$SPAD/src/input dop.input

Timothy Daly December 3, 2016

Abstract

Contents

2

1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

———-

— * —

)set break resume
)spool dop.output
)set message test on
)set message auto off
)clear all
--S 1 of 127
)d op binaryTree
--R
--R
--RThere are 2 exposed functions called binaryTree :
--R   [1] (BinaryTree(D1),D1,BinaryTree(D1)) -> BinaryTree(D1)
--R            from BinaryTree(D1) if D1 has SETCAT
--R   [2] D1 -> BinaryTree(D1) from BinaryTree(D1) if D1 has SETCAT
--R
--RExamples of binaryTree from BinaryTree
--R
--Rt1:=binaryTree([1,2,3])
--Rt2:=binaryTree([4,5,6])
--RbinaryTree(t1,[7,8,9],t2)
--R
--Rt1:=binaryTree([1,2,3])
--R
--E 1
--S 2 of 127
)d op rationalPoint?
--R
--R
--RThere is one exposed function called rationalPoint? :
--R   [1] (D2,D2) -> Boolean from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RThere is one unexposed function called rationalPoint? :
--R   [1] (D2,D2) -> Boolean from FunctionFieldCategory&(D3,D2,D4,D5)
--R            if D2 has UFD and D4 has UPOLYC(D2) and D5 has UPOLYC(FRAC(
--R            D4)) and D3 has FFCAT(D2,D4,D5)
--R
--RExamples of rationalPoint? from FunctionFieldCategory&

--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RrationalPoint?(0,0)$R
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
--RrationalPoint?(0,0)$R2
--R
--R
--RExamples of rationalPoint? from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RrationalPoint?(0,0)$R
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
--RrationalPoint?(0,0)$R2
--R
--E 2
--S 3 of 127
)d op nthFactor
--R
--R
--RThere are 2 exposed functions called nthFactor :
--R   [1] (D,Integer) -> D1 from D
--R            if D has FAMONC(D1,D3) and D3 has CABMON and D1 has SETCAT
--R
--R   [2] (Factored(D1),Integer) -> D1 from Factored(D1) if D1 has INTDOM
--R
--R
--RThere are 4 unexposed functions called nthFactor :
--R   [1] (FreeGroup(D1),Integer) -> D1 from FreeGroup(D1) if D1 has
--R            SETCAT
--R   [2] (FreeMonoid(D1),Integer) -> D1 from FreeMonoid(D1) if D1 has
--R            SETCAT
--R   [3] (ListMonoidOps(D1,D3,D4),Integer) -> D1 from ListMonoidOps(D1,D3
--R            ,D4)
--R            if D1 has SETCAT and D3 has ABELMON and D4: D3
--R   [4] (OrderedFreeMonoid(D1),Integer) -> D1 from OrderedFreeMonoid(D1)
--R            if D1 has ORDSET
--R
--RExamples of nthFactor from FreeAbelianMonoidCategory
--R
--R
--RExamples of nthFactor from FreeGroup
--R
--R
--RExamples of nthFactor from FreeMonoid
--R

--R
--RExamples of nthFactor from Factored
--R
--Ra:=factor 9720000
--RnthFactor(a,2)
--R
--R
--RExamples of nthFactor from ListMonoidOps
--R
--R
--RExamples of nthFactor from OrderedFreeMonoid
--R
--Rm1:=(x*y*y*z)$OFMONOID(Symbol)
--RnthFactor(m1,2)
--R
--E 3
--S 4 of 127
)d op qsetelt!
--R
--R
--RThere are 2 exposed functions called qsetelt! :
--R   [1] (D,Integer,Integer,D1) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
--R            (D1) and D4 has FLAGG(D1)
--R   [2] (D,D2,D1) -> D1 from D
--R            if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2
--R            has SETCAT and D1 has TYPE
--R
--RExamples of qsetelt! from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0)
--Rqsetelt!(arr,1,1,17)
--R
--R
--RExamples of qsetelt! from EltableAggregate
--R
--E 4
--S 5 of 127
)d op cycleElt
--R
--R
--RThere is one unexposed function called cycleElt :
--R   [1] D1 -> Union(D1,"failed") from CyclicStreamTools(D2,D1)
--R            if D2 has TYPE and D1 has LZSTAGG(D2)
--R
--RExamples of cycleElt from CyclicStreamTools
--R
--Rp:=repeating([1,2,3])

