]>
Book Contents Previous Section 17.1 Axiom Categories Next Section 19.1 Axiom Packages Book Index

## 18.1 Axiom Domains

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

This sample entry will help you read the following table:

DomainName{DomainAbbreviation}:{ Category 1 ... Category N}with { op 1... op M}

where

DomainName | is the full domain name, e.g., Integer.
DomainAbbreviation | is the domain abbreviation, e.g., INT.
Category i | is a category to which the domain belongs.
op j | is an operation exported by the domain.

Abbreviation: | ALGSC
Full name: | AlgebraGivenByStructuralConstants
Belongs to: | FramedNonAssociativeAlgebra LeftModule

Operations:

0 * ** + - = JacobiIdentity? JordanAlgebra? alternative? antiAssociative? antiCommutative? antiCommutator apply associative? associator associatorDependence basis coerce commutative? commutator conditionsForIdempotents convert coordinates elt flexible? jordanAdmissible? leftAlternative? leftCharacteristicPolynomial leftDiscriminant leftMinimalPolynomial leftNorm leftPower leftRankPolynomial leftRecip leftRegularRepresentation leftTrace leftTraceMatrix leftUnit leftUnits lieAdmissible? lieAlgebra? noncommutativeJordanAlgebra? plenaryPower powerAssociative? rank recip represents rightAlternative? rightCharacteristicPolynomial rightDiscriminant rightMinimalPolynomial rightNorm rightPower rightRankPolynomial rightRecip rightRegularRepresentation rightTrace rightTraceMatrix rightUnit rightUnits someBasis structuralConstants unit zero?

Abbreviation: | ALGFF
Full name: | AlgebraicFunctionField
Belongs to: | FunctionFieldCategory

Operations:

0 1 * ** + - / = D absolutelyIrreducible? associates? basis branchPoint? branchPointAtInfinity? characteristic characteristicPolynomial charthRoot coerce complementaryBasis convert coordinates definingPolynomial derivationCoordinates differentiate discriminant divide elt euclideanSize expressIdealMember exquo extendedEuclidean factor gcd generator genus integral? integralAtInfinity? integralBasis integralBasisAtInfinity integralCoordinates integralDerivationMatrix integralMatrix integralMatrixAtInfinity integralRepresents inv inverseIntegralMatrix inverseIntegralMatrixAtInfinity knownInfBasis lcm lift minimalPolynomial multiEuclidean nonSingularModel norm normalizeAtInfinity numberOfComponents one? prime? primitivePart principalIdeal quo ramified? ramifiedAtInfinity? rank rationalPoint? rationalPoints recip reduce reduceBasisAtInfinity reducedSystem regularRepresentation rem represents retract retractIfCan singular? singularAtInfinity? sizeLess? squareFree squareFreePart trace traceMatrix unit? unitCanonical unitNormal yCoordinates zero?

Abbreviation: | AN
Full name: | AlgebraicNumber
Belongs to: | AlgebraicallyClosedField CharacteristicZero ConvertibleTo DifferentialRing ExpressionSpace LinearlyExplicitRingOver RealConstant RetractableTo

Operations:

0 1 * ** + - / < = D associates? belong? box characteristic coerce convert definingPolynomial denom differentiate distribute divide elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor freeOf? gcd height inv is? kernel kernels lcm mainKernel map max min minPoly multiEuclidean nthRoot numer one? operator operators paren prime? principalIdeal quo recip reduce reducedSystem rem retract retractIfCan rootOf rootsOf sizeLess? sqrt squareFree squareFreePart subst tower unit? unitCanonical unitNormal zero? zeroOf zerosOf

Abbreviation: | ANON
Full name: | AnonymousFunction
Belongs to: | SetCategory
Operations: | = coerce

Abbreviation: | ANTISYM
Full name: | AntiSymm
Belongs to: | LeftAlgebra RetractableTo
Operations: | 0 1 * ** + - = characteristic coefficient coerce degree exp generator homogeneous? leadingBasisTerm leadingCoefficient map one? recip reductum retract retractIfCan retractable? zero?

Abbreviation: | ANY
Full name: | Any
Belongs to: | SetCategory
Operations: | = any coerce domain domainOf obj objectOf showTypeInOutput

Abbreviation: | ASTACK
Full name: | ArrayStack
Belongs to: | StackAggregate
Operations: | # = any? arrayStack bag coerce copy count depth empty empty? eq? every? extract! insert! inspect less? map map! member? members more? parts pop! push! size? top

Abbreviation: | JORDAN
Full name: | AssociatedJordanAlgebra
Belongs to: | CoercibleTo FiniteRankNonAssociativeAlgebra FramedNonAssociativeAlgebra NonAssociativeAlgebra

Operations:

0 * ** + - = JacobiIdentity? JordanAlgebra? alternative? antiAssociative? antiCommutative? antiCommutator apply associative? associator associatorDependence basis coerce commutative? commutator conditionsForIdempotents convert coordinates elt flexible? jordanAdmissible? leftAlternative? leftCharacteristicPolynomial leftDiscriminant leftMinimalPolynomial leftNorm leftPower leftRankPolynomial leftRecip leftRegularRepresentation leftTrace leftTraceMatrix leftUnit leftUnits lieAdmissible? lieAlgebra? noncommutativeJordanAlgebra? plenaryPower powerAssociative? rank recip represents rightAlternative? rightCharacteristicPolynomial rightDiscriminant rightMinimalPolynomial rightNorm rightPower rightRankPolynomial rightRecip rightRegularRepresentation rightTrace rightTraceMatrix rightUnit rightUnits someBasis structuralConstants unit zero?

Abbreviation: | LIE
Full name: | AssociatedLieAlgebra
Belongs to: | CoercibleTo FiniteRankNonAssociativeAlgebra FramedNonAssociativeAlgebra NonAssociativeAlgebra

Operations:

0 * ** + - = JacobiIdentity? JordanAlgebra? alternative? antiAssociative? antiCommutative? antiCommutator apply associative? associator associatorDependence basis coerce commutative? commutator conditionsForIdempotents convert coordinates elt flexible? jordanAdmissible? leftAlternative? leftCharacteristicPolynomial leftDiscriminant leftMinimalPolynomial leftNorm leftPower leftRankPolynomial leftRecip leftRegularRepresentation leftTrace leftTraceMatrix leftUnit leftUnits lieAdmissible? lieAlgebra? noncommutativeJordanAlgebra? plenaryPower powerAssociative? rank recip represents rightAlternative? rightCharacteristicPolynomial rightDiscriminant rightMinimalPolynomial rightNorm rightPower rightRankPolynomial rightRecip rightRegularRepresentation rightTrace rightTraceMatrix rightUnit rightUnits someBasis structuralConstants unit zero?

Abbreviation: | ALIST
Full name: | AssociationList
Belongs to: | AssociationListAggregate

Operations:

# = any? assoc bag child? children coerce concat concat! construct copy copyInto! count cycleEntry cycleLength cycleSplit! cycleTail cyclic? delete delete! dictionary distance elt empty empty? entries entry? eq? every? explicitlyFinite? extract! fill! find first index? indices insert insert! inspect key? keys last leaf? less? list map map! maxIndex member? members merge merge! minIndex more? new node? nodes parts position possiblyInfinite? qelt qsetelt! reduce remove remove! removeDuplicates removeDuplicates! rest reverse reverse! search second select select! setchildren! setelt setfirst! setlast! setrest! setvalue! size? sort sort! sorted? split! swap! table tail third value

Abbreviation: | BBTREE
Full name: | BalancedBinaryTree
Belongs to: | BinaryTreeCategory
Operations: | # = any? balancedBinaryTree children coerce copy count cyclic? elt empty empty? eq? every? leaf? leaves left less? map map! mapDown! mapUp! member? members more? node node? nodes parts right setchildren! setelt setleaves! setleft! setright! setvalue! size? value

Abbreviation: | BPADIC
Full name: | BalancedPAdicInteger
Belongs to: | PAdicIntegerCategory
Operations: | 0 1 * ** + - = approximate associates? characteristic coerce complete digits divide euclideanSize expressIdealMember exquo extend extendedEuclidean gcd lcm moduloP modulus multiEuclidean one? order principalIdeal quo quotientByP recip rem sizeLess? sqrt unit? unitCanonical unitNormal zero?

Abbreviation: | BPADICRT
Full name: | BalancedPAdicRational
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / = D approximate associates? characteristic coerce continuedFraction denom denominator differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor fractionPart gcd inv lcm map multiEuclidean numer numerator one? prime? principalIdeal quo recip reducedSystem rem removeZeroes retract retractIfCan sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | BOP
Full name: | BasicOperator
Belongs to: | OrderedSet
Operations: | < = arity assert coerce comparison copy deleteProperty! display equality has? input is? max min name nary? nullary? operator properties property setProperties setProperty unary? weight

Abbreviation: | BINARY
Full name: | BinaryExpansion
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs associates? binary ceiling characteristic coerce convert denom denominator differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor floor fractionPart gcd init inv lcm map max min multiEuclidean negative? nextItem numer numerator one? patternMatch positive? prime? principalIdeal quo random recip reducedSystem rem retract retractIfCan sign sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | BSTREE
Full name: | BinarySearchTree
Belongs to: | BinaryTreeCategory
Operations: | # = any? binarySearchTree children coerce copy count cyclic? elt empty empty? eq? every? insert! insertRoot! leaf? leaves left less? map map! member? members more? node node? nodes parts right setchildren! setelt setleft! setright! setvalue! size? split value

count cyclic? elt empty empty? eq? every? insert! leaf? leaves left less? map map! member? members more? node node? nodes parts right setchildren! setelt setleft! setright! setvalue! size? value}

Abbreviation: | BTREE
Full name: | BinaryTree
Belongs to: | BinaryTreeCategory
Operations: | # = any? binaryTree children coerce copy count cyclic? elt empty empty? eq? every? leaf? leaves left less? map map! member? members more? node node? nodes parts right setchildren! setelt setleft! setright! setvalue! size? value

Abbreviation: | BITS
Full name: | Bits
Belongs to: | BitAggregate
Operations: | # < = \^{} and any? bits coerce concat construct convert copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? nand new nor not or parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap! xor

Abbreviation: | BOOLEAN
Full name: | Boolean
Belongs to: | ConvertibleTo Finite OrderedSet
Operations: | < = \^{} and coerce convert false implies index lookup max min nand nor not or random size true xor

Abbreviation: | CARD
Full name: | CardinalNumber
Belongs to: | CancellationAbelianMonoid Monoid OrderedSet RetractableTo
Operations: | 0 1 * ** + - < = Aleph coerce countable? finite? generalizedContinuumHypothesisAssumed generalizedContinuumHypothesisAssumed? max min one? recip retract retractIfCan zero?

