path: root/src/doc/topics.data

AbelianGroup:
   CancellationAbelianMonoid
   *
   -

AbelianMonoid:
   AbelianSemiGroup
   *
   Zero
   zero?

AbelianSemiGroup:
   SetCategory
   *
   +

Aggregate:
   Object
   #
   copy
   empty
   empty?
   eq?
   less?
   more?
   size?

Algebra:
   Module
   Ring
   coerce

AlgebraicallyClosedField:
   Field
   RadicalCategory
   rootOf
   rootsOf
   zeroOf
   zerosOf

ArcHyperbolicFunctionCategory:
   acosh hy
   acoth hy
   acsch hy
   asech hy
   asinh hy
   atanh hy

ArcTrigonometricFunctionCategory:
   acos tg
   acot tg
   acsc tg 
   asec tg 
   asin tg 
   atan tg

AssociationListAggregate:
   ListAggregate
   TableAggregate
   assoc

AttributeRegistry:

BagAggregate:
   HomogeneousAggregate
   bag
   extract!
   insert!
   inspect

BiModule:
   LeftModule
   RightModule

BinaryRecursiveAggregate:
   RecursiveAggregate
   elt
   left
   right
   setelt
   setleft!
   setright!

BinaryTreeCategory:
   BinaryRecursiveAggregate
   node

BitAggregate:
   OneDimensionalArrayAggregate
   OrderedSet
   ^
   and
   nand
   nor
   not
   or
   xor

CachableSet:
   OrderedSet
   position
   setPosition

CancellationAbelianMonoid:
   AbelianMonoid
   subtractIfCan

CharacteristicZero:
   Ring

CoercibleTo:
   coerce v

Collection:
   ConvertibleTo
   HomogeneousAggregate
   construct
   find   e
   reduce e
   remove t
   removeDuplicates t
   select t e

CommutativeRing:
   BiModule
   Ring

ComplexCategory:
   CharacteristicNonZero
   CharacteristicZero
   CommutativeRing
   ConvertibleTo
   ConvertibleTo
   ConvertibleTo
   DifferentialExtension
   EuclideanDomain
   Field
   FullyEvalableOver
   FullyLinearlyExplicitRingOver
   FullyRetractableTo
   IntegralDomain
   MonogenicAlgebra
   OrderedSet
   PolynomialFactorizationExplicit
   RadicalCategory
   TranscendentalFunctionCategory
   abs b t
   argument h
   complex b c
   conjugate b t
   exquo a
   imag b x
   imaginary h
   norm b t
   polarCoordinates t
   rational h
   rational? h
   rationalIfCan h
   real b x

ConvertibleTo:
   convert v

DequeueAggregate:
   QueueAggregate
   StackAggregate
   bottom! x        
   dequeue b c
   extractBottom! b x
   extractTop! b x
   height 
   insertBottom! b t
   insertTop! b t
   reverse!
   top! x

Dictionary:
   DictionaryOperations

DictionaryOperations:
   BagAggregate
   Collection
   dictionary h
   remove! h
   select! h

DifferentialExtension:
   DifferentialRing
   PartialDifferentialRing
   Ring
   D g b
   differentiate g b

DifferentialPolynomialCategory:
   Category

DifferentialRing:
   Ring
   D a
   differentiate a

DifferentialVariableCategory:
   OrderedSet
   RetractableTo
   coerce 
   differentiate
   makeVariable
   order
   variable
   weight

DirectProductCategory:
   AbelianSemiGroup
   Algebra
   BiModule
   CancellationAbelianMonoid
   CoercibleTo
   CommutativeRing
   DifferentialExtension
   Finite
   FullyLinearlyExplicitRingOver
   FullyRetractableTo
   IndexedAggregate
   OrderedAbelianMonoidSup
   OrderedRing
   VectorSpace
   * b a
   directProduct c
   dot b a
   unitVector b

DivisionRing:
   Algebra
   EntireRing
   ** a
   inv a

DoublyLinkedAggregate:
   RecursiveAggregate
   concat! 
   head
   last
   next
   previous
   setnext!
   setprevious!
   tail

Eltable:
   elt x

EltableAggregate:
   Eltable
   elt
   qelt h
   qsetelt! h
   setelt

EntireRing:
   BiModule
   Ring

EuclideanDomain:
   PrincipalIdealDomain
   divide a
   euclideanSize g
   extendedEuclidean g
   multiEuclidean h
   quo a
   rem a
   sizeLess? h

Evalable:
   eval 

ExtensibleLinearAggregate:
   LinearAggregate
   concat! t
   delete! t
   insert! t
   merge! t
   remove! t
   removeDuplicates! t
   select! t 

Field:
   DivisionRing
   EuclideanDomain
   UniqueFactorizationDomain
   / a

FileCategory:
   SetCategory
   close! b
   iomode b
   name b
   open b
   read! b
   reopen! b
   write! b

FileNameCategory:
   SetCategory
   coerce v
   directory
   exists? b
   extension 
   filename
   name
   new c b
   readable? b
   writable? b

Finite:
   SetCategory
   index 
   lookup 
   random b
   size 


FiniteLinearAggregate:
   LinearAggregate
   OrderedSet
   copyInto!
   merge
   position
   reverse 
   reverse!
   sort
   sort!
   sorted?

