Section17.1

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## 17.1 Axiom Categories

This is a listing of all categories in the Axiom library at the time this book was produced. Use the Browse facility (described in Chapter ugBrowse ) to get more information about these constructors.

This sample entry will help you read the following table:

CategoryName{CategoryAbbreviation}:{ Category 1 ... Category N}with { op 1... op M}

where

CategoryName | is the full category name, e.g., CommutativeRing.
CategoryAbbreviation | is the category abbreviation, e.g., COMRING.
Category i | is a category to which the category belongs.
op j | is an operation exported by the category.

Abbreviation: | ABELGRP
Full name: | AbelianGroup
Belongs to: | CancellationAbelianMonoid
Operations: | * -

Abbreviation: | AMR
Full name: | AbelianMonoidRing
Belongs to: | Algebra BiModule CharacteristicNonZero CharacteristicZero CommutativeRing IntegralDomain Ring
Operations: | / coefficient degree leadingCoefficient leadingMonomial map monomial monomial? reductum

Abbreviation: | ABELMON
Full name: | AbelianMonoid
Belongs to: | AbelianSemiGroup
Operations: | * Zero zero?

Abbreviation: | ABELSG
Full name: | AbelianSemiGroup
Belongs to: | SetCategory
Operations: | * +

Abbreviation: | AGG
Full name: | Aggregate
Belongs to: | Object
Operations: | # copy empty empty? eq? less? more? size?

Abbreviation: | ACF
Full name: | AlgebraicallyClosedField
Belongs to: | Field RadicalCategory
Operations: | rootOf rootsOf zeroOf zerosOf

Abbreviation: | ACFS
Full name: | AlgebraicallyClosedFunctionSpace
Belongs to: | AlgebraicallyClosedField FunctionSpace
Operations: | rootOf rootsOf zeroOf zerosOf

Abbreviation: | ALGEBRA
Full name: | Algebra
Belongs to: | Module Ring
Operations: | coerce

Abbreviation: | AHYP
Full name: | ArcHyperbolicFunctionCategory
Belongs to: |
Operations: | acosh acoth acsch asech asinh atanh

Abbreviation: | ATRIG
Full name: | ArcTrigonometricFunctionCategory
Belongs to: |
Operations: | acos acot acsc asec asin atan

Abbreviation: | ALAGG
Full name: | AssociationListAggregate
Belongs to: | ListAggregate TableAggregate
Operations: | assoc

Abbreviation: | ATTREG
Full name: | AttributeRegistry
Belongs to: |
Operations: |

Abbreviation: | BGAGG
Full name: | BagAggregate
Belongs to: | HomogeneousAggregate
Operations: | bag extract! insert! inspect

Abbreviation: | BMODULE
Full name: | BiModule
Belongs to: | LeftModule RightModule
Operations: |

Abbreviation: | BRAGG
Full name: | BinaryRecursiveAggregate
Belongs to: | RecursiveAggregate
Operations: | elt left right setelt setleft! setright!

Abbreviation: | BTCAT
Full name: | BinaryTreeCategory
Belongs to: | BinaryRecursiveAggregate
Operations: | node

Abbreviation: | BTAGG
Full name: | BitAggregate
Belongs to: | OneDimensionalArrayAggregate OrderedSet
Operations: | \^{} and nand nor not or xor

Abbreviation: | CACHSET
Full name: | CachableSet
Belongs to: | OrderedSet
Operations: | position setPosition

Abbreviation: | CABMON
Full name: | CancellationAbelianMonoid
Belongs to: | AbelianMonoid
Operations: | -

Abbreviation: | CHARNZ
Full name: | CharacteristicNonZero
Belongs to: | Ring
Operations: | charthRoot

Abbreviation: | CHARZ
Full name: | CharacteristicZero
Belongs to: | Ring
Operations: |

Abbreviation: | KOERCE
Full name: | CoercibleTo
Belongs to: |
Operations: | coerce

Abbreviation: | CLAGG
Full name: | Collection
Belongs to: | ConvertibleTo HomogeneousAggregate
Operations: | construct find reduce remove removeDuplicates select

Abbreviation: | CFCAT
Full name: | CombinatorialFunctionCategory
Belongs to: |
Operations: | binomial factorial permutation

Abbreviation: | COMBOPC
Full name: | CombinatorialOpsCategory
Belongs to: | CombinatorialFunctionCategory
Operations: | factorials product summation