Abbreviation: | CARTEN
Full name: | CartesianTensor
Belongs to: | GradedAlgebra
Operations: | 0 1 * + - = coerce contract degree elt kroneckerDelta leviCivitaSymbol product rank ravel reindex retract retractIfCan transpose unravel

Abbreviation: | CCLASS
Full name: | CharacterClass
Belongs to: | ConvertibleTo FiniteSetAggregate SetCategory

Operations:

# < = alphabetic alphanumeric any? bag brace cardinality charClass coerce complement construct convert copy count dictionary difference digit empty empty? eq? every? extract! find hexDigit index insert! inspect intersect less? lookup lowerCase map map! max member? members min more? parts random reduce remove remove! removeDuplicates select select! size size? subset? symmetricDifference union universe upperCase

Abbreviation: | CHAR
Full name: | Character
Belongs to: | OrderedFinite
Operations: | < = alphabetic? alphanumeric? char coerce digit? escape hexDigit? index lookup lowerCase lowerCase? max min ord quote random size space upperCase upperCase?

Abbreviation: | CLIF
Full name: | CliffordAlgebra
Belongs to: | Algebra Ring VectorSpace
Operations: | 0 1 * ** + - / = characteristic coefficient coerce dimension e monomial one? recip zero?

Abbreviation: | COLOR
Full name: | Color
Belongs to: | AbelianSemiGroup
Operations: | * + = blue coerce color green hue numberOfHues red yellow

Abbreviation: | COMM
Full name: | Commutator
Belongs to: | SetCategory
Operations: | = coerce mkcomm

Abbreviation: | COMPLEX
Full name: | Complex
Belongs to: | ComplexCategory

Operations:

0 1 * ** + - / < = D abs acos acosh acot acoth acsc acsch argument asec asech asin asinh associates? atan atanh basis characteristic characteristicPolynomial charthRoot coerce complex conditionP conjugate convert coordinates cos cosh cot coth createPrimitiveElement csc csch definingPolynomial derivationCoordinates differentiate discreteLog discriminant divide elt euclideanSize eval exp expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial factorsOfCyclicGroupSize gcd gcdPolynomial generator imag imaginary index init inv lcm lift log lookup map max min minimalPolynomial multiEuclidean nextItem norm nthRoot one? order pi polarCoordinates prime? primeFrobenius primitive? primitiveElement principalIdeal quo random rank rational rational? rationalIfCan real recip reduce reducedSystem regularRepresentation rem representationType represents retract retractIfCan sec sech sin sinh size sizeLess? solveLinearPolynomialEquation sqrt squareFree squareFreePart squareFreePolynomial tableForDiscreteLogarithm tan tanh trace traceMatrix unit? unitCanonical unitNormal zero?

Abbreviation: | CONTFRAC
Full name: | ContinuedFraction
Belongs to: | Algebra Field

Operations:

0 1 * ** + - / = approximants associates? characteristic coerce complete continuedFraction convergents denominators divide euclideanSize expressIdealMember exquo extend extendedEuclidean factor gcd inv lcm multiEuclidean numerators one? partialDenominators partialNumerators partialQuotients prime? principalIdeal quo recip reducedContinuedFraction reducedForm rem sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | DBASE
Full name: | Database
Belongs to: | SetCategory
Operations: | + - = coerce display elt fullDisplay

Abbreviation: | DFLOAT
Full name: | DoubleFloat
Belongs to: | ConvertibleTo DifferentialRing FloatingPointSystem TranscendentalFunctionCategory

Operations:

0 1 * ** + - / < = D abs acos acosh acot acoth acsc acsch asec asech asin asinh associates? atan atanh base bits ceiling characteristic coerce convert cos cosh cot coth csc csch decreasePrecision differentiate digits divide euclideanSize exp exp1 exponent expressIdealMember exquo extendedEuclidean factor float floor fractionPart gcd hash increasePrecision inv lcm log log10 log2 mantissa max min multiEuclidean negative? norm nthRoot one? order patternMatch pi positive? precision prime? principalIdeal quo rationalApproximation recip rem retract retractIfCan round sec sech sign sin sinh sizeLess? sqrt squareFree squareFreePart tan tanh truncate unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | DLIST
Full name: | DataList
Belongs to: | ListAggregate

Operations:

# < = any? children coerce concat concat! construct convert copy copyInto! count cycleEntry cycleLength cycleSplit! cycleTail cyclic? datalist delete delete! elt empty empty? entries entry? eq? every? explicitlyFinite? fill! find first index? indices insert insert! last leaf? leaves less? list map map! max maxIndex member? members merge merge! min minIndex more? new node? nodes parts position possiblyInfinite? qelt qsetelt! reduce remove remove! removeDuplicates removeDuplicates! rest reverse reverse! second select select! setchildren! setelt setfirst! setlast! setrest! setvalue! size? sort sort! sorted? split! swap! tail third value

Abbreviation: | DECIMAL
Full name: | DecimalExpansion
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs associates? ceiling characteristic coerce convert decimal denom denominator differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor floor fractionPart gcd init inv lcm map max min multiEuclidean negative? nextItem numer numerator one? patternMatch positive? prime? principalIdeal quo random recip reducedSystem rem retract retractIfCan sign sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | DHMATRIX
Full name: | DenavitHartenbergMatrix
Belongs to: | MatrixCategory

Operations:

# * ** + - / = antisymmetric? any? coerce column copy count determinant diagonal? diagonalMatrix elt empty empty? eq? every? exquo fill! horizConcat identity inverse less? listOfLists map map! matrix maxColIndex maxRowIndex member? members minColIndex minRowIndex minordet more? ncols new nrows nullSpace nullity parts qelt qsetelt! rank rotatex rotatey rotatez row rowEchelon scalarMatrix scale setColumn! setRow! setelt setsubMatrix! size? square? squareTop subMatrix swapColumns! swapRows! symmetric? translate transpose vertConcat zero

Abbreviation: | DEQUEUE
Full name: | Dequeue
Belongs to: | DequeueAggregate
Operations: | # = any? back bag bottom! coerce copy count depth dequeue dequeue! empty empty? enqueue! eq? every? extract! extractBottom! extractTop! front height insert! insertBottom! insertTop! inspect length less? map map! member? members more? parts pop! push! reverse! rotate! size? top top!

Abbreviation: | DERHAM
Full name: | DeRhamComplex
Belongs to: | LeftAlgebra RetractableTo
Operations: | 0 1 * ** + - = characteristic coefficient coerce degree exteriorDifferential generator homogeneous? leadingBasisTerm leadingCoefficient map one? recip reductum retract retractIfCan retractable? totalDifferential zero?

Abbreviation: | DSMP
Full name: | DifferentialSparseMultivariatePolynomial
Belongs to: | DifferentialPolynomialCategory RetractableTo

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP content convert degree differentialVariables differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? initial isExpt isPlus isTimes isobaric? lcm leader leadingCoefficient leadingMonomial mainVariable makeVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? order patternMatch prime? primitiveMonomials primitivePart recip reducedSystem reductum resultant retract retractIfCan separant solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables weight weights zero?

Abbreviation: | DPMM
Full name: | DirectProductMatrixModule
Belongs to: | DirectProductCategory LeftModule

Operations:

0 1 # * ** + - / < = D abs any? characteristic coerce copy count differentiate dimension directProduct dot elt empty empty? entries entry? eq? every? fill! first index index? indices less? lookup map map! max maxIndex member? members min minIndex more? negative? one? parts positive? qelt qsetelt! random recip reducedSystem retract retractIfCan setelt sign size size? sup swap! unitVector zero?

Abbreviation: | DPMO
Full name: | DirectProductModule
Belongs to: | DirectProductCategory LeftModule

Operations:

0 1 # * ** + - / < = D abs any? characteristic coerce copy count differentiate dimension directProduct dot elt empty empty? entries entry? eq? every? fill! first index index? indices less? lookup map map! max maxIndex member? members min minIndex more? negative? one? parts positive? qelt qsetelt! random recip reducedSystem retract retractIfCan setelt sign size size? sup swap! unitVector zero?

Abbreviation: | DIRPROD
Full name: | DirectProduct
Belongs to: | DirectProductCategory

Operations:

0 1 # * ** + - / < = D abs any? characteristic coerce copy count differentiate dimension directProduct dot elt empty empty? entries entry? eq? every? fill! first index index? indices less? lookup map map! max maxIndex member? members min minIndex more? negative? one? parts positive? qelt qsetelt! random recip reducedSystem retract retractIfCan setelt sign size size? sup swap! unitVector zero?

Abbreviation: | DMP
Full name: | DistributedMultivariatePolynomial
Belongs to: | PolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP const content convert degree differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? prime? primitiveMonomials primitivePart recip reducedSystem reductum reorder resultant retract retractIfCan solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables zero?

Abbreviation: | DROPT
Full name: | DrawOption
Belongs to: | SetCategory
Operations: | = adaptive clip coerce colorFunction coordinate coordinates curveColor option option? pointColor range ranges space style title toScale tubePoints tubeRadius unit var1Steps var2Steps

Abbreviation: | EFULS
Full name: | ElementaryFunctionsUnivariateLaurentSeries
Belongs to: | PartialTranscendentalFunctions

Operations:

** acos acosIfCan acosh acoshIfCan acot acotIfCan acoth acothIfCan acsc acscIfCan acsch acschIfCan asec asecIfCan asech asechIfCan asin asinIfCan asinh asinhIfCan atan atanIfCan atanh atanhIfCan cos cosIfCan cosh coshIfCan cot cotIfCan coth cothIfCan csc cscIfCan csch cschIfCan exp expIfCan log logIfCan nthRootIfCan sec secIfCan sech sechIfCan sin sinIfCan sinh sinhIfCan tan tanIfCan tanh tanhIfCan

Abbreviation: | EFUPXS
Full name: | ElementaryFunctionsUnivariatePuiseuxSeries
Belongs to: | PartialTranscendentalFunctions

Operations:

** acos acosIfCan acosh acoshIfCan acot acotIfCan acoth acothIfCan acsc acscIfCan acsch acschIfCan asec asecIfCan asech asechIfCan asin asinIfCan asinh asinhIfCan atan atanIfCan atanh atanhIfCan cos cosIfCan cosh coshIfCan cot cotIfCan coth cothIfCan csc cscIfCan csch cschIfCan exp expIfCan log logIfCan nthRootIfCan sec secIfCan sech sechIfCan sin sinIfCan sinh sinhIfCan tan tanIfCan tanh tanhIfCan

Abbreviation: | EQTBL
Full name: | EqTable
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? map map! maxIndex member? members minIndex more? parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | EQ
Full name: | Equation
Belongs to: | CoercibleTo InnerEvalable Object SetCategory
Operations: | * ** + - = coerce equation eval lhs map rhs

Abbreviation: | EMR
Full name: | EuclideanModularRing
Belongs to: | EuclideanDomain
Operations: | 0 1 * ** + - = associates? characteristic coerce divide euclideanSize exQuo expressIdealMember exquo extendedEuclidean gcd inv lcm modulus multiEuclidean one? principalIdeal quo recip reduce rem sizeLess? unit? unitCanonical unitNormal zero?

