleTo(Pattern(Integer))
from ConvertibleTo(Pattern(Integer))
convert : % -> SparseUnivariatePolynomial(R)
from ConvertibleTo(SparseUnivariatePolynomial(R))
convert : % -> Vector(R)
from FramedModule(R)
coordinates : Vector(%) -> Matrix(R)
from FramedModule(R)
coordinates : (Vector(%), Vector(%)) -> Matrix(R)
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
coordinates : % -> Vector(R)
from FramedModule(R)
coordinates : (%, Vector(%)) -> Vector(R)
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
cos : % -> % if R has TranscendentalFunctionCategory
from TrigonometricFunctionCategory
cosh : % -> % if R has TranscendentalFunctionCategory
from HyperbolicFunctionCategory
cot : % -> % if R has TranscendentalFunctionCategory
from TrigonometricFunctionCategory
coth : % -> % if R has TranscendentalFunctionCategory
from HyperbolicFunctionCategory
createPrimitiveElement : () -> % if R has FiniteFieldCategory
from FiniteFieldCategory
csc : % -> % if R has TranscendentalFunctionCategory
from TrigonometricFunctionCategory
csch : % -> % if R has TranscendentalFunctionCategory
from HyperbolicFunctionCategory
definingPolynomial : () -> SparseUnivariatePolynomial(R)
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
derivationCoordinates : (Vector(%), Mapping(R, R)) -> Matrix(R) if R has Field
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
differentiate : % -> % if R has DifferentialRing
from DifferentialRing
differentiate : (%, List(Symbol)) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
differentiate : (%, List(Symbol), List(NonNegativeInteger)) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
differentiate : (%, Mapping(R, R)) -> %
from DifferentialExtension(R)
differentiate : (%, Mapping(R, R), NonNegativeInteger) -> %
from DifferentialExtension(R)
differentiate : (%, NonNegativeInteger) -> % if R has DifferentialRing
from DifferentialRing
differentiate : (%, Symbol) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
differentiate : (%, Symbol, NonNegativeInteger) -> % if R has PartialDifferentialRing(Symbol)
from PartialDifferentialRing(Symbol)
discreteLog : % -> NonNegativeInteger if R has FiniteFieldCategory
from FiniteFieldCategory
discreteLog : (%, %) -> Union(NonNegativeInteger, "failed") if R has FiniteFieldCategory
from FieldOfPrimeCharacteristic
discriminant : () -> R
from FramedAlgebra(R, SparseUnivariatePolynomial(R))
discriminant : Vector(%) -> R
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
divide : (%, %) -> Record(quotient : %, remainder : %) if R has Field or R has IntegerNumberSystem
from EuclideanDomain
elt : (%, R) -> % if R has Eltable(R, R)
from Eltable(R, %)
enumerate : () -> List(%) if R has Finite
from Finite
euclideanSize : % -> NonNegativeInteger if R has Field or R has IntegerNumberSystem
from EuclideanDomain
eval : (%, R, R) -> % if R has Evalable(R)
from InnerEvalable(R, R)
eval : (%, Equation(R)) -> % if R has Evalable(R)
from Evalable(R)
eval : (%, List(R), List(R)) -> % if R has Evalable(R)
from InnerEvalable(R, R)
eval : (%, List(Equation(R))) -> % if R has Evalable(R)
from Evalable(R)
eval : (%, List(Symbol), List(R)) -> % if R has InnerEvalable(Symbol, R)
from InnerEvalable(Symbol, R)
eval : (%, Symbol, R) -> % if R has InnerEvalable(Symbol, R)
from InnerEvalable(Symbol, R)
exp : % -> % if R has TranscendentalFunctionCategory
from ElementaryFunctionCategory
expressIdealMember : (List(%), %) -> Union(List(%), "failed") if R has Field or R has IntegerNumberSystem
from PrincipalIdealDomain
exquo : (%, %) -> Union(%, "failed") if R has IntegralDomain
from EntireRing
exquo : (%, R) -> Union(%, "failed") if R has IntegralDomain
from ComplexCategory(R)
extendedEuclidean : (%, %) -> Record(coef1 : %, coef2 : %, generator : %) if R has Field or R has IntegerNumberSystem
from EuclideanDomain
extendedEuclidean : (%, %, %) -> Union(Record(coef1 : %, coef2 : %), "failed") if R has Field or R has IntegerNumberSystem
from EuclideanDomain
factor : % -> Factored(%) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has Field or R has IntegerNumberSystem
from UniqueFactorizationDomain
factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has FiniteFieldCategory
from PolynomialFactorizationExplicit
factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has FiniteFieldCategory
from PolynomialFactorizationExplicit