Abbreviation: | COMRING
Full name: | CommutativeRing
Belongs to: | BiModule Ring
Operations: |

Abbreviation: | COMPCAT
Full name: | ComplexCategory
Belongs to: | CharacteristicNonZero CharacteristicZero CommutativeRing ConvertibleTo DifferentialExtension EuclideanDomain Field FullyEvalableOver FullyLinearlyExplicitRingOver FullyRetractableTo IntegralDomain MonogenicAlgebra OrderedSet PolynomialFactorizationExplicit RadicalCategory TranscendentalFunctionCategory
Operations: | abs argument complex conjugate exquo imag imaginary norm polarCoordinates rational rational? rationalIfCan real

Abbreviation: | KONVERT
Full name: | ConvertibleTo
Belongs to: |
Operations: | convert

Abbreviation: | DQAGG
Full name: | DequeueAggregate
Belongs to: | QueueAggregate StackAggregate
Operations: | bottom! dequeue extractBottom! extractTop! height insertBottom! insertTop! reverse! top!

Abbreviation: | DIOPS
Full name: | DictionaryOperations
Belongs to: | BagAggregate Collection
Operations: | dictionary remove! select!

Abbreviation: | DIAGG
Full name: | Dictionary
Belongs to: | DictionaryOperations
Operations: |

Abbreviation: | DIFEXT
Full name: | DifferentialExtension
Belongs to: | DifferentialRing PartialDifferentialRing Ring
Operations: | D differentiate

Abbreviation: | DPOLCAT
Full name: | DifferentialPolynomialCategory
Belongs to: | DifferentialExtension Evalable InnerEvalable PolynomialCategory RetractableTo
Operations: | degree differentialVariables initial isobaric? leader makeVariable order separant weight weights

Abbreviation: | DIFRING
Full name: | DifferentialRing
Belongs to: | Ring
Operations: | D differentiate

Abbreviation: | DVARCAT
Full name: | DifferentialVariableCategory
Belongs to: | OrderedSet RetractableTo
Operations: | D coerce differentiate makeVariable order variable weight

Abbreviation: | DIRPCAT
Full name: | DirectProductCategory
Belongs to: | AbelianSemiGroup Algebra BiModule CancellationAbelianMonoid CoercibleTo CommutativeRing DifferentialExtension Finite FullyLinearlyExplicitRingOver FullyRetractableTo IndexedAggregate OrderedAbelianMonoidSup OrderedRing VectorSpace
Operations: | * directProduct dot unitVector

Abbreviation: | DIVRING
Full name: | DivisionRing
Belongs to: | Algebra EntireRing
Operations: | ** inv

Abbreviation: | DLAGG
Full name: | DoublyLinkedAggregate
Belongs to: | RecursiveAggregate
Operations: | concat! head last next previous setnext! setprevious! tail

Abbreviation: | ELEMFUN
Full name: | ElementaryFunctionCategory
Belongs to: |
Operations: | ** exp log

Abbreviation: | ELTAGG
Full name: | EltableAggregate
Belongs to: | Eltable
Operations: | elt qelt qsetelt! setelt

Abbreviation: | ELTAB
Full name: | Eltable
Belongs to: |
Operations: | elt

Abbreviation: | ENTIRER
Full name: | EntireRing
Belongs to: | BiModule Ring
Operations: |

Abbreviation: | EUCDOM
Full name: | EuclideanDomain
Belongs to: | PrincipalIdealDomain
Operations: | divide euclideanSize extendedEuclidean multiEuclidean quo rem sizeLess?

Abbreviation: | EVALAB
Full name: | Evalable
Belongs to: |
Operations: | eval

Abbreviation: | ES
Full name: | ExpressionSpace
Belongs to: | Evalable InnerEvalable OrderedSet RetractableTo
Operations: | belong? box definingPolynomial distribute elt eval freeOf? height is? kernel kernels mainKernel map minPoly operator operators paren subst tower

Abbreviation: | ELAGG
Full name: | ExtensibleLinearAggregate
Belongs to: | LinearAggregate
Operations: | concat! delete! insert! merge! remove! removeDuplicates! select!

Abbreviation: | XF
Full name: | ExtensionField
Belongs to: | CharacteristicZero Field FieldOfPrimeCharacteristic RetractableTo VectorSpace
Operations: | Frobenius algebraic? degree extensionDegree inGroundField? transcendenceDegree transcendent?