FiniteSetAggregate:
   Dictionary
   Finite
   SetAggregate
   cardinality
   complement
   max
   min
   universe

FloatingPointSystem:
   RealNumberSystem
   base 
   bits
   decreasePrecision 
   digits b
   exponent b
   float
   increasePrecision
   mantissa b
   max
   order
   precision b


FreeAbelianMonoidCategory:
   Category

FullyEvalableOver:
   Eltable
   Evalable
   InnerEvalable
   map

FullyLinearlyExplicitRingOver:
   LinearlyExplicitRingOver
   LinearlyExplicitRingOver

FullyPatternMatchable:
   Object
   PatternMatchable
   PatternMatchable

FullyRetractableTo:
   RetractableTo
   RetractableTo
   RetractableTo

FunctionFieldCategory:
   Category

FunctionSpace:
   Category

GcdDomain:
   Category

GradedAlgebra:
   GradedModule
   One
   product

GradedModule:
   RetractableTo
   SetCategory
   *
   +
   -
   Zero
   degree

Group:
   Monoid
   ** a
   /  a
   commutator 
   conjugate
   inv a

HomogeneousAggregate:
   Aggregate
   SetCategory
   any? h
   count h
   every? h
   map t
   map! t
   member? 
   members h
   parts 

HyperbolicFunctionCategory:
   cosh t
   coth t
   csch t
   sech t
   sinh t 
   tanh t

IndexedAggregate:
   EltableAggregate
   HomogeneousAggregate
   entries h
   entry? h
   fill! t
   first x
   index? 
   indices h
   maxIndex b 
   minIndex h
   swap! t

IndexedDirectProductCategory:
   SetCategory
   leadingCoefficient
   leadingSupport
   map
   monomial
   reductum

InnerEvalable:
   eval

IntegerNumberSystem:
   CharacteristicZero
   CombinatorialFunctionCategory
   ConvertibleTo
   ConvertibleTo
   ConvertibleTo
   DifferentialRing
   EuclideanDomain
   LinearlyExplicitRingOver
   OrderedRing
   PatternMatchable
   RealConstant
   RetractableTo
   StepThrough
   UniqueFactorizationDomain
   addmod 
   base b
   bit? b
   copy 
   dec 
   even? b
   hash
   inc 
   invmod
   length b
   mask
   mulmod
   odd? b
   positiveRemainder
   powmod
   random
   rational h
   rational? h
   rationalIfCan h
   shift b
   submod
   symmetricRemainder

IntegralDomain:
   Algebra
   CommutativeRing
   EntireRing
   associates? 
   exquo a
   unit?
   unitCanonical h
   unitNormal h

KeyedDictionary:
   Dictionary
   key? 
   keys
   remove!
   search

LazyStreamAggregate:
   StreamAggregate
   complete
   explicitEntries? h
   explicitlyEmpty? h
   extend
   frst 
   lazy?
   lazyEvaluate h
   numberOfComputedEntries
   remove
   rst 
   select

LeftAlgebra:
   LeftModule
   Ring
   coerce

LeftModule:
   AbelianGroup
   * a

LinearAggregate:
   Collection
   IndexedAggregate
   concat t
   delete t
   elt x
   insert t
   map t
   new c
   setelt t

LinearlyExplicitRingOver:
   Ring
   reducedSystem

ListAggregate:
   ExtensibleLinearAggregate
   FiniteLinearAggregate
   StreamAggregate
   list c b

MatrixCategory:
   TwoDimensionalArrayCategory
   * a
   ** a
   + a
   - a
   / a
   antisymmetric?
   coerce
   determinant b
   diagonal? b
   diagonalMatrix c b
   elt h
   exquo a
   horizConcat
   inverse b t
   listOfLists
   matrix c
   minordet t
   nullSpace b
   nullity 
   rank b
   rowEchelon b c
   scalarMatrix 
   setelt h
   setsubMatrix! 
   square?
   squareTop
   subMatrix 
   swapColumns!
   swapRows!
   symmetric?
   transpose b t
   vertConcat 
   zero 

Module:
   BiModule

Monad:
   SetCategory
   *
   **
   leftPower
   rightPower

MonadWithUnit:
   Monad
   **
   One
   leftPower
   leftRecip
   one?
   recip
   rightPower
   rightRecip

MonogenicAlgebra:
   CommutativeRing
   ConvertibleTo
   DifferentialExtension
   Field
   Finite
   FiniteFieldCategory
   FramedAlgebra
   FullyLinearlyExplicitRingOver
   FullyRetractableTo
   convert
   definingPolynomial g
   derivationCoordinates g
   generator g
   lift g
   reduce t

MonogenicLinearOperator:
   Algebra
   BiModule
   Ring
   coefficient b x
   degree b x
   leadingCoefficient b x
   minimumDegree b x
   monomial b x
   reductum b x

Monoid:
   SemiGroup
   ** a
   One h
   one? h
   recip a

MultiDictionary:
   DictionaryOperations
   duplicates x
   insert! t
   removeDuplicates! t

MultisetAggregate:
   MultiDictionary
   SetAggregate

MultivariateTaylorSeriesCategory:
   Evalable
   InnerEvalable
   PartialDifferentialRing
   PowerSeriesCategory
   RadicalCategory
   TranscendentalFunctionCategory
   coefficient b x
   extend b t
   integrate t
   monomial b x
   order b x
   polynomial t

Object:

OctonionCategory:
   Algebra
   CharacteristicNonZero
   CharacteristicZero
   ConvertibleTo
   Finite
   FullyEvalableOver
   FullyRetractableTo
   OrderedSet
   abs a b
   conjugate t b
   imagE b x
   imagI b x
   imagJ b x
   imagK b x
   imagi b x
   imagj b x
   imagk b x
   inv   a t
   norm  b t
   octon c b
   rational h
   rational? h
   rationalIfCan h
   real b x

