.. status: ok


17.1 FriCAS Categories
----------------------

This is a listing of all categories in the FriCAS library at the time
this book was produced. Use the Browse facility (described in Chapter
`ugBrowse <section-14.0.html#ugBrowse>`__ ) to get more information
about these constructors.

This sample entry will help you read the following table:

CategoryName{CategoryAbbreviation}:{ Category1 ... CategoryN}with {
op1... opM}

where

+------------------------+-----------------------------------------------------+
| CategoryName           | is the full category name, e.g., CommutativeRing.   |
+------------------------+-----------------------------------------------------+
| CategoryAbbreviation   | is the category abbreviation, e.g., COMRING.        |
+------------------------+-----------------------------------------------------+
| Categoryi              | is a category to which the category belongs.        |
+------------------------+-----------------------------------------------------+
| opj                    | 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   |
+-----------------+---------------+