Abbreviation: | FPC
Full name: | FieldOfPrimeCharacteristic
Belongs to: | CharacteristicNonZero Field
Operations: | discreteLog order primeFrobenius

Abbreviation: | FIELD
Full name: | Field
Belongs to: | DivisionRing EuclideanDomain UniqueFactorizationDomain
Operations: | /

Abbreviation: | FILECAT
Full name: | FileCategory
Belongs to: | SetCategory
Operations: | close! iomode name open read! reopen! write!

Abbreviation: | FNCAT
Full name: | FileNameCategory
Belongs to: | SetCategory
Operations: | coerce directory exists? extension filename name new readable? writable?

Abbreviation: | FAMR
Full name: | FiniteAbelianMonoidRing
Belongs to: | AbelianMonoidRing FullyRetractableTo
Operations: | coefficients content exquo ground ground? mapExponents minimumDegree numberOfMonomials primitivePart

Abbreviation: | FAXF
Full name: | FiniteAlgebraicExtensionField
Belongs to: | ExtensionField FiniteFieldCategory RetractableTo
Operations: | basis coordinates createNormalElement definingPolynomial degree extensionDegree generator minimalPolynomial norm normal? normalElement represents trace

Abbreviation: | FFIELDC
Full name: | FiniteFieldCategory
Belongs to: | FieldOfPrimeCharacteristic Finite StepThrough
Operations: | charthRoot conditionP createPrimitiveElement discreteLog factorsOfCyclicGroupSize order primitive? primitiveElement representationType tableForDiscreteLogarithm

Abbreviation: | FLAGG
Full name: | FiniteLinearAggregate
Belongs to: | LinearAggregate OrderedSet
Operations: | copyInto! merge position reverse reverse! sort sort! sorted?

Abbreviation: | FINRALG
Full name: | FiniteRankAlgebra
Belongs to: | Algebra CharacteristicNonZero CharacteristicZero
Operations: | characteristicPolynomial coordinates discriminant minimalPolynomial norm rank regularRepresentation represents trace traceMatrix

Abbreviation: | FINAALG
Full name: | FiniteRankNonAssociativeAlgebra
Belongs to: | NonAssociativeAlgebra
Operations: | JacobiIdentity? JordanAlgebra? alternative? antiAssociative? antiCommutative? associative? associatorDependence commutative? conditionsForIdempotents coordinates flexible? jordanAdmissible? leftAlternative? leftCharacteristicPolynomial leftDiscriminant leftMinimalPolynomial leftNorm leftRecip leftRegularRepresentation leftTrace leftTraceMatrix leftUnit leftUnits lieAdmissible? lieAlgebra? noncommutativeJordanAlgebra? powerAssociative? rank recip represents rightAlternative? rightCharacteristicPolynomial rightDiscriminant rightMinimalPolynomial rightNorm rightRecip rightRegularRepresentation rightTrace rightTraceMatrix rightUnit rightUnits someBasis structuralConstants unit

Abbreviation: | FSAGG
Full name: | FiniteSetAggregate
Belongs to: | Dictionary Finite SetAggregate
Operations: | cardinality complement max min universe

Abbreviation: | FINITE
Full name: | Finite
Belongs to: | SetCategory
Operations: | index lookup random size

Abbreviation: | FPS
Full name: | FloatingPointSystem
Belongs to: | RealNumberSystem
Operations: | base bits decreasePrecision digits exponent float increasePrecision mantissa max order precision

Abbreviation: | FRAMALG
Full name: | FramedAlgebra
Belongs to: | FiniteRankAlgebra
Operations: | basis convert coordinates discriminant regularRepresentation represents traceMatrix

Abbreviation: | FRNAALG
Full name: | FramedNonAssociativeAlgebra
Belongs to: | FiniteRankNonAssociativeAlgebra
Operations: | apply basis conditionsForIdempotents convert coordinates elt leftDiscriminant leftRankPolynomial leftRegularRepresentation leftTraceMatrix represents rightDiscriminant rightRankPolynomial rightRegularRepresentation rightTraceMatrix structuralConstants

Abbreviation: | FAMONC
Full name: | FreeAbelianMonoidCategory
Belongs to: | CancellationAbelianMonoid RetractableTo
Operations: | * + coefficient highCommonTerms mapCoef mapGen nthCoef nthFactor size terms

Abbreviation: | FEVALAB
Full name: | FullyEvalableOver
Belongs to: | Eltable Evalable InnerEvalable
Operations: | map

