ComplexCategory(R)

gaussian.spad line 1 [edit on github]

This category represents the extension of a ring by a square root of -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)
^ : (%, %) -> % 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

abs(x) returns the absolute value of x = sqrt(norm(x)).

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

argument(x) returns the angle made by (1, 0) and x.

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 R has CharacteristicNonZero or % has CharacteristicNonZero and R has PolynomialFactorizationExplicit and R has EuclideanDomain
from CharacteristicNonZero
coerce : % -> %
from Algebra(%)
coerce : R -> %
from CoercibleFrom(R)
coerce : Fraction(Integer) -> % if R has RetractableTo(Fraction(Integer)) or R has Field
from Algebra(Fraction(Integer))
coerce : Integer -> %
from NonAssociativeRing
coerce : % -> OutputForm
from CoercibleTo(OutputForm)
commutator : (%, %) -> %
from NonAssociativeRng
complex : (R, R) -> %

complex(x, y) constructs x + %i*y.

conditionP : Matrix(%) -> Union(Vector(%), "failed") if R has FiniteFieldCategory or % has CharacteristicNonZero and R has PolynomialFactorizationExplicit and R has EuclideanDomain
from PolynomialFactorizationExplicit
conjugate : % -> %

conjugate(x + %i y) returns x - %i y.

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 IntegerNumberSystem or R has Field
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 IntegerNumberSystem or R has Field
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 IntegerNumberSystem or R has Field
from PrincipalIdealDomain
exquo : (%, %) -> Union(%, "failed") if R has IntegralDomain
from EntireRing
exquo : (%, R) -> Union(%, "failed") if R has IntegralDomain

exquo(x, r) returns the exact quotient of x by r, or "failed" if r does not divide x exactly.

extendedEuclidean : (%, %) -> Record(coef1 : %, coef2 : %, generator : %) if R has IntegerNumberSystem or R has Field
from EuclideanDomain
extendedEuclidean : (%, %, %) -> Union(Record(coef1 : %, coef2 : %), "failed") if R has IntegerNumberSystem or R has Field
from EuclideanDomain
factor : % -> Factored(%) if R has IntegerNumberSystem or R has Field or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from UniqueFactorizationDomain
factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has FiniteFieldCategory or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has FiniteFieldCategory or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
factorsOfCyclicGroupSize : () -> List(Record(factor : Integer, exponent : NonNegativeInteger)) if R has FiniteFieldCategory
from FiniteFieldCategory
gcd : (%, %) -> % if R has Field or R has IntegerNumberSystem or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from GcdDomain
gcd : List(%) -> % if R has Field or R has IntegerNumberSystem or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from GcdDomain
gcdPolynomial : (SparseUnivariatePolynomial(%), SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has Field or R has IntegerNumberSystem or R has EuclideanDomain and R has PolynomialFactorizationExplicit
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

imag(x) returns imaginary part of x.

imaginary : () -> %

imaginary() = sqrt(-1) = %i.

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 Field or R has IntegerNumberSystem or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from GcdDomain
lcm : List(%) -> % if R has Field or R has IntegerNumberSystem or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from GcdDomain
lcmCoef : (%, %) -> Record(llcm_res : %, coeff1 : %, coeff2 : %) if R has Field or R has IntegerNumberSystem or R has EuclideanDomain and R has PolynomialFactorizationExplicit
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 IntegerNumberSystem or R has Field
from EuclideanDomain
nextItem : % -> Union(%, "failed") if R has FiniteFieldCategory
from StepThrough
norm : % -> R

norm(x) returns x * conjugate(x)

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

polarCoordinates(x) returns (r, phi) such that x = r * exp(%i * phi).

prime? : % -> Boolean if R has IntegerNumberSystem or R has Field or R has EuclideanDomain and R has PolynomialFactorizationExplicit
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 IntegerNumberSystem or R has Field
from PrincipalIdealDomain
quo : (%, %) -> % if R has IntegerNumberSystem or R has Field
from EuclideanDomain
random : () -> % if R has Finite
from Finite
rank : () -> PositiveInteger
from FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))
rational : % -> Fraction(Integer) if R has IntegerNumberSystem

rational(x) returns x as a rational number. Error: if x is not a rational number.

rational? : % -> Boolean if R has IntegerNumberSystem

rational?(x) tests if x is a rational number.

rationalIfCan : % -> Union(Fraction(Integer), "failed") if R has IntegerNumberSystem

rationalIfCan(x) returns x as a rational number, or "failed" if x is not a rational number.

real : % -> R

real(x) returns real part of x.