OneDimensionalArrayAggregate:
   FiniteLinearAggregate

OrderedAbelianGroup:
   AbelianGroup
   OrderedCancellationAbelianMonoid

OrderedAbelianMonoid:
   AbelianMonoid
   OrderedAbelianSemiGroup

OrderedAbelianMonoidSup:
   OrderedCancellationAbelianMonoid
   sup

OrderedAbelianSemiGroup:
   AbelianMonoid
   OrderedSet

OrderedCancellationAbelianMonoid:
   CancellationAbelianMonoid
   OrderedAbelianMonoid

OrderedFinite:
   Finite
   OrderedSet

OrderedMonoid:
   Monoid
   OrderedSet

OrderedMultisetAggregate:
   MultisetAggregate
   PriorityQueueAggregate
   min

OrderedRing:
   Monoid
   OrderedAbelianGroup
   Ring
   abs t
   negative? h
   positive? h
   sign t

OrderedSet:
   SetCategory
   < 
   max x 
   min x

PAdicIntegerCategory:
   CharacteristicZero
   EuclideanDomain
   approximate
   complete
   digits
   extend
   moduloP
   modulus
   order
   quotientByP
   sqrt

PartialDifferentialRing:
   Ring
   D t
   differentiate t

PartialTranscendentalFunctions:
   acosIfCan h
   acoshIfCan h
   acotIfCan h
   acothIfCan h
   acscIfCan h
   acschIfCan h
   asecIfCan h
   asechIfCan h
   asinIfCan h
   asinhIfCan h
   atanIfCan h
   atanhIfCan h
   cosIfCan h
   coshIfCan h
   cotIfCan h
   cothIfCan h
   cscIfCan h
   cschIfCan h
   expIfCan h
   logIfCan h
   nthRootIfCan h
   secIfCan h
   sechIfCan h
   sinIfCan h
   sinhIfCan h
   tanIfCan h
   tanhIfCan h

PatternMatchable:
   SetCategory
   patternMatch h

Patternable:
   ConvertibleTo
   ConvertibleTo
   Object

PermutationCategory:
   Group
   OrderedSet
   OrderedSet
   < 
   cycle b
   cycles b
   elt
   eval 
   orbit b

PlottablePlaneCurveCategory:
   CoercibleTo
   listBranches 
   xRange 
   yRange 

PlottableSpaceCurveCategory:
   CoercibleTo
   listBranches
   xRange
   yRange
   zRange

PointCategory:
   VectorCategory
   convert
   cross b
   dimension b
   extend b 
   point b

PolynomialCategory:
   ConvertibleTo
   ConvertibleTo
   ConvertibleTo
   Evalable
   FiniteAbelianMonoidRing
   FullyLinearlyExplicitRingOver
   GcdDomain
   InnerEvalable
   InnerEvalable
   OrderedSet
   PartialDifferentialRing
   PatternMatchable
   PatternMatchable
   PolynomialFactorizationExplicit
   RetractableTo
   coefficient b x
   content x
   degree b x
   discriminant x
   isExpt h
   isPlus h
   isTimes h
   mainVariable b 
   minimumDegree b x
   monicDivide a
   monomial b c
   monomials b x
   multivariate  c
   primitiveMonomials
   primitivePart t
   resultant x
   squareFree g x
   squareFreePart g x
   totalDegree g x
   univariate c
   variables x b

PolynomialFactorizationExplicit:
   UniqueFactorizationDomain
   charthRoot g x
   conditionP g h
   factorPolynomial 
   factorSquareFreePolynomial
   gcdPolynomial
   solveLinearPolynomialEquation
   squareFreePolynomial

PowerSeriesCategory:
   AbelianMonoidRing
   complete b t
   degree b x
   leadingCoefficient b x
   leadingMonomial b x
   monomial b c
   pole?
   variables b x

PrincipalIdealDomain:
   GcdDomain
   expressIdealMember
   principalIdeal

PriorityQueueAggregate:
   BagAggregate
   max x
   merge t
   merge! t

QuaternionCategory:
   Algebra
   CharacteristicNonZero
   CharacteristicZero
   ConvertibleTo
   DifferentialExtension
   DivisionRing
   EntireRing
   FullyEvalableOver
   FullyLinearlyExplicitRingOver
   FullyRetractableTo
   OrderedSet
   abs b a
   conjugate b t
   imagI b x
   imagJ b x
   imagK b x
   norm b x
   quatern b c
   rational h
   rational? h
   rationalIfCan h 
   real b x

QueueAggregate:
   BagAggregate
   back p x
   dequeue! 
   enqueue!
   front p x
   length p x
   rotate!

QuotientFieldCategory:
   Algebra
   CharacteristicNonZero
   CharacteristicZero
   ConvertibleTo
   DifferentialExtension
   Field
   FullyEvalableOver
   FullyLinearlyExplicitRingOver
   FullyPatternMatchable
   OrderedRing
   OrderedSet
   Patternable
   PolynomialFactorizationExplicit
   RealConstant
   RetractableTo
   RetractableTo
   RetractableTo
   RetractableTo
   StepThrough
   / 
   ceiling t
   denom b x
   denominator h x
   floor t
   fractionPart x b
   numer b x
   numerator h x
   random c b
   wholePart x b

RadicalCategory:
   ** 
   nthRoot b a
   sqrt b a

RealConstant:
   ConvertibleTo
   ConvertibleTo

RealNumberSystem:
   CharacteristicZero
   ConvertibleTo
   Field
   OrderedRing
   PatternMatchable
   RadicalCategory
   RealConstant
   RetractableTo
   RetractableTo
   abs b t
   ceiling b t
   floor b t
   fractionPart b x
   norm b x
   round b t
   truncate b t
   wholePart b x

RectangularMatrixCategory:
   BiModule
   HomogeneousAggregate
   Module
   / a
   antisymmetric?
   column b x
   diagonal?
   elt
   exquo 
   listOfLists h
   map b t
   matrix b c
   maxColIndex b x
   maxRowIndex b x
   minColIndex h x
   minRowIndex h x
   ncols b x
   nrows b x
   nullSpace g
   nullity g b
   qelt
   rank b x
   row b x
   rowEchelon b x
   square? h
   symmetric?