Abbreviation: | FLINEXP
Full name: | FullyLinearlyExplicitRingOver
Belongs to: | LinearlyExplicitRingOver
Operations: |

Abbreviation: | FPATMAB
Full name: | FullyPatternMatchable
Belongs to: | Object PatternMatchable
Operations: |

Abbreviation: | FRETRCT
Full name: | FullyRetractableTo
Belongs to: | RetractableTo
Operations: |

Abbreviation: | FFCAT
Full name: | FunctionFieldCategory
Belongs to: | MonogenicAlgebra
Operations: | D absolutelyIrreducible? branchPoint? branchPointAtInfinity? complementaryBasis differentiate elt genus integral? integralAtInfinity? integralBasis integralBasisAtInfinity integralCoordinates integralDerivationMatrix integralMatrix integralMatrixAtInfinity integralRepresents inverseIntegralMatrix inverseIntegralMatrixAtInfinity nonSingularModel normalizeAtInfinity numberOfComponents primitivePart ramified? ramifiedAtInfinity? rationalPoint? rationalPoints reduceBasisAtInfinity represents singular? singularAtInfinity? yCoordinates

Abbreviation: | FS
Full name: | FunctionSpace
Belongs to: | AbelianGroup AbelianMonoid Algebra CharacteristicNonZero CharacteristicZero ConvertibleTo ExpressionSpace Field FullyLinearlyExplicitRingOver FullyPatternMatchable FullyRetractableTo Group Monoid PartialDifferentialRing Patternable RetractableTo Ring
Operations: | ** / applyQuote coerce convert denom denominator eval ground ground? isExpt isMult isPlus isPower isTimes numer numerator univariate variables

Abbreviation: | GCDDOM
Full name: | GcdDomain
Belongs to: | IntegralDomain
Operations: | gcd lcm

Abbreviation: | GRALG
Full name: | GradedAlgebra
Belongs to: | GradedModule
Operations: | One product

Abbreviation: | GRMOD
Full name: | GradedModule
Belongs to: | RetractableTo SetCategory
Operations: | * + - Zero degree

Abbreviation: | GROUP
Full name: | Group
Belongs to: | Monoid
Operations: | ** / commutator conjugate inv

Abbreviation: | HOAGG
Full name: | HomogeneousAggregate
Belongs to: | Aggregate SetCategory
Operations: | any? count every? map map! member? members parts

Abbreviation: | HYPCAT
Full name: | HyperbolicFunctionCategory
Belongs to: |
Operations: | cosh coth csch sech sinh tanh

Abbreviation: | IXAGG
Full name: | IndexedAggregate
Belongs to: | EltableAggregate HomogeneousAggregate
Operations: | entries entry? fill! first index? indices maxIndex minIndex swap!

Abbreviation: | IDPC
Full name: | IndexedDirectProductCategory
Belongs to: | SetCategory
Operations: | leadingCoefficient leadingSupport map monomial reductum

Abbreviation: | IEVALAB
Full name: | InnerEvalable
Belongs to: |
Operations: | eval

Abbreviation: | INS
Full name: | IntegerNumberSystem
Belongs to: | CharacteristicZero CombinatorialFunctionCategory ConvertibleTo DifferentialRing EuclideanDomain LinearlyExplicitRingOver OrderedRing PatternMatchable RealConstant RetractableTo StepThrough UniqueFactorizationDomain
Operations: | addmod base bit? copy dec even? hash inc invmod length mask mulmod odd? positiveRemainder powmod random rational rational? rationalIfCan shift submod symmetricRemainder

Abbreviation: | INTDOM
Full name: | IntegralDomain
Belongs to: | Algebra CommutativeRing EntireRing
Operations: | associates? exquo unit? unitCanonical unitNormal

Abbreviation: | KDAGG
Full name: | KeyedDictionary
Belongs to: | Dictionary
Operations: | key? keys remove! search

Abbreviation: | LZSTAGG
Full name: | LazyStreamAggregate
Belongs to: | StreamAggregate
Operations: | complete explicitEntries? explicitlyEmpty? extend frst lazy? lazyEvaluate numberOfComputedEntries remove rst select

Abbreviation: | LALG
Full name: | LeftAlgebra
Belongs to: | LeftModule Ring
Operations: | coerce

Abbreviation: | LMODULE
Full name: | LeftModule
Belongs to: | AbelianGroup
Operations: | *

Abbreviation: | LNAGG
Full name: | LinearAggregate
Belongs to: | Collection IndexedAggregate
Operations: | concat delete elt insert map new setelt