factorsOfCyclicGroupSize : () -> List(Record(factor : Integer, exponent : NonNegativeInteger)) if R has FiniteFieldCategory
from FiniteFieldCategory
gcd : (%, %) -> % if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has IntegerNumberSystem or R has Field
from GcdDomain
gcd : List(%) -> % if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has IntegerNumberSystem or R has Field
from GcdDomain
gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has IntegerNumberSystem or R has Field
from PolynomialFactorizationExplicit
generator : () -> %
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
hash : % -> SingleInteger if R has Hashable
from Hashable
hashUpdate! : (HashState, %) -> HashState if R has Hashable
from Hashable
imag : % -> R
from ComplexCategory(R)
imaginary : () -> %
from ComplexCategory(R)
index : PositiveInteger -> % if R has Finite
from Finite
init : () -> % if R has FiniteFieldCategory
from StepThrough
inv : % -> % if R has Field
from DivisionRing
latex : % -> String
from SetCategory
lcm : (%, %) -> % if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has IntegerNumberSystem or R has Field
from GcdDomain
lcm : List(%) -> % if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has IntegerNumberSystem or R has Field
from GcdDomain
lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has IntegerNumberSystem or R has Field
from LeftOreRing
leftPower : (%, NonNegativeInteger) -> %
from MagmaWithUnit
leftPower : (%, PositiveInteger) -> %
from Magma
leftRecip : % -> Union(%, "failed")
from MagmaWithUnit
lift : % -> SparseUnivariatePolynomial(R)
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
log : % -> % if R has TranscendentalFunctionCategory
from ElementaryFunctionCategory
lookup : % -> PositiveInteger if R has Finite
from Finite
map : (Mapping(R, R), %) -> %
from FullyEvalableOver(R)
minimalPolynomial : % -> SparseUnivariatePolynomial(R) if R has Field
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
multiEuclidean : (List(%), %) -> Union(List(%), "failed") if R has Field or R has IntegerNumberSystem
from EuclideanDomain
nextItem : % -> Union(%, "failed") if R has FiniteFieldCategory
from StepThrough
norm : % -> R
from ComplexCategory(R)
nthRoot : (%, Integer) -> % if R has RadicalCategory and R has TranscendentalFunctionCategory
from RadicalCategory
one? : % -> Boolean
from MagmaWithUnit
opposite? : (%, %) -> Boolean
from AbelianMonoid
order : % -> OnePointCompletion(PositiveInteger) if R has FiniteFieldCategory
from FieldOfPrimeCharacteristic
order : % -> PositiveInteger if R has FiniteFieldCategory
from FiniteFieldCategory
patternMatch : (%, Pattern(Float), PatternMatchResult(Float, %)) -> PatternMatchResult(Float, %) if R has PatternMatchable(Float)
from PatternMatchable(Float)
patternMatch : (%, Pattern(Integer), PatternMatchResult(Integer, %)) -> PatternMatchResult(Integer, %) if R has PatternMatchable(Integer)
from PatternMatchable(Integer)
pi : () -> % if R has TranscendentalFunctionCategory
from TranscendentalFunctionCategory
plenaryPower : (%, PositiveInteger) -> %
from NonAssociativeAlgebra(%)
polarCoordinates : % -> Record(r : R, phi : R) if R has RealNumberSystem and R has TranscendentalFunctionCategory
from ComplexCategory(R)
prime? : % -> Boolean if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has Field or R has IntegerNumberSystem
from UniqueFactorizationDomain
primeFrobenius : % -> % if R has FiniteFieldCategory
from FieldOfPrimeCharacteristic
primeFrobenius : (%, NonNegativeInteger) -> % if R has FiniteFieldCategory
from FieldOfPrimeCharacteristic
primitive? : % -> Boolean if R has FiniteFieldCategory
from FiniteFieldCategory
primitiveElement : () -> % if R has FiniteFieldCategory
from FiniteFieldCategory
principalIdeal : List(%) -> Record(coef : List(%), generator : %) if R has Field or R has IntegerNumberSystem
from PrincipalIdealDomain
quo : (%, %) -> % if R has Field or R has IntegerNumberSystem
from EuclideanDomain
random : () -> % if R has Finite
from Finite
rank : () -> PositiveInteger
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
rational : % -> Fraction(Integer) if R has IntegerNumberSystem
from ComplexCategory(R)
rational? : % -> Boolean if R has IntegerNumberSystem
from ComplexCategory(R)
rationalIfCan : % -> Union(Fraction(Integer), "failed") if R has IntegerNumberSystem
from ComplexCategory(R)
real : % -> R
from ComplexCategory(R)