RecursiveAggregate:
   HomogeneousAggregate
   child?
   children
   cyclic? m
   distance 
   elt
   leaf? 
   leaves 
   node? 
   nodes 
   setchildren!
   setelt
   setvalue!
   value

RetractableTo:
   coerce 
   retract 
   retractIfCan 

RightModule:
   AbelianGroup
   * 

Ring:
   LeftModule
   Monoid
   Rng 
   characteristic h
   coerce

Rng:
   AbelianGroup
   SemiGroup

SegmentCategory:
   SetCategory
   BY h
   SEGMENT h
   convert
   hi h
   high b x
   incr b x
   lo h
   low b x
   segment c b

SegmentExpansionCategory:
   SegmentCategory
   expand b t
   map b t

SemiGroup:
   SetCategory
   * a
   ** a

SegmentCategory:
   SetCategory
   BY
   SEGMENT
   convert
   hi
   high
   incr
   lo
   low
   segment

SetAggregate:
   Collection
   SetCategory
   < 
   brace h
   difference b t
   intersect b t
   subset? b
   symmetricDifference b t
   union b t

SetCategory:
   CoercibleTo
   Object
   = 
   hash h
   latex h

SpecialFunctionCategory:
   Category

SquareMatrixCategory:
   Algebra
   BiModule
   DifferentialExtension
   FullyLinearlyExplicitRingOver
   FullyRetractableTo
   Module
   RectangularMatrixCategory
   * 
   **
   determinant x a
   diagonal x
   diagonalMatrix b c
   diagonalProduct t
   inverse b t
   minordet t
   scalarMatrix b c
   trace b x

StackAggregate:
   BagAggregate
   depth
   pop! b x
   push! b t
   top b x

StepThrough:
   SetCategory
   init 
   nextItem

StreamAggregate:
   LinearAggregate
   UnaryRecursiveAggregate
   explicitlyFinite? b 
   possiblyInfinite? b

StringAggregate:
   OneDimensionalArrayAggregate
   coerce 
   elt 
   leftTrim
   lowerCase t
   lowerCase! t
   match 
   match?
   position b x
   prefix? 
   replace b x
   rightTrim
   split t
   substring? 
   suffix? 
   trim t
   upperCase t
   upperCase! t

StringCategory:
   StringAggregate
   string

TableAggregate:
   IndexedAggregate
   KeyedDictionary
   map
   setelt
   table c b

ThreeSpaceCategory:
   SetCategory
   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

TrigonometricFunctionCategory:
   cos t
   cot t
   csc t
   sec t
   sin t
   tan t

TwoDimensionalArrayCategory:
   HomogeneousAggregate
   column b x
   elt
   fill! t
   map 
   map!
   maxColIndex x b
   maxRowIndex x b
   minColIndex h 
   minRowIndex h 
   ncols b x
   new b c
   nrows b x
   parts b c
   qelt 
   qsetelt!
   row b x
   setColumn! b t
   setRow! b t
   setelt

Type:

UnaryRecursiveAggregate:
   RecursiveAggregate
   concat b t
   concat! b t
   cycleEntry m 
   cycleLength m 
   cycleSplit! m 
   cycleTail m
   elt 
   first x b
   last x b
   rest x b 
   second x b
   setelt 
   setfirst!  x b
   setlast! x b
   setrest! x b
   split! x b
   tail x b
   third x b

UniqueFactorizationDomain:
   GcdDomain
   factor t
   prime?
   squareFree  t
   squareFreePart t

UnivariateLaurentSeriesCategory:
   Field
   RadicalCategory
   TranscendentalFunctionCategory
   UnivariatePowerSeriesCategory
   integrate b t
   multiplyCoefficients b t
   rationalFunction t

UnivariateLaurentSeriesConstructorCategory:
   QuotientFieldCategory
   RetractableTo
   UnivariateLaurentSeriesCategory
   coerce 
   degree b x
   laurent c b
   removeZeroes 
   taylor
   taylorIfCan
   taylorRep

UnivariatePolynomialCategory:
   DifferentialExtension
   DifferentialRing
   Eltable
   Eltable
   Eltable
   EuclideanDomain
   PolynomialCategory
   StepThrough
   composite b
   differentiate b
   discriminant 
   divideExponents
   elt
   integrate
   makeSUP
   monicDivide
   multiplyExponents
   order
   pseudoDivide
   pseudoQuotient
   pseudoRemainder
   resultant
   separate
   subResultantGcd
   unmakeSUP
   vectorise

UnivariatePowerSeriesCategory:
   DifferentialRing
   Eltable
   PowerSeriesCategory
   approximate
   center
   elt
   eval
   extend
   multiplyExponents
   order
   series
   terms
   truncate
   variable

UnivariatePuiseuxSeriesCategory:
   Field
   RadicalCategory
   TranscendentalFunctionCategory
   UnivariatePowerSeriesCategory
   integrate
   multiplyExponents

UnivariatePuiseuxSeriesConstructorCategory:
   RetractableTo
   UnivariatePuiseuxSeriesCategory
   coerce
   degree b
   laurent v
   laurentIfCan v 
   laurentRep 
   puiseux c
   rationalPower

UnivariateTaylorSeriesCategory:
   RadicalCategory
   TranscendentalFunctionCategory
   UnivariatePowerSeriesCategory
   **
   coefficients b x
   integrate 
   multiplyCoefficients
   polynomial v
   quoByVar
   series c 