Abbreviation: | LINEXP
Full name: | LinearlyExplicitRingOver
Belongs to: | Ring
Operations: | reducedSystem

Abbreviation: | LFCAT
Full name: | LiouvillianFunctionCategory
Belongs to: | PrimitiveFunctionCategory TranscendentalFunctionCategory
Operations: | Ci Ei Si dilog erf li

Abbreviation: | LSAGG
Full name: | ListAggregate
Belongs to: | ExtensibleLinearAggregate FiniteLinearAggregate StreamAggregate
Operations: | list

Abbreviation: | MATCAT
Full name: | MatrixCategory
Belongs to: | TwoDimensionalArrayCategory
Operations: | * ** + - / antisymmetric? coerce determinant diagonal? diagonalMatrix elt exquo horizConcat inverse listOfLists matrix minordet nullSpace nullity rank rowEchelon scalarMatrix setelt setsubMatrix! square? squareTop subMatrix swapColumns! swapRows! symmetric? transpose vertConcat zero

Abbreviation: | MODULE
Full name: | Module
Belongs to: | BiModule
Operations: |

Abbreviation: | MONADWU
Full name: | MonadWithUnit
Belongs to: | Monad
Operations: | ** One leftPower leftRecip one? recip rightPower rightRecip

Abbreviation: | MONAD
Full name: | Monad
Belongs to: | SetCategory
Operations: | * ** leftPower rightPower

Abbreviation: | MONOGEN
Full name: | MonogenicAlgebra
Belongs to: | CommutativeRing ConvertibleTo DifferentialExtension Field Finite FiniteFieldCategory FramedAlgebra FullyLinearlyExplicitRingOver FullyRetractableTo
Operations: | convert definingPolynomial derivationCoordinates generator lift reduce

Abbreviation: | MLO
Full name: | MonogenicLinearOperator
Belongs to: | Algebra BiModule Ring
Operations: | coefficient degree leadingCoefficient minimumDegree monomial reductum

Abbreviation: | MONOID
Full name: | Monoid
Belongs to: | SemiGroup
Operations: | ** One one? recip

Abbreviation: | MDAGG
Full name: | MultiDictionary
Belongs to: | DictionaryOperations
Operations: | duplicates insert! removeDuplicates!

Abbreviation: | MSAGG
Full name: | MultiSetAggregate
Belongs to: | MultiDictionary SetAggregate
Operations: |

Abbreviation: | MTSCAT
Full name: | MultivariateTaylorSeriesCategory
Belongs to: | Evalable InnerEvalable PartialDifferentialRing PowerSeriesCategory RadicalCategory TranscendentalFunctionCategory
Operations: | coefficient extend integrate monomial order polynomial

Abbreviation: | NAALG
Full name: | NonAssociativeAlgebra
Belongs to: | Module NonAssociativeRng
Operations: | plenaryPower

Abbreviation: | NASRING
Full name: | NonAssociativeRing
Belongs to: | MonadWithUnit NonAssociativeRng
Operations: | characteristic coerce

Abbreviation: | NARNG
Full name: | NonAssociativeRng
Belongs to: | AbelianGroup Monad
Operations: | antiCommutator associator commutator

Abbreviation: | OBJECT
Full name: | Object
Belongs to: |
Operations: |

Abbreviation: | OC
Full name: | OctonionCategory
Belongs to: | Algebra CharacteristicNonZero CharacteristicZero ConvertibleTo Finite FullyEvalableOver FullyRetractableTo OrderedSet
Operations: | abs conjugate imagE imagI imagJ imagK imagi imagj imagk inv norm octon rational rational? rationalIfCan real

Abbreviation: | A1AGG
Full name: | OneDimensionalArrayAggregate
Belongs to: | FiniteLinearAggregate
Operations: |

Abbreviation: | OAGROUP
Full name: | OrderedAbelianGroup
Belongs to: | AbelianGroup OrderedCancellationAbelianMonoid
Operations: |

Abbreviation: | OAMONS
Full name: | OrderedAbelianMonoidSup
Belongs to: | OrderedCancellationAbelianMonoid
Operations: | sup

Abbreviation: | OAMON
Full name: | OrderedAbelianMonoid
Belongs to: | AbelianMonoid OrderedAbelianSemiGroup
Operations: |

Abbreviation: | OASGP
Full name: | OrderedAbelianSemiGroup
Belongs to: | AbelianMonoid OrderedSet
Operations: |