Abbreviation: | EXIT
Full name: | Exit
Belongs to: | SetCategory
Operations: | = coerce

Abbreviation: | EXPR
Full name: | Expression
Belongs to: | AlgebraicallyClosedFunctionSpace CombinatorialOpsCategory FunctionSpace LiouvillianFunctionCategory RetractableTo SpecialFunctionCategory TranscendentalFunctionCategory

Operations:

0 1 * ** + - / < = Beta Ci D Ei Gamma Si abs acos acosh acot acoth acsc acsch airyAi airyBi applyQuote asec asech asin asinh associates? atan atanh belong? besselI besselJ besselK besselY binomial box characteristic charthRoot coerce commutator conjugate convert cos cosh cot coth csc csch definingPolynomial denom denominator differentiate digamma dilog distribute divide elt erf euclideanSize eval exp expressIdealMember exquo extendedEuclidean factor factorial factorials freeOf? gcd ground ground? height integral inv is? isExpt isMult isPlus isPower isTimes kernel kernels lcm li log mainKernel map max min minPoly multiEuclidean nthRoot numer numerator one? operator operators paren patternMatch permutation pi polygamma prime? principalIdeal product quo recip reduce reducedSystem rem retract retractIfCan rootOf rootsOf sec sech sin sinh sizeLess? sqrt squareFree squareFreePart subst summation tan tanh tower unit? unitCanonical unitNormal univariate variables zero? zeroOf zerosOf

Abbreviation: | EAB
Full name: | ExtAlgBasis
Belongs to: | OrderedSet
Operations: | < = Nul coerce degree exponents max min

Abbreviation: | FR
Full name: | Factored
Belongs to: | Algebra DifferentialExtension Eltable Evalable FullyEvalableOver FullyRetractableTo GcdDomain InnerEvalable IntegralDomain RealConstant UniqueFactorizationDomain

Operations:

0 1 * ** + - = D associates? characteristic coerce convert differentiate elt eval expand exponent exquo factor factorList factors flagFactor gcd irreducibleFactor lcm makeFR map nilFactor nthExponent nthFactor nthFlag numberOfFactors one? prime? primeFactor rational rational? rationalIfCan recip retract retractIfCan sqfrFactor squareFree squareFreePart unit unit? unitCanonical unitNormal unitNormalize zero?

Abbreviation: | FNAME
Full name: | FileName
Belongs to: | FileNameCategory
Operations: | = coerce directory exists? extension filename name new readable? writable?

Abbreviation: | FILE
Full name: | File
Belongs to: | FileCategory
Operations: | = close! coerce iomode name open read! readIfCan! reopen! write!

Abbreviation: | FDIV
Full name: | FiniteDivisor
Belongs to: | AbelianGroup
Operations: | 0 * + - = algsplit coerce divisor finiteBasis generator ideal lSpaceBasis mkBasicDiv principal? reduce zero?

Abbreviation: | FFCGP
Full name: | FiniteFieldCyclicGroupExtensionByPolynomial
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator getZechTable inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFCGX
Full name: | FiniteFieldCyclicGroupExtension
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator getZechTable inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFCG
Full name: | FiniteFieldCyclicGroup
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator getZechTable inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFP
Full name: | FiniteFieldExtensionByPolynomial
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFX
Full name: | FiniteFieldExtension
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFNBP
Full name: | FiniteFieldNormalBasisExtensionByPolynomial
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator getMultiplicationMatrix getMultiplicationTable inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? sizeMultiplication squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFNBX
Full name: | FiniteFieldNormalBasisExtension
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator getMultiplicationMatrix getMultiplicationTable inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? sizeMultiplication squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FFNB
Full name: | FiniteFieldNormalBasis
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator getMultiplicationMatrix getMultiplicationTable inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? sizeMultiplication squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FF
Full name: | FiniteField
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | FARRAY
Full name: | FlexibleArray
Belongs to: | ExtensibleLinearAggregate OneDimensionalArrayAggregate

Operations:

# < = any? coerce concat concat! construct convert copy copyInto! count delete delete! elt empty empty? entries entry? eq? every? fill! find first flexibleArray index? indices insert insert! less? map map! max maxIndex member? members merge merge! min minIndex more? new parts physicalLength physicalLength! position qelt qsetelt! reduce remove remove! removeDuplicates removeDuplicates! reverse reverse! select select! setelt shrinkable size? sort sort! sorted? swap!

Abbreviation: | FLOAT
Full name: | Float
Belongs to: | CoercibleTo ConvertibleTo DifferentialRing FloatingPointSystem TranscendentalFunctionCategory

Operations:

0 1 * ** + - / < = D abs acos acosh acot acoth acsc acsch asec asech asin asinh associates? atan atanh base bits ceiling characteristic coerce convert cos cosh cot coth csc csch decreasePrecision differentiate digits divide euclideanSize exp exp1 exponent expressIdealMember exquo extendedEuclidean factor float floor fractionPart gcd increasePrecision inv lcm log log10 log2 mantissa max min multiEuclidean negative? norm normalize nthRoot one? order outputFixed outputFloating outputGeneral outputSpacing patternMatch pi positive? precision prime? principalIdeal quo rationalApproximation recip relerror rem retract retractIfCan round sec sech shift sign sin sinh sizeLess? sqrt squareFree squareFreePart tan tanh truncate unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | FRIDEAL
Full name: | FractionalIdeal
Belongs to: | Group
Operations: | 1 * ** / = basis coerce commutator conjugate denom ideal inv minimize norm numer one? randomLC recip

Abbreviation: | FRAC
Full name: | Fraction
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs associates? ceiling characteristic charthRoot coerce conditionP convert denom denominator differentiate divide elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial floor fractionPart gcd gcdPolynomial init inv lcm map max min multiEuclidean negative? nextItem numer numerator one? patternMatch positive? prime? principalIdeal quo random recip reducedSystem rem retract retractIfCan sign sizeLess? solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | FRMOD
Full name: | FramedModule
Belongs to: | Monoid
Operations: | 1 * ** = basis coerce module norm one? recip

Abbreviation: | FAGROUP
Full name: | FreeAbelianGroup
Belongs to: | AbelianGroup FreeAbelianMonoidCategory Module OrderedSet
Operations: | 0 * + - < = coefficient coerce highCommonTerms mapCoef mapGen max min nthCoef nthFactor retract retractIfCan size terms zero?

Abbreviation: | FAMONOID
Full name: | FreeAbelianMonoid
Belongs to: | FreeAbelianMonoidCategory
Operations: | 0 * + - = coefficient coerce highCommonTerms mapCoef mapGen nthCoef nthFactor retract retractIfCan size terms zero?

Abbreviation: | FGROUP
Full name: | FreeGroup
Belongs to: | Group RetractableTo
Operations: | 1 * ** / = coerce commutator conjugate factors inv mapExpon mapGen nthExpon nthFactor one? recip retract retractIfCan size

Abbreviation: | FM
Full name: | FreeModule
Belongs to: | BiModule IndexedDirectProductCategory Module
Operations: | 0 * + - = coerce leadingCoefficient leadingSupport map monomial reductum zero?

Abbreviation: | FMONOID
Full name: | FreeMonoid
Belongs to: | Monoid OrderedSet RetractableTo
Operations: | 1 * ** < = coerce divide factors hclf hcrf lquo mapExpon mapGen max min nthExpon nthFactor one? overlap recip retract retractIfCan rquo size

Abbreviation: | FNLA
Full name: | FreeNilpotentLie
Belongs to: | NonAssociativeAlgebra
Operations: | 0 * ** + - = antiCommutator associator coerce commutator deepExpand dimension generator leftPower rightPower shallowExpand zero?

Abbreviation: | FUNCTION
Full name: | FunctionCalled
Belongs to: | SetCategory
Operations: | = coerce name

Abbreviation: | GDMP
Full name: | GeneralDistributedMultivariatePolynomial
Belongs to: | PolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP const content convert degree differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? prime? primitiveMonomials primitivePart recip reducedSystem reductum reorder resultant retract retractIfCan solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables zero?

Abbreviation: | GSTBL
Full name: | GeneralSparseTable
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? map map! maxIndex member? members minIndex more? parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | GCNAALG
Full name: | GenericNonAssociativeAlgebra
Belongs to: | FramedNonAssociativeAlgebra LeftModule

Operations:

0 * ** + - = JacobiIdentity? JordanAlgebra? alternative? antiAssociative? antiCommutative? antiCommutator apply associative? associator associatorDependence basis coerce commutative? commutator conditionsForIdempotents convert coordinates elt flexible? generic genericLeftDiscriminant genericLeftMinimalPolynomial genericLeftNorm genericLeftTrace genericLeftTraceForm genericRightDiscriminant genericRightMinimalPolynomial genericRightNorm genericRightTrace genericRightTraceForm jordanAdmissible? leftAlternative? leftCharacteristicPolynomial leftDiscriminant leftMinimalPolynomial leftNorm leftPower leftRankPolynomial leftRecip leftRegularRepresentation leftTrace leftTraceMatrix leftUnit leftUnits lieAdmissible? lieAlgebra? noncommutativeJordanAlgebra? plenaryPower powerAssociative? rank recip represents rightAlternative? rightCharacteristicPolynomial rightDiscriminant rightMinimalPolynomial rightNorm rightPower rightRankPolynomial rightRecip rightRegularRepresentation rightTrace rightTraceMatrix rightUnit rightUnits someBasis structuralConstants unit zero?

Abbreviation: | GRIMAGE
Full name: | GraphImage
Belongs to: | SetCategory
Operations: | = appendPoint coerce component graphImage key makeGraphImage point pointLists putColorInfo ranges units

Abbreviation: | HASHTBL
Full name: | HashTable
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? map map! maxIndex member? members minIndex more? parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | HEAP
Full name: | Heap
Belongs to: | PriorityQueueAggregate
Operations: | # = any? bag coerce copy count empty empty? eq? every? extract! heap insert! inspect less? map map! max member? members merge merge! more? parts size?

Abbreviation: | HEXADEC
Full name: | HexadecimalExpansion
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs associates? ceiling characteristic coerce convert denom denominator differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor floor fractionPart gcd hex init inv lcm map max min multiEuclidean negative? nextItem numer numerator one? patternMatch positive? prime? principalIdeal quo random recip reducedSystem rem retract retractIfCan sign sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | ICARD
Full name: | IndexCard
Belongs to: | OrderedSet
Operations: | < = coerce display elt fullDisplay max min

Abbreviation: | IBITS
Full name: | IndexedBits
Belongs to: | BitAggregate

Operations:

# < = And Not Or \^{} and any? coerce concat construct convert copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? nand new nor not or parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap! xor

Abbreviation: | IDPAG
Full name: | IndexedDirectProductAbelianGroup
Belongs to: | AbelianGroup IndexedDirectProductCategory
Operations: | 0 * + - = coerce leadingCoefficient leadingSupport map monomial reductum zero?