--Rq:=cons(4,p)
--RcycleElt q
--Rr:=[1,2,3]::Stream(Integer)
--RcycleElt r
--R
--E 5
--S 6 of 127
)d op cyclicEntries
--R
--R
--RThere is one exposed function called cyclicEntries :
--R   [1] Tree(D2) -> List(Tree(D2)) from Tree(D2) if D2 has SETCAT
--R
--RExamples of cyclicEntries from Tree
--R
--Rt1:=tree [1,2,3,4]
--RcyclicEntries t1
--R
--E 6
--S 7 of 127
)d op oneDimensionalArray
--R
--R
--RThere are 2 exposed functions called oneDimensionalArray :
--R   [1] (NonNegativeInteger,D2) -> OneDimensionalArray(D2)
--R            from OneDimensionalArray(D2) if D2 has TYPE
--R   [2] List(D2) -> OneDimensionalArray(D2) from OneDimensionalArray(D2)
--R            if D2 has TYPE
--R
--RExamples of oneDimensionalArray from OneDimensionalArray
--R
--RoneDimensionalArray(10,0.0)
--R
--RoneDimensionalArray [i**2 for i in 1..10]
--R
--E 7
--S 8 of 127
)d op alphanumeric?
--R
--R
--RThere is one exposed function called alphanumeric? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of alphanumeric? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[alphanumeric? c for c in chars]

--R
--E 8
--S 9 of 127
)d op digit?
--R
--R
--RThere is one exposed function called digit? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of digit? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[digit? c for c in chars]
--R
--E 9
--S 10 of 127
)d op sqfrFactor
--R
--R
--RThere is one exposed function called sqfrFactor :
--R   [1] (D1,Integer) -> Factored(D1) from Factored(D1) if D1 has INTDOM
--R
--R
--RExamples of sqfrFactor from Factored
--R
--Ra:=sqfrFactor(3,5)
--RnthFlag(a,1)
--R
--E 10
--S 11 of 127
)d op integralMatrix
--R
--R
--RThere is one exposed function called integralMatrix :
--R   [1]  -> Matrix(Fraction(D3)) from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RExamples of integralMatrix from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RintegralMatrix()$R
--R
--E 11

--S 12 of 127
)d op ptree
--R
--R
--RThere are 2 exposed functions called ptree :
--R   [1] (PendantTree(D1),PendantTree(D1)) -> PendantTree(D1)
--R            from PendantTree(D1) if D1 has SETCAT
--R   [2] D1 -> PendantTree(D1) from PendantTree(D1) if D1 has SETCAT
--R
--RExamples of ptree from PendantTree
--R
--Rt1:=ptree([1,2,3])
--Rptree(t1,ptree([1,2,3]))
--R
--Rt1:=ptree([1,2,3])
--R
--E 12
--S 13 of 127
)d op insert!
--R
--R
--RThere are 13 exposed functions called insert! :
--R   [1] (D1,ArrayStack(D1)) -> ArrayStack(D1) from ArrayStack(D1)
--R            if D1 has SETCAT
--R   [2] (D1,D) -> D from D if D has BGAGG(D1) and D1 has TYPE
--R   [3] (D1,BinarySearchTree(D1)) -> BinarySearchTree(D1)
--R            from BinarySearchTree(D1) if D1 has ORDSET
--R   [4] (D1,BinaryTournament(D1)) -> BinaryTournament(D1)
--R            from BinaryTournament(D1) if D1 has ORDSET
--R   [5] (D1,Dequeue(D1)) -> Dequeue(D1) from Dequeue(D1) if D1 has
--R            SETCAT
--R   [6] (D,D,Integer) -> D from D if D has ELAGG(D2) and D2 has TYPE
--R   [7] (D1,D,Integer) -> D from D if D has ELAGG(D1) and D1 has TYPE
--R
--R   [8] (D1,Heap(D1)) -> Heap(D1) from Heap(D1) if D1 has ORDSET
--R   [9] Record(key: Record(var: Symbol,fn: Expression(DoubleFloat),range
--R            : Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,
--R            relerr: DoubleFloat),entry: Record(endPointContinuity: Union(
--R            continuous: Continuous at the end points,lowerSingular:
--R            There is a singularity at the lower end point,upperSingular:
--R            There is a singularity at the upper end point,bothSingular:
--R            There are singularities at both end points,notEvaluated:
--R            End point continuity not yet evaluated),singularitiesStream:
--R            Union(str: Stream(DoubleFloat),notEvaluated:
--R            Internal singularities not yet evaluated),range: Union(finite:
--R            The range is finite,lowerInfinite:
--R            The bottom of range is infinite,upperInfinite:
--R            The top of range is infinite,bothInfinite:
--R            Both top and bottom points are infinite,notEvaluated:

--R            Range not yet evaluated))) -> IntegrationFunctionsTable
--R            from IntegrationFunctionsTable
--R   [10] (D1,D,NonNegativeInteger) -> D from D
--R            if D has MDAGG(D1) and D1 has SETCAT
--R   [11] Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn:
--R            Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals
--R            : List(DoubleFloat),g: Expression(DoubleFloat),abserr:
--R            DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float,
--R            stability: Float,expense: Float,accuracy: Float,
--R            intermediateResults: Float)) -> ODEIntensityFunctionsTable
--R            from ODEIntensityFunctionsTable
--R   [12] (D1,Queue(D1)) -> Queue(D1) from Queue(D1) if D1 has SETCAT
--R   [13] (D1,Stack(D1)) -> Stack(D1) from Stack(D1) if D1 has SETCAT
--R
--RThere is one unexposed function called insert! :
--R   [1] (D2,D3) -> Void from TabulatedComputationPackage(D2,D3)
--R            if D2 has SETCAT and D3 has SETCAT
--R
--RExamples of insert! from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5]
--Rinsert!(8,a)
--Ra
--R
--R
--RExamples of insert! from BagAggregate
--R
--R
--RExamples of insert! from BinarySearchTree
--R
--Rt1:=binarySearchTree [1,2,3,4]
--Rinsert!(5,t1)
--R
--R
--RExamples of insert! from BinaryTournament
--R
--Rt1:=binaryTournament [1,2,3,4]
--Rinsert!(5,t1)
--Rt1
--R
--R
--RExamples of insert! from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5]
--Rinsert! (8,a)
--Ra
--R
--R
--RExamples of insert! from ExtensibleLinearAggregate
--R

--R
--RExamples of insert! from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5]
--Rinsert!(8,a)
--Ra
--R
--R
--RExamples of insert! from IntegrationFunctionsTable
--R
--R
--RExamples of insert! from MultiDictionary
--R
--R
--RExamples of insert! from ODEIntensityFunctionsTable
--R
--R
--RExamples of insert! from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5]
--Rinsert! (8,a)
--Ra
--R
--R
--RExamples of insert! from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5]
--Rinsert!(8,a)
--Ra
--R
--R
--RExamples of insert! from TabulatedComputationPackage
--R
--E 13
--S 14 of 127
)d op genus
--R
--R
--RThere are 5 exposed functions called genus :
--R   [1] D6 -> NonNegativeInteger
--R            from DesingTreePackage(D7,D8,D6,D9,D10,D11,D12,D1,D2,D3,D4)
--R            if D7 has FIELD and D8: LIST(SYMBOL) and D6 has POLYCAT(D7,
--R            D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D10 has
--R            PRSPCAT(D7) and D11 has LOCPOWC(D7) and D12 has PLACESC(D7,
--R            D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D7,D8,D6,D9,
--R            D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2
--R            )
--R   [2]  -> NonNegativeInteger from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(

--R            D2) and D4 has UPOLYC(FRAC(D3))
--R   [3]  -> NonNegativeInteger
--R            from GeneralPackageForAlgebraicFunctionField(D6,D7,D8,D9,
--R            D10,D11,D12,D1,D2,D3,D4)
--R            if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6,
--R            D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has
--R            PRSPCAT(D6) and D11 has LOCPOWC(D6) and D12 has PLACESC(D6,
--R            D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D6,D7,D8,D9,
--R            D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2
--R            )
--R   [4]  -> NonNegativeInteger
--R            from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3,
--R            D4)
--R            if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT
--R
--R   [5]  -> NonNegativeInteger from PackageForAlgebraicFunctionField(D2,
--R            D3,D4)
--R            if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT
--R
--RThere is one unexposed function called genus :
--R   [1]  -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
--R            if D3 has UFD and D4 has UPOLYC(D3) and D5 has UPOLYC(FRAC(
--R            D4)) and D2 has FFCAT(D3,D4,D5)
--R
--RExamples of genus from DesingTreePackage
--R
--R
--RExamples of genus from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--Rgenus()$R
--R
--R
--RExamples of genus from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--Rgenus()$R
--R
--R
--RExamples of genus from GeneralPackageForAlgebraicFunctionField
--R
--R
--RExamples of genus from PackageForAlgebraicFunctionFieldOverFiniteField
--R
--R
--RExamples of genus from PackageForAlgebraicFunctionField