recip : % -> Union(%, "failed")
from MagmaWithUnit
reduce : SparseUnivariatePolynomial(R) -> %
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
reduce : Fraction(SparseUnivariatePolynomial(R)) -> Union(%, "failed") if R has Field
from MonogenicAlgebra(R, SparseUnivariatePolynomial(R))
reducedSystem : Matrix(%) -> Matrix(R)
from LinearlyExplicitOver(R)
reducedSystem : Matrix(%) -> Matrix(Integer) if R has LinearlyExplicitOver(Integer)
from LinearlyExplicitOver(Integer)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(R), vec : Vector(R))
from LinearlyExplicitOver(R)
reducedSystem : (Matrix(%), Vector(%)) -> Record(mat : Matrix(Integer), vec : Vector(Integer)) if R has LinearlyExplicitOver(Integer)
from LinearlyExplicitOver(Integer)
regularRepresentation : % -> Matrix(R)
from FramedAlgebra(R, SparseUnivariatePolynomial(R))
regularRepresentation : (%, Vector(%)) -> Matrix(R)
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
rem : (%, %) -> % if R has Field or R has IntegerNumberSystem
from EuclideanDomain
representationType : () -> Union("prime", "polynomial", "normal", "cyclic") if R has FiniteFieldCategory
from FiniteFieldCategory
represents : Vector(R) -> %
from FramedModule(R)
represents : (Vector(R), Vector(%)) -> %
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
retract : % -> R
from RetractableTo(R)
retract : % -> Fraction(Integer) if R has RetractableTo(Fraction(Integer))
from RetractableTo(Fraction(Integer))
retract : % -> Integer if R has RetractableTo(Integer)
from RetractableTo(Integer)
retractIfCan : % -> Union(R, "failed")
from RetractableTo(R)
retractIfCan : % -> Union(Fraction(Integer), "failed") if R has RetractableTo(Fraction(Integer))
from RetractableTo(Fraction(Integer))
retractIfCan : % -> Union(Integer, "failed") if R has RetractableTo(Integer)
from RetractableTo(Integer)
rightPower : (%, NonNegativeInteger) -> %
from MagmaWithUnit
rightPower : (%, PositiveInteger) -> %
from Magma
rightRecip : % -> Union(%, "failed")
from MagmaWithUnit
sample : () -> %
from AbelianMonoid
sec : % -> % if R has TranscendentalFunctionCategory
from TrigonometricFunctionCategory
sech : % -> % if R has TranscendentalFunctionCategory
from HyperbolicFunctionCategory
sin : % -> % if R has TranscendentalFunctionCategory
from TrigonometricFunctionCategory
sinh : % -> % if R has TranscendentalFunctionCategory
from HyperbolicFunctionCategory
size : () -> NonNegativeInteger if R has Finite
from Finite
sizeLess? : (%, %) -> Boolean if R has Field or R has IntegerNumberSystem
from EuclideanDomain
smaller? : (%, %) -> Boolean if R has Comparable
from Comparable
solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)), SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)), "failed") if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has FiniteFieldCategory
from PolynomialFactorizationExplicit
sqrt : % -> % if R has RadicalCategory and R has TranscendentalFunctionCategory
from RadicalCategory
squareFree : % -> Factored(%) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has Field or R has IntegerNumberSystem
from UniqueFactorizationDomain
squareFreePart : % -> % if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has Field or R has IntegerNumberSystem
from UniqueFactorizationDomain
squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has EuclideanDomain and R has PolynomialFactorizationExplicit or R has FiniteFieldCategory
from PolynomialFactorizationExplicit
subtractIfCan : (%, %) -> Union(%, "failed")
from CancellationAbelianMonoid
tableForDiscreteLogarithm : Integer -> Table(PositiveInteger, NonNegativeInteger) if R has FiniteFieldCategory
from FiniteFieldCategory
tan : % -> % if R has TranscendentalFunctionCategory
from TrigonometricFunctionCategory
tanh : % -> % if R has TranscendentalFunctionCategory
from HyperbolicFunctionCategory
trace : % -> R
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
traceMatrix : () -> Matrix(R)
from FramedAlgebra(R, SparseUnivariatePolynomial(R))
traceMatrix : Vector(%) -> Matrix(R)
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
unit? : % -> Boolean if R has IntegralDomain
from EntireRing
unitCanonical : % -> % if R has IntegralDomain
from EntireRing
unitNormal : % -> Record(unit : %, canonical : %, associate : %) if R has IntegralDomain
from EntireRing
zero? : % -> Boolean
from AbelianMonoid
~= : (%, %) -> Boolean
from BasicType