Abbreviation: | IDPAM
Full name: | IndexedDirectProductAbelianMonoid
Belongs to: | AbelianMonoid IndexedDirectProductCategory
Operations: | 0 * + = coerce leadingCoefficient leadingSupport map monomial reductum zero?

Abbreviation: | IDPO
Full name: | IndexedDirectProductObject
Belongs to: | IndexedDirectProductCategory
Operations: | = coerce leadingCoefficient leadingSupport map monomial reductum

Abbreviation: | IDPOAMS
Full name: | IndexedDirectProductOrderedAbelianMonoidSup
Belongs to: | IndexedDirectProductCategory OrderedAbelianMonoidSup
Operations: | 0 * + - < = coerce leadingCoefficient leadingSupport map max min monomial reductum sup zero?

Abbreviation: | IDPOAM
Full name: | IndexedDirectProductOrderedAbelianMonoid
Belongs to: | IndexedDirectProductCategory OrderedAbelianMonoid
Operations: | 0 * + < = coerce leadingCoefficient leadingSupport map max min monomial reductum zero?

Abbreviation: | INDE
Full name: | IndexedExponents
Belongs to: | IndexedDirectProductCategory OrderedAbelianMonoidSup
Operations: | 0 * + - < = coerce leadingCoefficient leadingSupport map max min monomial reductum sup zero?

Abbreviation: | IFARRAY
Full name: | IndexedFlexibleArray
Belongs to: | ExtensibleLinearAggregate OneDimensionalArrayAggregate

Operations:

# < = any? coerce concat concat! construct convert copy copyInto! count delete delete! elt empty empty? entries entry? eq? every? fill! find first flexibleArray index? indices insert insert! less? map map! max maxIndex member? members merge merge! min minIndex more? new parts physicalLength physicalLength! position qelt qsetelt! reduce remove remove! removeDuplicates removeDuplicates! reverse reverse! select select! setelt shrinkable size? sort sort! sorted? swap!

Abbreviation: | ILIST
Full name: | IndexedList
Belongs to: | ListAggregate

Operations:

# < = any? child? children coerce concat concat! construct convert copy copyInto! count cycleEntry cycleLength cycleSplit! cycleTail cyclic? delete delete! distance elt empty empty? entries entry? eq? every? explicitlyFinite? fill! find first index? indices insert insert! last leaf? less? list map map! max maxIndex member? members merge merge! min minIndex more? new node? nodes parts position possiblyInfinite? qelt qsetelt! reduce remove remove! removeDuplicates removeDuplicates! rest reverse reverse! second select select! setchildren! setelt setfirst! setlast! setrest! setvalue! size? sort sort! sorted? split! swap! tail third value

Abbreviation: | IMATRIX
Full name: | IndexedMatrix
Belongs to: | MatrixCategory

Operations:

# * ** + - / = antisymmetric? any? coerce column copy count determinant diagonal? diagonalMatrix elt empty empty? eq? every? exquo fill! horizConcat inverse less? listOfLists map map! matrix maxColIndex maxRowIndex member? members minColIndex minRowIndex minordet more? ncols new nrows nullSpace nullity parts qelt qsetelt! rank row rowEchelon scalarMatrix setColumn! setRow! setelt setsubMatrix! size? square? squareTop subMatrix swapColumns! swapRows! symmetric? transpose vertConcat zero

Abbreviation: | IARRAY1
Full name: | IndexedOneDimensionalArray
Belongs to: | OneDimensionalArrayAggregate
Operations: | # < = any? coerce concat construct convert copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? new parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap!

Abbreviation: | ISTRING
Full name: | IndexedString
Belongs to: | StringAggregate

Operations:

# < = any? coerce concat construct copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first hash index? indices insert leftTrim less? lowerCase lowerCase! map map! match? max maxIndex member? members merge min minIndex more? new parts position prefix? qelt qsetelt! reduce remove removeDuplicates replace reverse reverse! rightTrim select setelt size? sort sort! sorted? split substring? suffix? swap! trim upperCase upperCase!

Abbreviation: | IARRAY2
Full name: | IndexedTwoDimensionalArray
Belongs to: | TwoDimensionalArrayCategory
Operations: | # = any? coerce column copy count elt empty empty? eq? every? fill! less? map map! maxColIndex maxRowIndex member? members minColIndex minRowIndex more? ncols new nrows parts qelt qsetelt! row setColumn! setRow! setelt size?

Abbreviation: | IVECTOR
Full name: | IndexedVector
Belongs to: | VectorCategory
Operations: | # * + - < = any? coerce concat construct convert copy copyInto! count delete dot elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? new parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap! zero

Abbreviation: | ITUPLE
Full name: | InfiniteTuple
Belongs to: | CoercibleTo
Operations: | coerce construct filterUntil filterWhile generate map select

Abbreviation: | IFF
Full name: | InnerFiniteField
Belongs to: | FiniteAlgebraicExtensionField

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | IFAMON
Full name: | InnerFreeAbelianMonoid
Belongs to: | FreeAbelianMonoidCategory
Operations: | 0 * + - = coefficient coerce highCommonTerms mapCoef mapGen nthCoef nthFactor retract retractIfCan size terms zero?

Abbreviation: | IIARRAY2
Full name: | InnerIndexedTwoDimensionalArray
Belongs to: | TwoDimensionalArrayCategory
Operations: | # = any? coerce column copy count elt empty empty? eq? every? fill! less? map map! maxColIndex maxRowIndex member? members minColIndex minRowIndex more? ncols new nrows parts qelt qsetelt! row setColumn! setRow! setelt size?

Abbreviation: | IPADIC
Full name: | InnerPAdicInteger
Belongs to: | PAdicIntegerCategory
Operations: | 0 1 * ** + - = approximate associates? characteristic coerce complete digits divide euclideanSize expressIdealMember exquo extend extendedEuclidean gcd lcm moduloP modulus multiEuclidean one? order principalIdeal quo quotientByP recip rem sizeLess? sqrt unit? unitCanonical unitNormal zero?

Abbreviation: | IPF
Full name: | InnerPrimeField
Belongs to: | ConvertibleTo FiniteAlgebraicExtensionField FiniteFieldCategory

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP convert coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | ITAYLOR
Full name: | InnerTaylorSeries
Belongs to: | IntegralDomain Ring
Operations: | 0 1 * ** + - = associates? characteristic coefficients coerce exquo one? order pole? recip series unit? unitCanonical unitNormal zero?

Abbreviation: | INFORM
Full name: | InputForm
Belongs to: | ConvertibleTo SExpressionCategory
Operations: | 0 1 # * ** + / = atom? binary car cdr coerce compile convert declare destruct elt eq expr flatten float float? function integer integer? interpret lambda list? null? pair? string string? symbol symbol? uequal unparse

Abbreviation: | ZMOD
Full name: | IntegerMod
Belongs to: | CommutativeRing ConvertibleTo Finite StepThrough
Operations: | 0 1 * ** + - = characteristic coerce convert index init lookup nextItem one? random recip size zero?

Abbreviation: | INT
Full name: | Integer
Belongs to: | ConvertibleTo IntegerNumberSystem

Operations:

0 1 * ** + - < = D abs addmod associates? base binomial bit? characteristic coerce convert copy dec differentiate divide euclideanSize even? expressIdealMember exquo extendedEuclidean factor factorial gcd hash inc init invmod lcm length mask max min mulmod multiEuclidean negative? nextItem odd? one? patternMatch permutation positive? positiveRemainder powmod prime? principalIdeal quo random rational rational? rationalIfCan recip reducedSystem rem retract retractIfCan shift sign sizeLess? squareFree squareFreePart submod symmetricRemainder unit? unitCanonical unitNormal zero?

Abbreviation: | IR
Full name: | IntegrationResult
Belongs to: | Module RetractableTo
Operations: | 0 * + - = D coerce differentiate elem? integral logpart mkAnswer notelem ratpart retract retractIfCan zero?

Abbreviation: | KERNEL
Full name: | Kernel
Belongs to: | CachableSet ConvertibleTo Patternable
Operations: | < = argument coerce convert height is? kernel max min name operator position setPosition symbolIfCan

Abbreviation: | KAFILE
Full name: | KeyedAccessFile
Belongs to: | FileCategory TableAggregate
Operations: | # = any? bag close! coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect iomode key? keys less? map map! maxIndex member? members minIndex more? name open pack! parts qelt qsetelt! read! reduce remove remove! removeDuplicates reopen! search select select! setelt size? swap! table write!

Abbreviation: | LAUPOL
Full name: | LaurentPolynomial
Belongs to: | CharacteristicNonZero CharacteristicZero ConvertibleTo DifferentialExtension EuclideanDomain FullyRetractableTo IntegralDomain RetractableTo
Operations: | 0 1 * ** + - = D associates? characteristic charthRoot coefficient coerce convert degree differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean gcd lcm leadingCoefficient monomial monomial? multiEuclidean one? order principalIdeal quo recip reductum rem retract retractIfCan separate sizeLess? trailingCoefficient unit? unitCanonical unitNormal zero?

Abbreviation: | LIB
Full name: | Library
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? library map map! maxIndex member? members minIndex more? pack! parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | LSQM
Full name: | LieSquareMatrix
Belongs to: | CoercibleTo FramedNonAssociativeAlgebra SquareMatrixCategory

Operations:

0 1 # * ** + - / = D JacobiIdentity? JordanAlgebra? alternative? antiAssociative? antiCommutative? antiCommutator antisymmetric? any? apply associative? associator associatorDependence basis characteristic coerce column commutative? commutator conditionsForIdempotents convert coordinates copy count determinant diagonal diagonal? diagonalMatrix diagonalProduct differentiate elt empty empty? eq? every? exquo flexible? inverse jordanAdmissible? leftAlternative? leftCharacteristicPolynomial leftDiscriminant leftMinimalPolynomial leftNorm leftPower leftRankPolynomial leftRecip leftRegularRepresentation leftTrace leftTraceMatrix leftUnit leftUnits less? lieAdmissible? lieAlgebra? listOfLists map map! matrix maxColIndex maxRowIndex member? members minColIndex minRowIndex minordet more? ncols noncommutativeJordanAlgebra? nrows nullSpace nullity one? parts plenaryPower powerAssociative? qelt rank recip reducedSystem represents retract retractIfCan rightAlternative? rightCharacteristicPolynomial rightDiscriminant rightMinimalPolynomial rightNorm rightPower rightRankPolynomial rightRecip rightRegularRepresentation rightTrace rightTraceMatrix rightUnit rightUnits row rowEchelon scalarMatrix size? someBasis square? structuralConstants symmetric? trace unit zero?

Abbreviation: | LODO
Full name: | LinearOrdinaryDifferentialOperator
Belongs to: | MonogenicLinearOperator
Operations: | 0 1 * ** + - = D characteristic coefficient coerce degree elt leadingCoefficient leftDivide leftExactQuotient leftGcd leftLcm leftQuotient leftRemainder minimumDegree monomial one? recip reductum rightDivide rightExactQuotient rightGcd rightLcm rightQuotient rightRemainder zero?