Abbreviation: | OCAMON
Full name: | OrderedCancellationAbelianMonoid
Belongs to: | CancellationAbelianMonoid OrderedAbelianMonoid
Operations: |

Abbreviation: | ORDFIN
Full name: | OrderedFinite
Belongs to: | Finite OrderedSet
Operations: |

Abbreviation: | ORDMON
Full name: | OrderedMonoid
Belongs to: | Monoid OrderedSet
Operations: |

Abbreviation: | OMAGG
Full name: | OrderedMultiSetAggregate
Belongs to: | MultiSetAggregate PriorityQueueAggregate
Operations: | min

Abbreviation: | ORDRING
Full name: | OrderedRing
Belongs to: | OrderedAbelianGroup OrderedMonoid Ring
Operations: | abs negative? positive? sign

Abbreviation: | ORDSET
Full name: | OrderedSet
Belongs to: | SetCategory
Operations: | < max min

Abbreviation: | PADICCT
Full name: | PAdicIntegerCategory
Belongs to: | CharacteristicZero EuclideanDomain
Operations: | approximate complete digits extend moduloP modulus order quotientByP sqrt

Abbreviation: | PDRING
Full name: | PartialDifferentialRing
Belongs to: | Ring
Operations: | D differentiate

Abbreviation: | PTRANFN
Full name: | PartialTranscendentalFunctions
Belongs to: |
Operations: | acosIfCan acoshIfCan acotIfCan acothIfCan acscIfCan acschIfCan asecIfCan asechIfCan asinIfCan asinhIfCan atanIfCan atanhIfCan cosIfCan coshIfCan cotIfCan cothIfCan cscIfCan cschIfCan expIfCan logIfCan nthRootIfCan secIfCan sechIfCan sinIfCan sinhIfCan tanIfCan tanhIfCan

Abbreviation: | PATAB
Full name: | Patternable
Belongs to: | ConvertibleTo Object
Operations: |

Abbreviation: | PATMAB
Full name: | PatternMatchable
Belongs to: | SetCategory
Operations: | patternMatch

Abbreviation: | PERMCAT
Full name: | PermutationCategory
Belongs to: | Group OrderedSet
Operations: | < cycle cycles elt eval orbit

Abbreviation: | PPCURVE
Full name: | PlottablePlaneCurveCategory
Belongs to: | CoercibleTo
Operations: | listBranches xRange yRange

Abbreviation: | PSCURVE
Full name: | PlottableSpaceCurveCategory
Belongs to: | CoercibleTo
Operations: | listBranches xRange yRange zRange

Abbreviation: | PTCAT
Full name: | PointCategory
Belongs to: | VectorCategory
Operations: | convert cross dimension extend length point

Abbreviation: | POLYCAT
Full name: | PolynomialCategory
Belongs to: | ConvertibleTo Evalable FiniteAbelianMonoidRing FullyLinearlyExplicitRingOver GcdDomain InnerEvalable OrderedSet PartialDifferentialRing PatternMatchable PolynomialFactorizationExplicit RetractableTo
Operations: | coefficient content degree discriminant isExpt isPlus isTimes mainVariable minimumDegree monicDivide monomial monomials multivariate primitiveMonomials primitivePart resultant squareFree squareFreePart totalDegree univariate variables

Abbreviation: | PFECAT
Full name: | PolynomialFactorizationExplicit
Belongs to: | UniqueFactorizationDomain
Operations: | charthRoot conditionP factorPolynomial factorSquareFreePolynomial gcdPolynomial solveLinearPolynomialEquation squareFreePolynomial

Abbreviation: | PSCAT
Full name: | PowerSeriesCategory
Belongs to: | AbelianMonoidRing
Operations: | complete monomial pole? variables

Abbreviation: | PRIMCAT
Full name: | PrimitiveFunctionCategory
Belongs to: |
Operations: | integral

Abbreviation: | PID
Full name: | PrincipalIdealDomain
Belongs to: | GcdDomain
Operations: | expressIdealMember principalIdeal

Abbreviation: | PRQAGG
Full name: | PriorityQueueAggregate
Belongs to: | BagAggregate
Operations: | max merge merge!