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 IntegerNumberSystem or R has Field
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 IntegerNumberSystem or R has Field
from EuclideanDomain
smaller? : (%, %) -> Boolean if R has Comparable
from Comparable
solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)), SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)), "failed") if R has FiniteFieldCategory or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from PolynomialFactorizationExplicit
sqrt : % -> % if R has RadicalCategory and R has TranscendentalFunctionCategory
from RadicalCategory
squareFree : % -> Factored(%) if R has IntegerNumberSystem or R has Field or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from UniqueFactorizationDomain
squareFreePart : % -> % if R has IntegerNumberSystem or R has Field or R has EuclideanDomain and R has PolynomialFactorizationExplicit
from UniqueFactorizationDomain
squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has FiniteFieldCategory or R has EuclideanDomain and R has PolynomialFactorizationExplicit
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

Algebra(Fraction(Integer))

Module(Fraction(Integer))

PrincipalIdealDomain

NonAssociativeSemiRing

LeftModule(R)

Evalable(R)

ConvertibleTo(InputForm)

Field

canonicalUnitNormal

Rng

BiModule(R, R)

ArcTrigonometricFunctionCategory

CoercibleFrom(Integer)

TwoSidedRecip

FullyRetractableTo(R)

TranscendentalFunctionCategory

SemiRing

EntireRing

FiniteRankAlgebra(R, SparseUnivariatePolynomial(R))

NonAssociativeAlgebra(Fraction(Integer))

CharacteristicNonZero

Eltable(R, %)

FullyLinearlyExplicitOver(R)

Algebra(R)

PatternMatchable(Float)

LinearlyExplicitOver(Integer)

noZeroDivisors

RetractableTo(Fraction(Integer))

CoercibleFrom(R)

ConvertibleTo(SparseUnivariatePolynomial(R))

UniqueFactorizationDomain

SemiGroup

RightModule(Fraction(Integer))

RightModule(R)

GcdDomain

LeftModule(%)

NonAssociativeRing

ArcHyperbolicFunctionCategory

Magma

PartialDifferentialRing(Symbol)

CharacteristicZero

Module(R)

BiModule(%, %)

CoercibleFrom(Fraction(Integer))

Algebra(%)

unitsKnown

HyperbolicFunctionCategory

DifferentialRing

FieldOfPrimeCharacteristic

RadicalCategory

DivisionRing

arbitraryPrecision

CommutativeRing

InnerEvalable(R, R)

LeftOreRing

CancellationAbelianMonoid

EuclideanDomain

canonicalsClosed

Comparable

RetractableTo(Integer)

FramedAlgebra(R, SparseUnivariatePolynomial(R))

CommutativeStar

AbelianMonoid

ElementaryFunctionCategory

MagmaWithUnit

NonAssociativeSemiRng

RightModule(%)

Hashable

StepThrough

Module(%)

ConvertibleTo(Pattern(Integer))

CoercibleTo(OutputForm)

DifferentialExtension(R)

FullyEvalableOver(R)

InnerEvalable(Symbol, R)

ConvertibleTo(Pattern(Float))

SemiRng

Patternable(R)

Monoid

PolynomialFactorizationExplicit

FiniteFieldCategory

NonAssociativeAlgebra(R)

NonAssociativeAlgebra(%)

FramedModule(R)

Finite

ConvertibleTo(Complex(DoubleFloat))

BasicType

Ring

ConvertibleTo(Complex(Float))

RightModule(Integer)

LeftModule(Fraction(Integer))

AbelianSemiGroup

IntegralDomain

SetCategory

MonogenicAlgebra(R, SparseUnivariatePolynomial(R))

multiplicativeValuation

TrigonometricFunctionCategory

LinearlyExplicitOver(R)

NonAssociativeRng

PatternMatchable(Integer)

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

FullyPatternMatchable(R)

RetractableTo(R)

AbelianGroup