Abbreviation: | LMOPS
Full name: | ListMonoidOps
Belongs to: | RetractableTo SetCategory
Operations: | = coerce leftMult listOfMonoms makeMulti makeTerm makeUnit mapExpon mapGen nthExpon nthFactor outputForm plus retract retractIfCan reverse reverse! rightMult size

Abbreviation: | LMDICT
Full name: | ListMultiDictionary
Belongs to: | MultiDictionary
Operations: | # = any? bag coerce construct convert copy count dictionary duplicates duplicates? empty empty? eq? every? extract! find insert! inspect less? map map! member? members more? parts reduce remove remove! removeDuplicates removeDuplicates! select select! size? substitute

Abbreviation: | LIST
Full name: | List
Belongs to: | ListAggregate

Operations:

# < = any? append child? children coerce concat concat! cons construct convert copy copyInto! count cycleEntry cycleLength cycleSplit! cycleTail cyclic? delete delete! distance elt empty empty? entries entry? eq? every? explicitlyFinite? fill! find first index? indices insert insert! last leaf? less? list map map! max maxIndex member? members merge merge! min minIndex more? new nil node? nodes null parts position possiblyInfinite? qelt qsetelt! reduce remove remove! removeDuplicates removeDuplicates! rest reverse reverse! second select select! setDifference setIntersection setUnion setchildren! setelt setfirst! setlast! setrest! setvalue! size? sort sort! sorted? split! swap! tail third value

Abbreviation: | LA
Full name: | LocalAlgebra
Belongs to: | Algebra OrderedRing
Operations: | 0 1 * ** + - / < = abs characteristic coerce denom max min negative? numer one? positive? recip sign zero?

Abbreviation: | LO
Full name: | Localize
Belongs to: | Module OrderedAbelianGroup
Operations: | 0 * + - / < = coerce denom max min numer zero?

Abbreviation: | MKCHSET
Full name: | MakeCachableSet
Belongs to: | CachableSet CoercibleTo
Operations: | < = coerce max min position setPosition

Abbreviation: | MKODRING
Full name: | MakeOrdinaryDifferentialRing
Belongs to: | CoercibleTo DifferentialRing
Operations: | 0 1 * ** + - = D characteristic coerce differentiate one? recip zero?

Abbreviation: | MATRIX
Full name: | Matrix
Belongs to: | MatrixCategory

Operations:

# * ** + - / = antisymmetric? any? coerce column copy count determinant diagonal? diagonalMatrix elt empty empty? eq? every? exquo fill! horizConcat inverse less? listOfLists map map! matrix maxColIndex maxRowIndex member? members minColIndex minRowIndex minordet more? ncols new nrows nullSpace nullity parts qelt qsetelt! rank row rowEchelon scalarMatrix setColumn! setRow! setelt setsubMatrix! size? square? squareTop subMatrix swapColumns! swapRows! symmetric? transpose vertConcat zero

Abbreviation: | MODMON
Full name: | ModMonic
Belongs to: | Finite UnivariatePolynomialCategory

Operations:

0 1 * ** + - / < = An D UnVectorise Vectorise associates? characteristic charthRoot coefficient coefficients coerce composite computePowers conditionP content degree differentiate discriminant divide divideExponents elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? index init integrate isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial lift lookup mainVariable makeSUP map mapExponents max min minimumDegree modulus monicDivide monomial monomial? monomials multiEuclidean multiplyExponents multivariate nextItem numberOfMonomials one? order pow prime? primitiveMonomials primitivePart principalIdeal pseudoDivide pseudoQuotient pseudoRemainder quo random recip reduce reducedSystem reductum rem resultant retract retractIfCan separate setPoly size sizeLess? solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial subResultantGcd totalDegree unit? unitCanonical unitNormal univariate unmakeSUP variables vectorise zero?

Abbreviation: | MODFIELD
Full name: | ModularField
Belongs to: | Field
Operations: | 0 1 * ** + - / = associates? characteristic coerce divide euclideanSize exQuo expressIdealMember exquo extendedEuclidean factor gcd inv lcm modulus multiEuclidean one? prime? principalIdeal quo recip reduce rem sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal zero?

Abbreviation: | MODRING
Full name: | ModularRing
Belongs to: | Ring
Operations: | 0 1 * ** + - = characteristic coerce exQuo inv modulus one? recip reduce zero?

Abbreviation: | MOEBIUS
Full name: | MoebiusTransform
Belongs to: | Group
Operations: | 1 * ** / = coerce commutator conjugate eval inv moebius one? recip scale shift

Abbreviation: | MRING
Full name: | MonoidRing
Belongs to: | Algebra CharacteristicNonZero CharacteristicZero Finite RetractableTo Ring
Operations: | 0 1 * ** + - = characteristic charthRoot coefficient coefficients coerce index leadingCoefficient leadingMonomial lookup map monomial monomial? monomials numberOfMonomials one? random recip reductum retract retractIfCan size terms zero?

Abbreviation: | MSET
Full name: | Multiset
Belongs to: | MultiSetAggregate
Operations: | # < = any? bag brace coerce construct convert copy count dictionary difference duplicates empty empty? eq? every? extract! find insert! inspect intersect less? map map! member? members more? multiset parts reduce remove remove! removeDuplicates removeDuplicates! select select! size? subset? symmetricDifference union

Abbreviation: | MPOLY
Full name: | MultivariatePolynomial
Belongs to: | PolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP content convert degree differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? prime? primitiveMonomials primitivePart recip reducedSystem reductum resultant retract retractIfCan solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables zero?

Abbreviation: | NDP
Full name: | NewDirectProduct
Belongs to: | DirectProductCategory

Operations:

0 1 # * ** + - / < = D abs any? characteristic coerce copy count differentiate dimension directProduct dot elt empty empty? entries entry? eq? every? fill! first index index? indices less? lookup map map! max maxIndex member? members min minIndex more? negative? one? parts positive? qelt qsetelt! random recip reducedSystem retract retractIfCan setelt sign size size? sup swap! unitVector zero?

Abbreviation: | NDMP
Full name: | NewDistributedMultivariatePolynomial
Belongs to: | PolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP const content convert degree differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? prime? primitiveMonomials primitivePart recip reducedSystem reductum reorder resultant retract retractIfCan solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables zero?

Abbreviation: | NONE
Full name: | None
Belongs to: | SetCategory
Operations: | = coerce

Abbreviation: | NNI
Full name: | NonNegativeInteger
Belongs to: | Monoid OrderedAbelianMonoidSup
Operations: | 0 1 * ** + - < = coerce divide exquo gcd max min one? quo recip rem sup zero?

Abbreviation: | OCT
Full name: | Octonion
Belongs to: | FullyRetractableTo OctonionCategory
Operations: | 0 1 * ** + - < = abs characteristic charthRoot coerce conjugate convert elt eval imagE imagI imagJ imagK imagi imagj imagk index inv lookup map max min norm octon one? random rational rational? rationalIfCan real recip retract retractIfCan size zero?

Abbreviation: | ARRAY1
Full name: | OneDimensionalArray
Belongs to: | OneDimensionalArrayAggregate
Operations: | # < = any? coerce concat construct convert copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? new oneDimensionalArray parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap!

Abbreviation: | ONECOMP
Full name: | OnePointCompletion
Belongs to: | AbelianGroup FullyRetractableTo OrderedRing SetCategory
Operations: | 0 1 * ** + - < = abs characteristic coerce finite? infinite? infinity max min negative? one? positive? rational rational? rationalIfCan recip retract retractIfCan sign zero?

Abbreviation: | OP
Full name: | Operator
Belongs to: | Algebra CharacteristicNonZero CharacteristicZero Eltable RetractableTo Ring
Operations: | 0 1 * ** + - = characteristic charthRoot coerce elt evaluate one? opeval recip retract retractIfCan zero?

Abbreviation: | OMLO
Full name: | OppositeMonogenicLinearOperator
Belongs to: | DifferentialRing MonogenicLinearOperator
Operations: | 0 1 * ** + - = D characteristic coefficient coerce degree differentiate leadingCoefficient minimumDegree monomial one? op po recip reductum zero?

Abbreviation: | ORDCOMP
Full name: | OrderedCompletion
Belongs to: | AbelianGroup FullyRetractableTo OrderedRing SetCategory
Operations: | 0 1 * ** + - < = abs characteristic coerce finite? infinite? max min minusInfinity negative? one? plusInfinity positive? rational rational? rationalIfCan recip retract retractIfCan sign whatInfinity zero?

Abbreviation: | ODP
Full name: | OrderedDirectProduct
Belongs to: | DirectProductCategory

Operations:

0 1 # * ** + - / < = D abs any? characteristic coerce copy count differentiate dimension directProduct dot elt empty empty? entries entry? eq? every? fill! first index index? indices less? lookup map map! max maxIndex member? members min minIndex more? negative? one? parts positive? qelt qsetelt! random recip reducedSystem retract retractIfCan setelt sign size size? sup swap! unitVector zero?

Abbreviation: | OVAR
Full name: | OrderedVariableList
Belongs to: | ConvertibleTo OrderedFinite
Operations: | < = coerce convert index lookup max min random size variable

Abbreviation: | ODPOL
Full name: | OrderlyDifferentialPolynomial
Belongs to: | DifferentialPolynomialCategory RetractableTo

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP content degree differentialVariables differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? initial isExpt isPlus isTimes isobaric? lcm leader leadingCoefficient leadingMonomial mainVariable makeVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? order prime? primitiveMonomials primitivePart recip reducedSystem reductum resultant retract retractIfCan separant solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables weight weights zero?

Abbreviation: | ODVAR
Full name: | OrderlyDifferentialVariable
Belongs to: | DifferentialVariableCategory
Operations: | < = D coerce differentiate makeVariable max min order retract retractIfCan variable weight

Abbreviation: | ODR
Full name: | OrdinaryDifferentialRing
Belongs to: | Algebra DifferentialRing Field
Operations: | 0 1 * ** + - / = D associates? characteristic coerce differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor gcd inv lcm multiEuclidean one? prime? principalIdeal quo recip rem sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal zero?

Abbreviation: | OSI
Full name: | OrdSetInts
Belongs to: | OrderedSet
Operations: | < = coerce max min value

Abbreviation: | OUTFORM
Full name: | OutputForm
Belongs to: | SetCategory

Operations:

* ** + - / < <= = > >= D SEGMENT \^{}= and assign blankSeparate box brace bracket center coerce commaSeparate differentiate div dot elt empty exquo hconcat height hspace infix infix? int label left matrix message messagePrint not or outputForm over overbar paren pile postfix prefix presub presuper prime print prod quo quote rarrow rem right root rspace scripts semicolonSeparate slash string sub subHeight sum super superHeight supersub vconcat vspace width zag

Abbreviation: | PADIC
Full name: | PAdicInteger
Belongs to: | PAdicIntegerCategory
Operations: | 0 1 * ** + - = approximate associates? characteristic coerce complete digits divide euclideanSize expressIdealMember exquo extend extendedEuclidean gcd lcm moduloP modulus multiEuclidean one? order principalIdeal quo quotientByP recip rem sizeLess? sqrt unit? unitCanonical unitNormal zero?