VectorCategory:
   OneDimensionalArrayAggregate
   *
   +
   -
   dot t b
   length b x
   magnitude b x
   zero b c

VectorSpace:
   Module
   /
   dimension b x

--Manuel's list
AlgebraicallyClosedFunctionSpace:
   AlgebraicallyClosedField
   FunctionSpace
   rootOf  b x
   rootsOf b x
   zeroOf  b x
   zerosOf b x
 
CombinatorialFunctionCategory:
   binomial     
   factorial    
   permutation  
 
CombinatorialOpsCategory:
   CombinatorialFunctionCategory
   factorials   e t
   product      b a
   summation    b a
 
ElementaryFunctionCategory:
   **          b a
   exp g       b t
   log g       b t
 
ExpressionSpace:
   Evalable
   InnerEvalable
   OrderedSet
   RetractableTo
   belong?                h
   box                    h t
   definingPolynomial     e x
   distribute             e t
   elt                    b t
   eval                   b t
   freeOf?                b
   height                 h x
   is?                    b
   kernel                 h c
   kernels                e x
   mainKernel             e x
   map                    e t
   minPoly                h x
   operator               h t
   operators              e x
   paren                  e t
   subst                  b t
   tower                  e x
 
LiouvillianFunctionCategory:
   PrimitiveFunctionCategory
   TranscendentalFunctionCategory
   Ci          b t
   Ei          b t
   Si          b t
   dilog       b t
   erf         b t
   li          b t
 
PrimitiveFunctionCategory:
   integral    e t
 
-- SEXCAT should probably be annotated by Stephen
SExpressionCategory:
   SetCategory
   # b
   atom? b
   car b
   cdr b
   convert
   destruct
   elt
   eq b
   expr
   float
   float? b
   integer
   integer? b
   list? b
   null? b
   pair? b
   string
   string? b
   symbol
   symbol? b
 
TranscendentalFunctionCategory:
   ArcHyperbolicFunctionCategory
   ArcTrigonometricFunctionCategory
   ElementaryFunctionCategory
   HyperbolicFunctionCategory
   TrigonometricFunctionCategory
   pi   b c
 
--Johannes's list
AbelianMonoidRing:
   Algebra h a
   Algebra h a
   BiModule h a
   CharacteristicNonZero h a
   CharacteristicZero h a
   CommutativeRing h a
   IntegralDomain h a
   Ring h a
   /   
   coefficient b x
   degree  b x
   leadingCoefficient b x
   leadingMonomial b x
   map t
   monomial b c
   monomial?  p
   reductum b t
 
CharacteristicNonZero:
   Ring b a
   charthRoot a
 
ExtensionField:
   CharacteristicZero h a
   Field h a
   FieldOfPrimeCharacteristic h a
   FieldOfPrimeCharacteristic h a
   RetractableTo h d
   VectorSpace h a
   Frobenius a
   algebraic? b p
   degree  b x
   extensionDegree b d
   inGroundField? b x p
   transcendenceDegree b d
   transcendent? b p
 
FieldOfPrimeCharacteristic: 
   CharacteristicNonZero h a
   Field h a
   discreteLog b a
   order x
   primeFrobenius a
 
 
FiniteAbelianMonoidRing:
   AbelianMonoidRing h a
   FullyRetractableTo h d
   coefficients b x
   content x
   exquo a
   ground x
   ground? p
   mapExponents t
   minimumDegree x
   numberOfMonomials x
   primitivePart t
 
FiniteAlgebraicExtensionField:
   ExtensionField h a
   FiniteFieldCategory h a
   RetractableTo h d
   basis  b c d
   coordinates b x
   createNormalElement c
   definingPolynomial d
   degree x
   extensionDegree b d
   generator c a
   linearAssociatedExp a
   linearAssociatedLog a
   linearAssociatedOrder a
   minimalPolynomial d
   norm b x a
   normal? a p
   normalElement a c
   represents v
   trace e a
 
FiniteDivisorCategory:
   Category h d
 
FiniteFieldCategory:
   FieldOfPrimeCharacteristic h a
   Finite h d
   StepThrough h d
   charthRoot a
   conditionP h a
   createPrimitiveElement c
   discreteLog b a
   factorsOfCyclicGroupSize h a
   order a e
   primitive? a p
   primitiveElement a c
   representationType h a d
   tableForDiscreteLogarithm h a d
 
FiniteRankAlgebra:
   Algebra h a
   CharacteristicNonZero h a
   CharacteristicZero h a
   characteristicPolynomial b a d
   coordinates b x v
   discriminant b d a
   minimalPolynomial b d a
   norm b x a
   rank b d a
   regularRepresentation a v
   represents b x
   trace b a
   traceMatrix a
 
FiniteRankNonAssociativeAlgebra:
   NonAssociativeAlgebra h a
   alternative?     p a d
   antiAssociative? p a d
   antiCommutative? p a d
   associative? p a d
   associatorDependence p a
   commutative? p a d
   conditionsForIdempotents p a
   coordinates b x
   flexible? p a d
   jacobiIdentity? p a d
   jordanAdmissible? p a d
   jordanAlgebra? p a d
   leftAlternative? p a d
   leftCharacteristicPolynomial b a d
   leftDiscriminant b a
   leftMinimalPolynomial b a  d
   leftNorm b a x
   leftRecip b  a
   leftRegularRepresentation a
   leftTrace  b a d
   leftTraceMatrix a
   leftUnit a
   leftUnits a
   lieAdmissible? p a d
   lieAlgebra? p a d
   noncommutativeJordanAlgebra? p a d
   powerAssociative? b a d
   rank  b d a
   recip  a
   represents b  c
   rightAlternative? p a d
   rightCharacteristicPolynomial b a d
   rightDiscriminant b a
   rightMinimalPolynomial b a d
   rightNorm b a x
   rightRecip b a
   rightRegularRepresentation a
   rightTrace b a d
   rightTraceMatrix a
   rightUnit a
   rightUnits a
   someBasis b c
   structuralConstants b d
   unit a
 