Abbreviation: | QUATCAT
Full name: | QuaternionCategory
Belongs to: | Algebra CharacteristicNonZero CharacteristicZero ConvertibleTo DifferentialExtension DivisionRing EntireRing FullyEvalableOver FullyLinearlyExplicitRingOver FullyRetractableTo OrderedSet
Operations: | abs conjugate imagI imagJ imagK norm quatern rational rational? rationalIfCan real

Abbreviation: | QUAGG
Full name: | QueueAggregate
Belongs to: | BagAggregate
Operations: | back dequeue! enqueue! front length rotate!

Abbreviation: | QFCAT
Full name: | QuotientFieldCategory
Belongs to: | Algebra CharacteristicNonZero CharacteristicZero ConvertibleTo DifferentialExtension Field FullyEvalableOver FullyLinearlyExplicitRingOver FullyPatternMatchable OrderedRing OrderedSet Patternable PolynomialFactorizationExplicit RealConstant RetractableTo StepThrough
Operations: | / ceiling denom denominator floor fractionPart numer numerator random wholePart

Abbreviation: | RADCAT
Full name: | RadicalCategory
Belongs to: |
Operations: | ** nthRoot sqrt

Abbreviation: | REAL
Full name: | RealConstant
Belongs to: | ConvertibleTo
Operations: |

Abbreviation: | RNS
Full name: | RealNumberSystem
Belongs to: | CharacteristicZero ConvertibleTo Field OrderedRing PatternMatchable RadicalCategory RealConstant RetractableTo
Operations: | abs ceiling floor fractionPart norm round truncate wholePart

Abbreviation: | RMATCAT
Full name: | RectangularMatrixCategory
Belongs to: | BiModule HomogeneousAggregate Module
Operations: | / antisymmetric? column diagonal? elt exquo listOfLists map matrix maxColIndex maxRowIndex minColIndex minRowIndex ncols nrows nullSpace nullity qelt rank row rowEchelon square? symmetric?

Abbreviation: | RCAGG
Full name: | RecursiveAggregate
Belongs to: | HomogeneousAggregate
Operations: | children cyclic? elt leaf? leaves node? nodes setchildren! setelt setvalue! value

Abbreviation: | RETRACT
Full name: | RetractableTo
Belongs to: |
Operations: | coerce retract retractIfCan

Abbreviation: | RMODULE
Full name: | RightModule
Belongs to: | AbelianGroup
Operations: | *

Abbreviation: | RING
Full name: | Ring
Belongs to: | LeftModule Monoid Rng
Operations: | characteristic coerce

Abbreviation: | RNG
Full name: | Rng
Belongs to: | AbelianGroup SemiGroup
Operations: |

Abbreviation: | SEGCAT
Full name: | SegmentCategory
Belongs to: | SetCategory
Operations: | BY SEGMENT convert hi high incr lo low segment

Abbreviation: | SEGXCAT
Full name: | SegmentExpansionCategory
Belongs to: | SegmentCategory
Operations: | expand map

Abbreviation: | SGROUP
Full name: | SemiGroup
Belongs to: | SetCategory
Operations: | * **

Abbreviation: | SETAGG
Full name: | SetAggregate
Belongs to: | Collection SetCategory
Operations: | < brace difference intersect subset? symmetricDifference union

Abbreviation: | SETCAT
Full name: | SetCategory
Belongs to: | CoercibleTo Object
Operations: | =

Abbreviation: | SEXCAT
Full name: | SExpressionCategory
Belongs to: | SetCategory
Operations: | # atom? car cdr convert destruct elt eq expr float float? integer integer? list? null? pair? string string? symbol symbol? uequal

Abbreviation: | SPFCAT
Full name: | SpecialFunctionCategory
Belongs to: |
Operations: | Beta Gamma abs airyAi airyBi besselI besselJ besselK besselY digamma polygamma

Abbreviation: | SMATCAT
Full name: | SquareMatrixCategory
Belongs to: | Algebra BiModule DifferentialExtension FullyLinearlyExplicitRingOver FullyRetractableTo Module RectangularMatrixCategory
Operations: | * ** determinant diagonal diagonalMatrix diagonalProduct inverse minordet scalarMatrix trace

Abbreviation: | SKAGG
Full name: | StackAggregate
Belongs to: | BagAggregate
Operations: | depth pop! push! top

Abbreviation: | STEP
Full name: | StepThrough
Belongs to: | SetCategory
Operations: | init nextItem

Abbreviation: | STAGG
Full name: | StreamAggregate
Belongs to: | LinearAggregate UnaryRecursiveAggregate
Operations: | explicitlyFinite? possiblyInfinite?