ConvertibleTo(Complex(Float))

Eltable(R, %)

PrincipalIdealDomain

NonAssociativeSemiRing

LeftModule(R)

LinearlyExplicitOver(R)

Evalable(R)

ConvertibleTo(InputForm)

Field

canonicalUnitNormal

Rng

BiModule(R, R)

ArcTrigonometricFunctionCategory

Ring

CoercibleFrom(Integer)

TwoSidedRecip

FullyRetractableTo(R)

TranscendentalFunctionCategory

SemiRing

EntireRing

NonAssociativeAlgebra(Fraction(Integer))

CharacteristicNonZero

RetractableTo(R)

AbelianSemiGroup

unitsKnown

FullyLinearlyExplicitOver(R)

Algebra(R)

PatternMatchable(Float)

MagmaWithUnit

FramedModule(R)

noZeroDivisors

RetractableTo(Fraction(Integer))

CoercibleFrom(R)

ConvertibleTo(SparseUnivariatePolynomial(R))

UniqueFactorizationDomain

SemiGroup

RightModule(Fraction(Integer))

Magma

RightModule(R)

GcdDomain

LeftModule(%)

NonAssociativeRing

multiplicativeValuation

ArcHyperbolicFunctionCategory

NonAssociativeAlgebra(%)

PartialDifferentialRing(Symbol)

CharacteristicZero

ComplexCategory(R)

Module(R)

BiModule(%, %)

CommutativeRing

Algebra(%)

FullyEvalableOver(R)

DifferentialRing

PolynomialFactorizationExplicit

RadicalCategory

DivisionRing

IntegralDomain

arbitraryPrecision

NonAssociativeRng

OpenMath

ConvertibleTo(Pattern(Float))

InnerEvalable(R, R)

LeftOreRing

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

RetractableTo(Integer)

CommutativeStar

AbelianMonoid

InnerEvalable(Symbol, R)

Comparable

RightModule(%)

Hashable

SemiRng

Patternable(R)

FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))

Module(%)

LinearlyExplicitOver(Integer)

CoercibleTo(OutputForm)

Monoid

FiniteFieldCategory

NonAssociativeAlgebra(R)

HyperbolicFunctionCategory

Finite

Algebra(Fraction(Integer))

Module(Fraction(Integer))

MonogenicAlgebra(R, SparseUnivariatePolynomial(R))

BasicType

RightModule(Integer)

LeftModule(Fraction(Integer))

FramedAlgebra(R, SparseUnivariatePolynomial(R))

ConvertibleTo(Complex(DoubleFloat))

ConvertibleTo(Pattern(Integer))

TrigonometricFunctionCategory

CoercibleFrom(Fraction(Integer))

SetCategory

NonAssociativeSemiRng

FieldOfPrimeCharacteristic

BiModule(Fraction(Integer), Fraction(Integer))

FullyPatternMatchable(R)

PatternMatchable(Integer)

StepThrough

AbelianGroup

DifferentialExtension(R)

ElementaryFunctionCategory