FramedAlgebra:
   FiniteRankAlgebra h a
   basis b c
   convert b x v
   coordinates b x v
   discriminant b a
   regularRepresentation  a v
   represents b c
   traceMatrix a
 
FramedNonAssociativeAlgebra:
   FiniteRankNonAssociativeAlgebra  h a
   apply a
   basis b c
   conditionsForIdempotents a
   convert  b x
   coordinates b x
   elt b x
   leftDiscriminant a
   leftRankPolynomial a d
   leftRegularRepresentation a v
   leftTraceMatrix a
   represents  b c
   rightDiscriminant a
   rightRankPolynomial a d
   rightRegularRepresentation a
   rightTraceMatrix a
   structuralConstants b d
 
NonAssociativeAlgebra:
   Module h a
   NonAssociativeRng h a
   plenaryPower a
 
NonAssociativeRing:
   MonadWithUnit h a
   NonAssociativeRng h a
   characteristic b d
   coerce b c
 
NonAssociativeRng:
   AbelianGroup h a
   Monad h a
   antiCommutator b a
   associator b a
   commutator b a
 
------> Domains 
AlgebraGivenByStructuralConstants:
   FramedNonAssociativeAlgebra
   LeftModule
   coerce

AlgebraicNumber:
   AlgebraicallyClosedField
   CharacteristicZero
   ConvertibleTo
   DifferentialRing
   ExpressionSpace
   LinearlyExplicitRingOver
   LinearlyExplicitRingOver
   RealConstant
   RetractableTo
   RetractableTo
   coerce
   denom
   numer
   reduce

Any:
   SetCategory
   any
   dom
   domainOf
   obj
   objectOf
   showTypeInOutput

ArrayStack:
   StackAggregate
   arrayStack

AssociatedJordanAlgebra:
   CoercibleTo
   FiniteRankNonAssociativeAlgebra
   FramedNonAssociativeAlgebra
   NonAssociativeAlgebra
   coerce

AssociatedLieAlgebra:
   CoercibleTo
   FiniteRankNonAssociativeAlgebra
   FramedNonAssociativeAlgebra
   NonAssociativeAlgebra
   coerce

BalancedBinaryTree:
   BinaryTreeCategory
   balancedBinaryTree
   mapDown!
   mapUp!
   setleaves!

BasicOperator:
   OrderedSet
   arity
   assert
   comparison
   copy
   deleteProperty!
   display
   equality
   has?
   input
   is?
   name
   nary?
   nullary?
   operator
   properties
   property
   setProperties
   setProperty
   unary?
   weight

BinaryExpansion:
   QuotientFieldCategory
   binary
   coerce
   fractionPart

BinaryFile:
   FileCategory
   #
   position
   position!
   readIfCan!

BinarySearchTree:
   BinaryTreeCategory
   binarySearchTree
   insert!
   insertRoot!
   split

BinaryTournament:
   BinaryTreeCategory
   binaryTournament
   insert!

BinaryTree:
   BinaryTreeCategory
   binaryTree

Bits:
   BitAggregate
   bits

Boolean:
   ConvertibleTo
   Finite
   OrderedSet
   ^
   and
   false
   implies
   nand
   nor
   not
   or
   true
   xor

CardinalNumber:
   AbelianMonoid
   Monoid
   OrderedSet
   RetractableTo
   **
   -
   Aleph
   countable?
   finite?
   generalizedContinuumHypothesisAssumed
   generalizedContinuumHypothesisAssumed?

CartesianTensor:
   GradedAlgebra
   GradedAlgebra
   *
   coerce
   contract
   elt
   kroneckerDelta
   leviCivitaSymbol
   product
   rank
   ravel
   reindex
   transpose
   unravel

Character:
   OrderedFinite
   alphabetic?
   alphanumeric?
   char
   digit?
   escape
   hexDigit?
   lowerCase
   lowerCase?
   ord
   quote
   space
   upperCase
   upperCase?

CharacterClass:
   ConvertibleTo
   ConvertibleTo
   FiniteSetAggregate
   SetCategory
   alphabetic
   alphanumeric
   charClass
   digit
   hexDigit
   lowerCase
   upperCase

CliffordAlgebra:
   Algebra
   Ring
   VectorSpace
   coefficient
   e
   monomial

Color:
   AbelianSemiGroup
   *
   +
   blue
   color
   green
   hue
   numberOfHues
   red
   yellow

Commutator:
   SetCategory
   mkcomm

Complex:
   ComplexCategory

ContinuedFraction:
   Algebra
   Algebra
   Field
   approximants
   complete
   continuedFraction
   convergents
   denominators
   extend
   numerators
   partialDenominators
   partialNumerators
   partialQuotients
   reducedContinuedFraction
   reducedForm
   wholePart

DataList:
   ListAggregate
   coerce
   datalist
   elt

Database:
   SetCategory
   +
   -
   coerce
   display
   elt
   fullDisplay

DecimalExpansion:
   QuotientFieldCategory
   coerce
   decimal
   fractionPart

DenavitHartenbergMatrix:
   MatrixCategory
   *
   identity
   rotatex
   rotatey
   rotatez
   scale
   translate