Abbreviation: | PADICRC
Full name: | PAdicRationalConstructor
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs approximate associates? ceiling characteristic charthRoot coerce conditionP continuedFraction convert denom denominator differentiate divide elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial floor fractionPart gcd gcdPolynomial init inv lcm map max min multiEuclidean negative? nextItem numer numerator one? patternMatch positive? prime? principalIdeal quo random recip reducedSystem rem removeZeroes retract retractIfCan sign sizeLess? solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | PADICRAT
Full name: | PAdicRational
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / = D approximate associates? characteristic coerce continuedFraction denom denominator differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor fractionPart gcd inv lcm map multiEuclidean numer numerator one? prime? principalIdeal quo recip reducedSystem rem removeZeroes retract retractIfCan sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | PALETTE
Full name: | Palette
Belongs to: | SetCategory
Operations: | = bright coerce dark dim hue light pastel shade

Abbreviation: | PARPCURV
Full name: | ParametricPlaneCurve
Belongs to: |
Operations: | coordinate curve

Abbreviation: | PARSCURV
Full name: | ParametricSpaceCurve
Belongs to: |
Operations: | coordinate curve

Abbreviation: | PARSURF
Full name: | ParametricSurface
Belongs to: |
Operations: | coordinate surface

Abbreviation: | PFR
Full name: | PartialFraction
Belongs to: | Algebra Field

Operations:

0 1 * ** + - / = associates? characteristic coerce compactFraction divide euclideanSize expressIdealMember exquo extendedEuclidean factor firstDenom firstNumer gcd inv lcm multiEuclidean nthFractionalTerm numberOfFractionalTerms one? padicFraction padicallyExpand partialFraction prime? principalIdeal quo recip rem sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | PRTITION
Full name: | Partition
Belongs to: | ConvertibleTo OrderedCancellationAbelianMonoid
Operations: | 0 * + - < = coerce conjugate convert max min partition pdct powers zero?

Abbreviation: | PATLRES
Full name: | PatternMatchListResult
Belongs to: | SetCategory
Operations: | = atoms coerce failed failed? lists makeResult new

Abbreviation: | PATRES
Full name: | PatternMatchResult
Belongs to: | SetCategory
Operations: | = addMatch addMatchRestricted coerce construct destruct failed failed? getMatch insertMatch new satisfy? union

Abbreviation: | PATTERN
Full name: | Pattern
Belongs to: | RetractableTo SetCategory
Operations: | 0 1 * ** + / = addBadValue coerce constant? convert copy depth elt generic? getBadValues hasPredicate? hasTopPredicate? inR? isExpt isList isOp isPlus isPower isQuotient isTimes multiple? optional? optpair patternVariable predicates quoted? resetBadValues retract retractIfCan setPredicates setTopPredicate symbol? topPredicate variables withPredicates

Abbreviation: | PENDTREE
Full name: | PendantTree
Belongs to: | BinaryRecursiveAggregate
Operations: | # = any? children coerce copy count cyclic? elt empty empty? eq? every? leaf? leaves left less? map map! member? members more? node? nodes parts ptree right setchildren! setelt setleft! setright! setvalue! size? value

Abbreviation: | PERMGRP
Full name: | PermutationGroup
Belongs to: | SetCategory
Operations: | < <= = base coerce degree elt generators initializeGroupForWordProblem member? movedPoints orbit orbits order permutationGroup random strongGenerators wordInGenerators wordInStrongGenerators wordsForStrongGenerators

Abbreviation: | PERM
Full name: | Permutation
Belongs to: | PermutationCategory
Operations: | 1 * ** / < = coerce coerceImages coerceListOfPairs coercePreimagesImages commutator conjugate cycle cyclePartition cycles degree elt eval even? fixedPoints inv listRepresentation max min movedPoints numberOfCycles odd? one? orbit order recip sign sort

Abbreviation: | HACKPI
Full name: | Pi
Belongs to: | CharacteristicZero CoercibleTo ConvertibleTo Field RealConstant RetractableTo
Operations: | 0 1 * ** + - / = associates? characteristic coerce convert divide euclideanSize expressIdealMember exquo extendedEuclidean factor gcd inv lcm multiEuclidean one? pi prime? principalIdeal quo recip rem retract retractIfCan sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal zero?

Abbreviation: | ACPLOT
Full name: | PlaneAlgebraicCurvePlot
Belongs to: | PlottablePlaneCurveCategory
Operations: | coerce listBranches makeSketch refine xRange yRange

Abbreviation: | PLOT3D
Full name: | Plot3D
Belongs to: | PlottableSpaceCurveCategory
Operations: | adaptive3D? coerce debug3D listBranches maxPoints3D minPoints3D numFunEvals3D plot pointPlot refine screenResolution3D setAdaptive3D setMaxPoints3D setMinPoints3D setScreenResolution3D tRange tValues xRange yRange zRange zoom

Abbreviation: | PLOT
Full name: | Plot
Belongs to: | PlottablePlaneCurveCategory
Operations: | adaptive? coerce debug listBranches maxPoints minPoints numFunEvals parametric? plot plotPolar pointPlot refine screenResolution setAdaptive setMaxPoints setMinPoints setScreenResolution tRange xRange yRange zoom

Abbreviation: | POINT
Full name: | Point
Belongs to: | PointCategory

Operations:

# * + - < = any? coerce concat construct convert copy copyInto! count cross delete dimension dot elt empty empty? entries entry? eq? every? extend fill! find first index? indices insert length less? map map! max maxIndex member? members merge min minIndex more? new parts point position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap! zero

Abbreviation: | IDEAL
Full name: | PolynomialIdeals
Belongs to: | SetCategory
Operations: | * ** + = backOldPos coerce contract dimension element? generalPosition generators groebner groebner? groebnerIdeal ideal in? inRadical? intersect leadingIdeal quotient relationsIdeal saturate zeroDim?

Abbreviation: | PR
Full name: | PolynomialRing
Belongs to: | FiniteAbelianMonoidRing
Operations: | 0 1 * ** + - / = associates? characteristic charthRoot coefficient coefficients coerce content degree exquo ground ground? leadingCoefficient leadingMonomial map mapExponents minimumDegree monomial monomial? numberOfMonomials one? primitivePart recip reductum retract retractIfCan unit? unitCanonical unitNormal zero?

Abbreviation: | POLY
Full name: | Polynomial
Belongs to: | PolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP content convert degree differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? integrate isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? patternMatch prime? primitiveMonomials primitivePart recip reducedSystem reductum resultant retract retractIfCan solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables zero?

Abbreviation: | PI
Full name: | PositiveInteger
Belongs to: | AbelianSemiGroup Monoid OrderedSet
Operations: | 1 * ** + < = coerce gcd max min one? recip

Abbreviation: | PF
Full name: | PrimeField
Belongs to: | ConvertibleTo FiniteAlgebraicExtensionField FiniteFieldCategory

Operations:

0 1 * ** + - / = Frobenius algebraic? associates? basis characteristic charthRoot coerce conditionP convert coordinates createNormalElement createPrimitiveElement definingPolynomial degree dimension discreteLog divide euclideanSize expressIdealMember exquo extendedEuclidean extensionDegree factor factorsOfCyclicGroupSize gcd generator inGroundField? index init inv lcm lookup minimalPolynomial multiEuclidean nextItem norm normal? normalElement one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random recip rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace transcendenceDegree transcendent? unit? unitCanonical unitNormal zero?

Abbreviation: | PRIMARR
Full name: | PrimitiveArray
Belongs to: | OneDimensionalArrayAggregate
Operations: | # < = any? coerce concat construct convert copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? new parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap!

Abbreviation: | PRODUCT
Full name: | Product
Belongs to: | AbelianGroup AbelianMonoid CancellationAbelianMonoid Finite Group Monoid OrderedAbelianMonoidSup OrderedSet SetCategory
Operations: | 0 1 * ** + - / < = coerce commutator conjugate index inv lookup makeprod max min one? random recip selectfirst selectsecond size sup zero?

Abbreviation: | QFORM
Full name: | QuadraticForm
Belongs to: | AbelianGroup
Operations: | 0 * + - = coerce elt matrix quadraticForm zero?

Abbreviation: | QALGSET
Full name: | QuasiAlgebraicSet
Belongs to: | CoercibleTo SetCategory
Operations: | = coerce definingEquations definingInequation empty? idealSimplify quasiAlgebraicSet setStatus simplify

Abbreviation: | QUAT
Full name: | Quaternion
Belongs to: | QuaternionCategory
Operations: | 0 1 * ** + - < = D abs characteristic charthRoot coerce conjugate convert differentiate elt eval imagI imagJ imagK inv map max min norm one? quatern rational rational? rationalIfCan real recip reducedSystem retract retractIfCan zero?

Abbreviation: | QEQUAT
Full name: | QueryEquation
Belongs to: |
Operations: | equation value variable

Abbreviation: | QUEUE
Full name: | Queue
Belongs to: | QueueAggregate
Operations: | # = any? back bag coerce copy count dequeue! empty empty? enqueue! eq? every? extract! front insert! inspect length less? map map! member? members more? parts queue rotate! size?

Abbreviation: | RADFF
Full name: | RadicalFunctionField
Belongs to: | FunctionFieldCategory

Operations:

0 1 * ** + - / = D absolutelyIrreducible? associates? basis branchPoint? branchPointAtInfinity? characteristic characteristicPolynomial charthRoot coerce complementaryBasis convert coordinates definingPolynomial derivationCoordinates differentiate discriminant divide elt euclideanSize expressIdealMember exquo extendedEuclidean factor gcd generator genus integral? integralAtInfinity? integralBasis integralBasisAtInfinity integralCoordinates integralDerivationMatrix integralMatrix integralMatrixAtInfinity integralRepresents inv inverseIntegralMatrix inverseIntegralMatrixAtInfinity lcm lift minimalPolynomial multiEuclidean nonSingularModel norm normalizeAtInfinity numberOfComponents one? prime? primitivePart principalIdeal quo ramified? ramifiedAtInfinity? rank rationalPoint? rationalPoints recip reduce reduceBasisAtInfinity reducedSystem regularRepresentation rem represents retract retractIfCan singular? singularAtInfinity? sizeLess? squareFree squareFreePart trace traceMatrix unit? unitCanonical unitNormal yCoordinates zero?