Abbreviation: | SRAGG
Full name: | StringAggregate
Belongs to: | OneDimensionalArrayAggregate
Operations: | coerce elt leftTrim lowerCase lowerCase! match match? position prefix? replace rightTrim split substring? suffix? trim upperCase upperCase!

Abbreviation: | STRICAT
Full name: | StringCategory
Belongs to: | StringAggregate
Operations: | string

Abbreviation: | TBAGG
Full name: | TableAggregate
Belongs to: | IndexedAggregate KeyedDictionary
Operations: | map setelt table

Abbreviation: | SPACEC
Full name: | ThreeSpaceCategory
Belongs to: | SetCategory
Operations: | check closedCurve closedCurve? coerce components composite composites copy create3Space curve curve? enterPointData lllip lllp llprop lp lprop merge mesh mesh? modifyPointData numberOfComponents numberOfComposites objects point point? polygon polygon? subspace

Abbreviation: | TRANFUN
Full name: | TranscendentalFunctionCategory
Belongs to: | ArcHyperbolicFunctionCategory ArcTrigonometricFunctionCategory ElementaryFunctionCategory HyperbolicFunctionCategory TrigonometricFunctionCategory
Operations: | pi

Abbreviation: | TRIGCAT
Full name: | TrigonometricFunctionCategory
Belongs to: |
Operations: | cos cot csc sec sin tan

Abbreviation: | ARR2CAT
Full name: | TwoDimensionalArrayCategory
Belongs to: | HomogeneousAggregate
Operations: | column elt fill! map map! maxColIndex maxRowIndex minColIndex minRowIndex ncols new nrows parts qelt qsetelt! row setColumn! setRow! setelt

Abbreviation: | URAGG
Full name: | UnaryRecursiveAggregate
Belongs to: | RecursiveAggregate
Operations: | concat concat! cycleEntry cycleLength cycleSplit! cycleTail elt first last rest second setelt setfirst! setlast! setrest! split! tail third

Abbreviation: | UFD
Full name: | UniqueFactorizationDomain
Belongs to: | GcdDomain
Operations: | factor prime? squareFree squareFreePart

Abbreviation: | ULSCAT
Full name: | UnivariateLaurentSeriesCategory
Belongs to: | Field RadicalCategory TranscendentalFunctionCategory UnivariatePowerSeriesCategory
Operations: | integrate multiplyCoefficients rationalFunction

Abbreviation: | ULSCCAT
Full name: | UnivariateLaurentSeriesConstructorCategory
Belongs to: | QuotientFieldCategory RetractableTo UnivariateLaurentSeriesCategory
Operations: | coerce degree laurent removeZeroes taylor taylorIfCan taylorRep

Abbreviation: | UPOLYC
Full name: | UnivariatePolynomialCategory
Belongs to: | DifferentialExtension DifferentialRing Eltable EuclideanDomain PolynomialCategory StepThrough
Operations: | D composite differentiate discriminant divideExponents elt integrate makeSUP monicDivide multiplyExponents order pseudoDivide pseudoQuotient pseudoRemainder resultant separate subResultantGcd unmakeSUP vectorise

Abbreviation: | UPSCAT
Full name: | UnivariatePowerSeriesCategory
Belongs to: | DifferentialRing Eltable PowerSeriesCategory
Operations: | approximate center elt eval extend multiplyExponents order series terms truncate variable

Abbreviation: | UPXSCAT
Full name: | UnivariatePuiseuxSeriesCategory
Belongs to: | Field RadicalCategory TranscendentalFunctionCategory UnivariatePowerSeriesCategory
Operations: | integrate multiplyExponents

Abbreviation: | UPXSCCA
Full name: | UnivariatePuiseuxSeriesConstructorCategory
Belongs to: | RetractableTo UnivariatePuiseuxSeriesCategory
Operations: | coerce degree laurent laurentIfCan laurentRep puiseux rationalPower

Abbreviation: | UTSCAT
Full name: | UnivariateTaylorSeriesCategory
Belongs to: | RadicalCategory TranscendentalFunctionCategory UnivariatePowerSeriesCategory
Operations: | ** coefficients integrate multiplyCoefficients polynomial quoByVar series

Abbreviation: | VECTCAT
Full name: | VectorCategory
Belongs to: | OneDimensionalArrayAggregate
Operations: | * + - dot zero

Abbreviation: | VSPACE
Full name: | VectorSpace
Belongs to: | Module
Operations: | / dimension

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