Dequeue:
   DequeueAggregate
   dequeue

DrawOption:
   SetCategory
   adaptive
   clip
   colorFunction
   coord
   coordinates
   curveColor
   option
   option?
   pointColor
   range
   ranges
   space
   style
   title
   toScale
   tubePoints
   tubeRadius
   unit
   var1Steps
   var2Steps
   viewpoint

Equation:
   AbelianGroup
   AbelianSemiGroup
   BiModule
   CoercibleTo
   Group
   InnerEvalable
   Module
   Monoid
   Object
   PartialDifferentialRing
   Ring
   SemiGroup
   SetCategory
   VectorSpace
   *
   +
   -
   =
   equation
   eval
   factorAndSplit
   leftOne
   leftZero
   lhs
   map
   rhs
   rightOne
   rightZero
   switch

Exit:
   SetCategory

Expression:
   AlgebraicallyClosedFunctionSpace
   CombinatorialOpsCategory
   FunctionSpace
   LiouvillianFunctionCategory
   RetractableTo
   SpecialFunctionCategory
   TranscendentalFunctionCategory
   reduce

Factored:
   Algebra
   ConvertibleTo
   DifferentialExtension
   Eltable
   Evalable
   FullyEvalableOver
   FullyRetractableTo
   GcdDomain
   InnerEvalable
   IntegralDomain
   RealConstant
   UniqueFactorizationDomain
   expand
   exponent
   factorList
   factors
   flagFactor
   irreducibleFactor
   makeFR
   map
   nilFactor
   nthExponent
   nthFactor
   nthFlag
   numberOfFactors
   primeFactor
   rational
   rational?
   rationalIfCan
   sqfrFactor
   unit
   unitNormalize

File:
   FileCategory
   readIfCan!

FileName:
   FileNameCategory

FiniteField:
   FiniteAlgebraicExtensionField

FiniteFieldCyclicGroup:
   FiniteAlgebraicExtensionField
   getZechTable

FiniteFieldNormalBasis:
   FiniteAlgebraicExtensionField
   getMultiplicationMatrix
   getMultiplicationTable
   sizeMultiplication

FlexibleArray:
   ExtensibleLinearAggregate
   OneDimensionalArrayAggregate
   flexibleArray
   physicalLength
   physicalLength!
   shrinkable

Float:
   CoercibleTo
   ConvertibleTo
   ConvertibleTo
   DifferentialRing
   FloatingPointSystem
   TranscendentalFunctionCategory
   **
   /
   atan
   convert
   exp1
   log10
   log2
   normalize
   outputFixed
   outputFloating
   outputGeneral
   outputSpacing
   rationalApproximation
   relerror
   shift

Fraction:
   QuotientFieldCategory

FreeNilpotentLie:
   NonAssociativeAlgebra
   deepExpand
   dimension
   generator
   shallowExpand

Heap:
   PriorityQueueAggregate
   heap

HexadecimalExpansion:
   QuotientFieldCategory
   coerce
   fractionPart
   hex

IndexCard:
   OrderedSet
   coerce
   display
   elt
   fullDisplay

InfiniteTuple:
   CoercibleTo
   construct
   filterUntil
   filterWhile
   generate
   map
   select

Integer:
   ConvertibleTo
   IntegerNumberSystem
   random

KeyedAccessFile:
   FileCategory
   TableAggregate
   pack!

Library:
   TableAggregate
   elt
   library
   pack!
   setelt

LieSquareMatrix:
   CoercibleTo
   FramedNonAssociativeAlgebra
   SquareMatrixCategory

LinearOrdinaryDifferentialOperator:
   MonogenicLinearOperator
   D
   adjoint 
   coerce
   elt
   leftDivide 
   leftExactQuotient
   leftGcd
   leftLcm
   leftQuotient
   leftRemainder
   rightDivide
   rightExactQuotient
   rightGcd
   rightLcm
   rightQuotient
   rightRemainder
   symmetricPower
   symmetricProduct
   symmetricSquare

List:
   ListAggregate
   append
   cons
   nil
   null
   setDifference
   setIntersection
   setUnion

Matrix:
   ConvertibleTo
   MatrixCategory
   diagonalMatrix
   inverse

ModuleOperator:
   Algebra
   CharacteristicNonZero
   CharacteristicZero
   Eltable
   RetractableTo
   RetractableTo
   Ring
   **
   evaluate
   evaluateInverse
   opeval

Multiset:
   MultisetAggregate
   multiset

MultivariatePolynomial:
   PolynomialCategory

NonNegativeInteger:
   Monoid
   OrderedAbelianMonoidSup
   divide
   exquo
   gcd
   quo
   rem

Octonion:
   FullyRetractableTo
   OctonionCategory
   octon

OneDimensionalArray:
   OneDimensionalArrayAggregate
   oneDimensionalArray

OnePointCompletion:
   AbelianGroup
   FullyRetractableTo
   OrderedRing
   SetCategory
   finite?
   infinite?
   infinity
   rational
   rational?
   rationalIfCan

Operator:
   Algebra
   CharacteristicNonZero
   CharacteristicZero
   Eltable
   RetractableTo
   RetractableTo
   Ring
   **
   evaluate
   evaluateInverse
   opeval

OrdSetInts:
   OrderedSet
   coerce
   value

OrderedCompletion:
   AbelianGroup
   FullyRetractableTo
   OrderedRing
   SetCategory
   finite?
   infinite?
   minusInfinity
   plusInfinity
   rational
   rational?
   rationalIfCan
   whatInfinity

OrdinaryDifferentialRing:
   Algebra
   DifferentialRing
   Field
   coerce

Palette:
   SetCategory
   bright
   coerce
   dark
   dim
   hue
   light
   pastel
   shade