Abbreviation: | RADIX
Full name: | RadixExpansion
Belongs to: | QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs associates? ceiling characteristic coerce convert cycleRagits denom denominator differentiate divide euclideanSize expressIdealMember exquo extendedEuclidean factor floor fractRadix fractRagits fractionPart gcd init inv lcm map max min multiEuclidean negative? nextItem numer numerator one? patternMatch positive? prefixRagits prime? principalIdeal quo random recip reducedSystem rem retract retractIfCan sign sizeLess? squareFree squareFreePart unit? unitCanonical unitNormal wholePart wholeRadix wholeRagits zero?

Abbreviation: | RMATRIX
Full name: | RectangularMatrix
Belongs to: | CoercibleTo RectangularMatrixCategory VectorSpace
Operations: | 0 # * + - / = antisymmetric? any? coerce column copy count diagonal? dimension elt empty empty? eq? every? exquo less? listOfLists map map! matrix maxColIndex maxRowIndex member? members minColIndex minRowIndex more? ncols nrows nullSpace nullity parts qelt rank rectangularMatrix row rowEchelon size? square? symmetric? zero?

Abbreviation: | REF
Full name: | Reference
Belongs to: | Object SetCategory
Operations: | = coerce deref elt ref setelt setref

Abbreviation: | RULE
Full name: | RewriteRule
Belongs to: | Eltable RetractableTo SetCategory
Operations: | = coerce elt lhs pattern quotedOperators retract retractIfCan rhs rule suchThat

Abbreviation: | ROMAN
Full name: | RomanNumeral
Belongs to: | IntegerNumberSystem

Operations:

0 1 * ** + - < = D abs addmod associates? base binomial bit? characteristic coerce convert copy dec differentiate divide euclideanSize even? expressIdealMember exquo extendedEuclidean factor factorial gcd hash inc init invmod lcm length mask max min mulmod multiEuclidean negative? nextItem odd? one? patternMatch permutation positive? positiveRemainder powmod prime? principalIdeal quo random rational rational? rationalIfCan recip reducedSystem rem retract retractIfCan roman shift sign sizeLess? squareFree squareFreePart submod symmetricRemainder unit? unitCanonical unitNormal zero?

Abbreviation: | RULECOLD
Full name: | RuleCalled
Belongs to: | SetCategory
Operations: | = coerce name

Abbreviation: | RULESET
Full name: | Ruleset
Belongs to: | Eltable SetCategory
Operations: | = coerce elt rules ruleset

Abbreviation: | FORMULA1
Full name: | ScriptFormulaFormat1
Belongs to: | Object
Operations: | coerce

Abbreviation: | FORMULA
Full name: | ScriptFormulaFormat
Belongs to: | SetCategory
Operations: | = coerce convert display epilogue formula new prologue setEpilogue! setFormula! setPrologue!

Abbreviation: | SEGBIND
Full name: | SegmentBinding
Belongs to: | SetCategory
Operations: | = coerce equation segment variable

Abbreviation: | SEG
Full name: | Segment
Belongs to: | SegmentCategory SegmentExpansionCategory
Operations: | = BY SEGMENT coerce convert expand hi high incr lo low map segment

Abbreviation: | SCFRAC
Full name: | SemiCancelledFraction
Belongs to: | ConvertibleTo QuotientFieldCategory

Operations:

0 1 * ** + - / < = D abs associates? ceiling characteristic charthRoot coerce conditionP convert denom denominator differentiate divide elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial floor fractionPart gcd gcdPolynomial init inv lcm map max min multiEuclidean negative? nextItem normalize numer numerator one? patternMatch positive? prime? principalIdeal quo random recip reducedSystem rem retract retractIfCan sign sizeLess? solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial unit? unitCanonical unitNormal wholePart zero?

Abbreviation: | SDPOL
Full name: | SequentialDifferentialPolynomial
Belongs to: | DifferentialPolynomialCategory RetractableTo

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP content degree differentialVariables differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? initial isExpt isPlus isTimes isobaric? lcm leader leadingCoefficient leadingMonomial mainVariable makeVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? order prime? primitiveMonomials primitivePart recip reducedSystem reductum resultant retract retractIfCan separant solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables weight weights zero?

Abbreviation: | SDVAR
Full name: | SequentialDifferentialVariable
Belongs to: | DifferentialVariableCategory
Operations: | < = D coerce differentiate makeVariable max min order retract retractIfCan variable weight

Abbreviation: | SET
Full name: | Set
Belongs to: | FiniteSetAggregate
Operations: | # < = any? bag brace cardinality coerce complement construct convert copy count dictionary difference empty empty? eq? every? extract! find index insert! inspect intersect less? lookup map map! max member? members min more? parts random reduce remove remove! removeDuplicates select select! size size? subset? symmetricDifference union universe

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

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

Abbreviation: | SAE
Full name: | SimpleAlgebraicExtension
Belongs to: | MonogenicAlgebra

Operations:

0 1 * ** + - / = D associates? basis characteristic characteristicPolynomial charthRoot coerce conditionP convert coordinates createPrimitiveElement definingPolynomial derivationCoordinates differentiate discreteLog discriminant divide euclideanSize expressIdealMember exquo extendedEuclidean factor factorsOfCyclicGroupSize gcd generator index init inv lcm lift lookup minimalPolynomial multiEuclidean nextItem norm one? order prime? primeFrobenius primitive? primitiveElement principalIdeal quo random rank recip reduce reducedSystem regularRepresentation rem representationType represents retract retractIfCan size sizeLess? squareFree squareFreePart tableForDiscreteLogarithm trace traceMatrix unit? unitCanonical unitNormal zero?

Abbreviation: | SAOS
Full name: | SingletonAsOrderedSet
Belongs to: | OrderedSet
Operations: | < = coerce create max min

Abbreviation: | SINT
Full name: | SingleInteger
Belongs to: | IntegerNumberSystem

Operations:

0 1 * ** + - < = And D Not Or \^{} abs addmod and associates? base binomial bit? characteristic coerce convert copy dec differentiate divide euclideanSize even? expressIdealMember exquo extendedEuclidean factor factorial gcd hash inc init invmod lcm length mask max min mulmod multiEuclidean negative? nextItem not odd? one? or patternMatch permutation positive? positiveRemainder powmod prime? principalIdeal quo random rational rational? rationalIfCan recip reducedSystem rem retract retractIfCan shift sign sizeLess? squareFree squareFreePart submod symmetricRemainder unit? unitCanonical unitNormal xor zero?

Abbreviation: | SMP
Full name: | SparseMultivariatePolynomial
Belongs to: | PolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce conditionP content convert degree differentiate discriminant eval exquo factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multivariate numberOfMonomials one? patternMatch prime? primitiveMonomials primitivePart recip reducedSystem reductum resultant retract retractIfCan solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial totalDegree unit? unitCanonical unitNormal univariate variables zero?

Abbreviation: | SMTS
Full name: | SparseMultivariateTaylorSeries
Belongs to: | MultivariateTaylorSeriesCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch asec asech asin asinh associates? atan atanh characteristic charthRoot coefficient coerce complete cos cosh cot coth csc csch csubst degree differentiate eval exp exquo extend fintegrate integrate leadingCoefficient leadingMonomial log map monomial monomial? nthRoot one? order pi pole? polynomial recip reductum sec sech sin sinh sqrt tan tanh unit? unitCanonical unitNormal variables zero?

Abbreviation: | STBL
Full name: | SparseTable
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? map map! maxIndex member? members minIndex more? parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | SUP
Full name: | SparseUnivariatePolynomial
Belongs to: | UnivariatePolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce composite conditionP content degree differentiate discriminant divide divideExponents elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? init integrate isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable makeSUP map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multiEuclidean multiplyExponents multivariate nextItem numberOfMonomials one? order outputForm prime? primitiveMonomials primitivePart principalIdeal pseudoDivide pseudoQuotient pseudoRemainder quo recip reducedSystem reductum rem resultant retract retractIfCan separate sizeLess? solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial subResultantGcd totalDegree unit? unitCanonical unitNormal univariate unmakeSUP variables vectorise zero?

Abbreviation: | SUTS
Full name: | SparseUnivariateTaylorSeries
Belongs to: | UnivariateTaylorSeriesCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch approximate asec asech asin asinh associates? atan atanh center characteristic charthRoot coefficient coefficients coerce complete cos cosh cot coth csc csch degree differentiate elt eval exp exquo extend integrate leadingCoefficient leadingMonomial log map monomial monomial? multiplyCoefficients multiplyExponents nthRoot one? order pi pole? polynomial quoByVar recip reductum sec sech series sin sinh sqrt tan tanh terms truncate unit? unitCanonical unitNormal variable variables zero?

Abbreviation: | SQMATRIX
Full name: | SquareMatrix
Belongs to: | CoercibleTo SquareMatrixCategory

Operations:

0 1 # * ** + - / = D antisymmetric? any? characteristic coerce column copy count determinant diagonal diagonal? diagonalMatrix diagonalProduct differentiate elt empty empty? eq? every? exquo inverse less? listOfLists map map! matrix maxColIndex maxRowIndex member? members minColIndex minRowIndex minordet more? ncols nrows nullSpace nullity one? parts qelt rank recip reducedSystem retract retractIfCan row rowEchelon scalarMatrix size? square? squareMatrix symmetric? trace transpose zero?

Abbreviation: | STACK
Full name: | Stack
Belongs to: | StackAggregate
Operations: | # = any? bag coerce copy count depth empty empty? eq? every? extract! insert! inspect less? map map! member? members more? parts pop! push! size? stack top

Abbreviation: | STREAM
Full name: | Stream
Belongs to: | LazyStreamAggregate

Operations:

# = any? child? children coerce complete concat concat! cons construct convert copy count cycleEntry cycleLength cycleSplit! cycleTail cyclic? delay delete distance elt empty empty? entries entry? eq? every? explicitEntries? explicitlyEmpty? explicitlyFinite? extend fill! filterUntil filterWhile find findCycle first frst generate index? indices insert last lazy? lazyEvaluate leaf? less? map map! maxIndex member? members minIndex more? new node? nodes numberOfComputedEntries output parts possiblyInfinite? qelt qsetelt! reduce remove removeDuplicates repeating repeating? rest rst second select setchildren! setelt setfirst! setlast! setrest! setvalue! showAll? showAllElements size? split! swap! tail third value

Abbreviation: | STRTBL
Full name: | StringTable
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? map map! maxIndex member? members minIndex more? parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | STRING
Full name: | String
Belongs to: | StringCategory

Operations:

# < = any? coerce concat construct copy copyInto! count delete elt empty empty? entries entry? eq? every? fill! find first index? indices insert leftTrim less? lowerCase lowerCase! map map! match? max maxIndex member? members merge min minIndex more? new parts position prefix? qelt qsetelt! reduce remove removeDuplicates replace reverse reverse! rightTrim select setelt size? sort sort! sorted? split string substring? suffix? swap! trim upperCase upperCase!