ParametricPlaneCurve:
   coordinate
   curve

ParametricSpaceCurve:
   coordinate
   curve

ParametricSurface:
   coordinate
   surface

PartialFraction:
   Algebra
   Field
   coerce
   compactFraction
   firstDenom
   firstNumer
   nthFractionalTerm
   numberOfFractionalTerms
   padicFraction
   padicallyExpand
   partialFraction
   wholePart

PendantTree:
   BinaryRecursiveAggregate
   coerce
   ptree

Permutation:
   PermutationCategory
   coerce
   coerceImages
   coerceListOfPairs
   coercePreimagesImages
   cyclePartition
   degree
   even?
   fixedPoints
   listRepresentation
   movedPoints
   numberOfCycles
   odd?
   order
   sign
   sort

PermutationGroup:
   SetCategory
   <
   <=
   base
   coerce
   degree
   elt
   generators
   initializeGroupForWordProblem
   member?
   movedPoints
   orbit
   orbits
   order
   permutationGroup
   random
   strongGenerators
   wordInGenerators
   wordInStrongGenerators
   wordsForStrongGenerators

Pi:
   CharacteristicZero
   CoercibleTo
   CoercibleTo
   ConvertibleTo
   ConvertibleTo
   Field
   RealConstant
   RetractableTo
   RetractableTo
   pi

Polynomial:
   PolynomialCategory
   integrate

PolynomialIdeals:
   SetCategory
   *
   **
   +
   backOldPos
   coerce
   contract
   dimension
   element?
   generalPosition
   generators
   groebner
   groebner?
   groebnerIdeal
   ideal
   in?
   inRadical?
   intersect
   leadingIdeal
   one?
   quotient
   relationsIdeal
   saturate
   zeroDim?

PositiveInteger:
   AbelianSemiGroup
   Monoid
   OrderedSet
   gcd

PrimeField:
   ConvertibleTo
   FiniteAlgebraicExtensionField
   FiniteFieldCategory

QuadraticForm:
   AbelianGroup
   elt
   matrix
   quadraticForm

Quaternion:
   QuaternionCategory

QueryEquation:
   equation
   value
   variable

Queue:
   QueueAggregate
   queue

RadixExpansion:
   QuotientFieldCategory
   coerce
   cycleRagits
   fractRadix
   fractRagits
   fractionPart
   prefixRagits
   wholeRadix
   wholeRagits

RewriteRule:
   Eltable
   RetractableTo
   SetCategory
   elt
   lhs
   pattern
   quotedOperators
   rhs
   rule
   suchThat

RomanNumeral:
   IntegerNumberSystem
   convert
   roman

Ruleset:
   Eltable
   SetCategory
   elt
   rules
   ruleset

ScriptFormulaFormat:
   SetCategory
   coerce
   convert
   display
   epilogue
   formula
   new
   prologue
   setEpilogue!
   setFormula!
   setPrologue!

ScriptFormulaFormat1:
   Object
   coerce

Segment:
   SegmentCategory
   SegmentExpansionCategory

SegmentBinding:
   SetCategory
   equation
   segment
   variable

Set:
   FiniteSetAggregate

SmallFloat:
   ConvertibleTo
   DifferentialRing
   FloatingPointSystem
   TranscendentalFunctionCategory
   **
   /
   Beta
   Gamma
   atan
   exp1
   hash
   log10
   log2
   rationalApproximation

SmallInteger:
   IntegerNumberSystem
   And
   Not
   Or
   ^
   and
   max
   min
   not
   or
   xor

Stack:
   StackAggregate
   stack

Stream:
   LazyStreamAggregate
   coerce
   cons
   delay
   filterUntil
   filterWhile
   findCycle
   generate
   output
   repeating
   repeating?
   setrest!
   showAll?
   showAllElements

String:
   StringCategory

Symbol:
   ConvertibleTo
   ConvertibleTo
   ConvertibleTo
   ConvertibleTo
   OrderedSet
   PatternMatchable
   PatternMatchable
   argscript
   coerce
   elt
   list
   name
   new
   resetNew
   script
   scripted?
   scripts
   string
   subscript
   superscript

Tableau:
   Object
   coerce
   listOfLists
   tableau

TaylorSeries:
   MultivariateTaylorSeriesCategory
   coefficient
   coerce
   fintegrate
   integrate

TexFormat:
   SetCategory
   coerce
   convert
   display
   epilogue
   new
   prologue
   setEpilogue!
   setPrologue!
   setTex!
   tex

TexFormat1:
   Object
   coerce

TextFile:
   FileCategory
   endOfFile?
   readIfCan!
   readLine!
   readLineIfCan!
   writeLine!

ThreeDimensionalViewport:
   SetCategory
   axes
   clipSurface
   close
   colorDef
   controlPanel
   diagonals
   dimensions
   drawStyle
   eyeDistance
   hitherPlane
   intensity
   key
   lighting
   makeViewport3D
   modifyPointData
   move
   options
   outlineRender
   perspective
   reset
   resize
   rotate
   showClipRegion
   showRegion
   subspace
   title
   translate
   viewDeltaXDefault
   viewDeltaYDefault
   viewPhiDefault
   viewThetaDefault
   viewZoomDefault
   viewpoint
   viewport3D
   write
   zoom

ThreeSpace:
   ThreeSpaceCategory

Tree:
   RecursiveAggregate
   tree

UnivariatePolynomial:
   UnivariatePolynomialCategory
   coerce

UniversalSegment:
   SegmentCategory
   SegmentExpansionCategory
   SEGMENT
   coerce
   hasHi
   segment

Vector:
   VectorCategory
   vector

Void:
   coerce
   void