Abbreviation: | COMPPROP
Full name: | SubSpaceComponentProperty
Belongs to: | SetCategory
Operations: | = close closed? coerce copy new solid solid?

Abbreviation: | SUBSPACE
Full name: | SubSpace
Belongs to: | SetCategory
Operations: | = addPoint addPoint2 addPointLast birth child children closeComponent coerce deepCopy defineProperty extractClosed extractIndex extractPoint extractProperty internal? leaf? level merge modifyPoint new numberOfChildren parent pointData root? separate shallowCopy subspace traverse

Abbreviation: | SUCH
Full name: | SuchThat
Belongs to: | SetCategory
Operations: | = coerce construct lhs rhs

Abbreviation: | SYMBOL
Full name: | Symbol
Belongs to: | ConvertibleTo OrderedSet PatternMatchable
Operations: | < = argscript coerce convert elt list max min name new patternMatch resetNew script scripted? scripts string subscript superscript

Abbreviation: | SYMPOLY
Full name: | SymmetricPolynomial
Belongs to: | FiniteAbelianMonoidRing
Operations: | 0 1 * ** + - / = associates? characteristic charthRoot coefficient coefficients coerce content degree exquo ground ground? leadingCoefficient leadingMonomial map mapExponents minimumDegree monomial monomial? numberOfMonomials one? primitivePart recip reductum retract retractIfCan unit? unitCanonical unitNormal zero?

Abbreviation: | TABLEAU
Full name: | Tableau
Belongs to: | Object
Operations: | coerce listOfLists tableau

Abbreviation: | TABLE
Full name: | Table
Belongs to: | TableAggregate
Operations: | # = any? bag coerce construct copy count dictionary elt empty empty? entries entry? eq? every? extract! fill! find first index? indices insert! inspect key? keys less? map map! maxIndex member? members minIndex more? parts qelt qsetelt! reduce remove remove! removeDuplicates search select select! setelt size? swap! table

Abbreviation: | TS
Full name: | TaylorSeries
Belongs to: | MultivariateTaylorSeriesCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch asec asech asin asinh associates? atan atanh characteristic charthRoot coefficient coerce complete cos cosh cot coth csc csch degree differentiate eval exp exquo extend fintegrate integrate leadingCoefficient leadingMonomial log map monomial monomial? nthRoot one? order pi pole? polynomial recip reductum sec sech sin sinh sqrt tan tanh unit? unitCanonical unitNormal variables zero?

Abbreviation: | TEX1
Full name: | TexFormat1
Belongs to: | Object
Operations: | coerce

Abbreviation: | TEX
Full name: | TexFormat
Belongs to: | SetCategory
Operations: | = coerce convert display epilogue new prologue setEpilogue! setPrologue! setTex! tex

Abbreviation: | TEXTFILE
Full name: | TextFile
Belongs to: | FileCategory
Operations: | = close! coerce endOfFile? iomode name open read! readIfCan! readLine! readLineIfCan! reopen! write! writeLine!

Abbreviation: | VIEW3D
Full name: | ThreeDimensionalViewport
Belongs to: | SetCategory

Operations:

= axes clipSurface close coerce 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

Abbreviation: | SPACE3
Full name: | ThreeSpace
Belongs to: | ThreeSpaceCategory
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: | TREE
Full name: | Tree
Belongs to: | RecursiveAggregate
Operations: | # = any? children coerce copy count cyclic? elt empty empty? eq? every? leaf? leaves less? map map! member? members more? node? nodes parts setchildren! setelt setvalue! size? tree value

Abbreviation: | TUBE
Full name: | TubePlot
Belongs to: |
Operations: | closed? getCurve listLoops open? setClosed tube

Abbreviation: | TUPLE
Full name: | Tuple
Belongs to: | CoercibleTo SetCategory
Operations: | = coerce length select

Abbreviation: | ARRAY2
Full name: | TwoDimensionalArray
Belongs to: | TwoDimensionalArrayCategory
Operations: | # = any? coerce column copy count elt empty empty? eq? every? fill! less? map map! maxColIndex maxRowIndex member? members minColIndex minRowIndex more? ncols new nrows parts qelt qsetelt! row setColumn! setRow! setelt size?

Abbreviation: | VIEW2D
Full name: | TwoDimensionalViewport
Belongs to: | SetCategory
Operations: | = axes close coerce connect controlPanel dimensions getGraph graphState graphStates graphs key makeViewport2D move options points putGraph region reset resize scale show title translate units viewport2D write

Abbreviation: | ULSCONS
Full name: | UnivariateLaurentSeriesConstructor
Belongs to: | UnivariateLaurentSeriesConstructorCategory

Operations:

0 1 * ** + - / < = D abs acos acosh acot acoth acsc acsch approximate asec asech asin asinh associates? atan atanh ceiling center characteristic charthRoot coefficient coerce complete conditionP convert cos cosh cot coth csc csch degree denom denominator differentiate divide elt euclideanSize eval exp expressIdealMember exquo extend extendedEuclidean factor factorPolynomial factorSquareFreePolynomial floor fractionPart gcd gcdPolynomial init integrate inv laurent lcm leadingCoefficient leadingMonomial log map max min monomial monomial? multiEuclidean multiplyCoefficients multiplyExponents negative? nextItem nthRoot numer numerator one? order patternMatch pi pole? positive? prime? principalIdeal quo random rationalFunction recip reducedSystem reductum rem removeZeroes retract retractIfCan sec sech series sign sin sinh sizeLess? solveLinearPolynomialEquation sqrt squareFree squareFreePart squareFreePolynomial tan tanh taylor taylorIfCan taylorRep terms truncate unit? unitCanonical unitNormal variable variables wholePart zero?

Abbreviation: | ULS
Full name: | UnivariateLaurentSeries
Belongs to: | UnivariateLaurentSeriesConstructorCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch approximate asec asech asin asinh associates? atan atanh center characteristic charthRoot coefficient coerce complete cos cosh cot coth csc csch degree denom denominator differentiate divide elt euclideanSize eval exp expressIdealMember exquo extend extendedEuclidean factor gcd integrate inv laurent lcm leadingCoefficient leadingMonomial log map monomial monomial? multiEuclidean multiplyCoefficients multiplyExponents nthRoot numer numerator one? order pi pole? prime? principalIdeal quo rationalFunction recip reducedSystem reductum rem removeZeroes retract retractIfCan sec sech series sin sinh sizeLess? sqrt squareFree squareFreePart tan tanh taylor taylorIfCan taylorRep terms truncate unit? unitCanonical unitNormal variable variables zero?

Abbreviation: | UP
Full name: | UnivariatePolynomial
Belongs to: | UnivariatePolynomialCategory

Operations:

0 1 * ** + - / < = D associates? characteristic charthRoot coefficient coefficients coerce composite conditionP content degree differentiate discriminant divide divideExponents elt euclideanSize eval expressIdealMember exquo extendedEuclidean factor factorPolynomial factorSquareFreePolynomial gcd gcdPolynomial ground ground? init integrate isExpt isPlus isTimes lcm leadingCoefficient leadingMonomial mainVariable makeSUP map mapExponents max min minimumDegree monicDivide monomial monomial? monomials multiEuclidean multiplyExponents multivariate nextItem numberOfMonomials one? order prime? primitiveMonomials primitivePart principalIdeal pseudoDivide pseudoQuotient pseudoRemainder quo recip reducedSystem reductum rem resultant retract retractIfCan separate sizeLess? solveLinearPolynomialEquation squareFree squareFreePart squareFreePolynomial subResultantGcd totalDegree unit? unitCanonical unitNormal univariate unmakeSUP variables vectorise zero?

Abbreviation: | UPXSCONS
Full name: | UnivariatePuiseuxSeriesConstructor
Belongs to: | UnivariatePuiseuxSeriesConstructorCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch approximate asec asech asin asinh associates? atan atanh center characteristic charthRoot coefficient coerce complete cos cosh cot coth csc csch degree differentiate divide elt euclideanSize eval exp expressIdealMember exquo extend extendedEuclidean factor gcd integrate inv laurent laurentIfCan laurentRep lcm leadingCoefficient leadingMonomial log map monomial monomial? multiEuclidean multiplyExponents nthRoot one? order pi pole? prime? principalIdeal puiseux quo rationalPower recip reductum rem retract retractIfCan sec sech series sin sinh sizeLess? sqrt squareFree squareFreePart tan tanh terms truncate unit? unitCanonical unitNormal variable variables zero?

Abbreviation: | UPXS
Full name: | UnivariatePuiseuxSeries
Belongs to: | UnivariatePuiseuxSeriesConstructorCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch approximate asec asech asin asinh associates? atan atanh center characteristic charthRoot coefficient coerce complete cos cosh cot coth csc csch degree differentiate divide elt euclideanSize eval exp expressIdealMember exquo extend extendedEuclidean factor gcd integrate inv laurent laurentIfCan laurentRep lcm leadingCoefficient leadingMonomial log map monomial monomial? multiEuclidean multiplyExponents nthRoot one? order pi pole? prime? principalIdeal puiseux quo rationalPower recip reductum rem retract retractIfCan sec sech series sin sinh sizeLess? sqrt squareFree squareFreePart tan tanh terms truncate unit? unitCanonical unitNormal variable variables zero?

Abbreviation: | UTS
Full name: | UnivariateTaylorSeries
Belongs to: | UnivariateTaylorSeriesCategory

Operations:

0 1 * ** + - / = D acos acosh acot acoth acsc acsch approximate asec asech asin asinh associates? atan atanh center characteristic charthRoot coefficient coefficients coerce complete cos cosh cot coth csc csch degree differentiate elt eval evenlambert exp exquo extend generalLambert integrate invmultisect lagrange lambert leadingCoefficient leadingMonomial log map monomial monomial? multiplyCoefficients multiplyExponents multisect nthRoot oddlambert one? order pi pole? polynomial quoByVar recip reductum revert sec sech series sin sinh sqrt tan tanh terms truncate unit? unitCanonical unitNormal univariatePolynomial variable variables zero?

Abbreviation: | UNISEG
Full name: | UniversalSegment
Belongs to: | SegmentCategory SegmentExpansionCategory
Operations: | = BY SEGMENT coerce convert expand hasHi hi high incr lo low map segment

Abbreviation: | VARIABLE
Full name: | Variable
Belongs to: | CoercibleTo SetCategory
Operations: | = coerce variable

Abbreviation: | VECTOR
Full name: | Vector
Belongs to: | VectorCategory
Operations: | # * + - < = any? coerce concat construct convert copy copyInto! count delete dot elt empty empty? entries entry? eq? every? fill! find first index? indices insert less? map map! max maxIndex member? members merge min minIndex more? new parts position qelt qsetelt! reduce remove removeDuplicates reverse reverse! select setelt size? sort sort! sorted? swap! vector zero

Abbreviation: | VOID
Full name: | Void
Belongs to: |
Operations: | coerce void

Book Contents Previous Section 17.1 Axiom Categories Next Section 19.1 Axiom Packages Book Index