--S 15 of 127
)d op hexDigit?
--R
--R
--RThere is one exposed function called hexDigit? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of hexDigit? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[hexDigit? c for c in chars]
--R
--E 15
--S 16 of 127
)d op computeCycleLength
--R
--R
--RThere is one unexposed function called computeCycleLength :
--R   [1] D2 -> NonNegativeInteger from CyclicStreamTools(D3,D2)
--R            if D3 has TYPE and D2 has LZSTAGG(D3)
--R
--RExamples of computeCycleLength from CyclicStreamTools
--R
--Rp:=repeating([1,2,3])
--Rq:=cons(4,p)
--RcomputeCycleLength(cycleElt(q))
--R
--E 16
--S 17 of 127
)d op findCycle
--R
--R
--RThere is one exposed function called findCycle :
--R   [1] (NonNegativeInteger,Stream(D3)) -> Record(cycle?: Boolean,prefix
--R            : NonNegativeInteger,period: NonNegativeInteger)
--R            from Stream(D3) if D3 has TYPE
--R
--RExamples of findCycle from Stream
--R
--Rm:=[1,2,3]
--Rn:=repeating(m)
--RfindCycle(3,n)
--RfindCycle(2,n)
--R
--E 17

--S 18 of 127
)d op draw
--R
--R
--RThere are 31 exposed functions called draw :
--R   [1] ((DoubleFloat -> DoubleFloat),Segment(Float),List(DrawOption))
--R             -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [2] ((DoubleFloat -> DoubleFloat),Segment(Float)) ->
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [3] (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment(
--R            Float),List(DrawOption)) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [4] (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment(
--R            Float)) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [5] (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(
--R            Float),List(DrawOption)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [6] (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment(
--R            Float)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [7] ((DoubleFloat -> Point(DoubleFloat)),Segment(Float),List(
--R            DrawOption)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [8] ((DoubleFloat -> Point(DoubleFloat)),Segment(Float)) ->
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [9] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float),
--R            Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [10] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float),
--R            Segment(Float)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [11] (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(
--R            Float),Segment(Float),List(DrawOption)) ->
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [12] (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment(
--R            Float),Segment(Float)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [13] (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)),
--R            Segment(Float),Segment(Float),List(DrawOption)) ->
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions
--R   [14] (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)),
--R            Segment(Float),Segment(Float)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForCompiledFunctions

--R   [15] (Equation(D6),Symbol,Symbol,List(DrawOption)) ->
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForAlgebraicCurves(D5,D6)
--R            if D6 has FS(D5) and D5 has Join(IntegralDomain,OrderedSet,
--R            RetractableTo(Integer))
--R   [16] (D2,SegmentBinding(Float),List(DrawOption)) ->
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctions(D2)
--R            if D2 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [17] (D2,SegmentBinding(Float)) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctions(D2)
--R            if D2 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [18] (ParametricPlaneCurve(D5),SegmentBinding(Float),List(DrawOption
--R            )) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctions(D5)
--R            if D5 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [19] (ParametricPlaneCurve(D4),SegmentBinding(Float)) ->
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctions(D4)
--R            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [20] (ParametricSpaceCurve(D5),SegmentBinding(Float),List(DrawOption
--R            )) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions(D5)
--R            if D5 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [21] (ParametricSpaceCurve(D4),SegmentBinding(Float)) ->
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctions(D4)
--R            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [22] (D2,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption
--R            )) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions(D2)
--R            if D2 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [23] (D2,SegmentBinding(Float),SegmentBinding(Float)) ->
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctions(D2)
--R            if D2 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [24] (ParametricSurface(D5),SegmentBinding(Float),SegmentBinding(
--R            Float),List(DrawOption)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions(D5)
--R            if D5 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [25] (ParametricSurface(D4),SegmentBinding(Float),SegmentBinding(
--R            Float)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctions(D4)
--R            if D4 has Join(ConvertibleTo(InputForm),SetCategory)
--R   [26] (List(DoubleFloat),List(DoubleFloat)) -> TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [27] (List(DoubleFloat),List(DoubleFloat),List(DrawOption)) ->
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [28] List(Point(DoubleFloat)) -> TwoDimensionalViewport

--R            from TopLevelDrawFunctionsForPoints
--R   [29] (List(Point(DoubleFloat)),List(DrawOption)) ->
--R            TwoDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [30] (List(DoubleFloat),List(DoubleFloat),List(DoubleFloat)) ->
--R            ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R   [31] (List(DoubleFloat),List(DoubleFloat),List(DoubleFloat),List(
--R            DrawOption)) -> ThreeDimensionalViewport
--R            from TopLevelDrawFunctionsForPoints
--R
--RExamples of draw from TopLevelDrawFunctionsForCompiledFunctions
--R
--R
--RExamples of draw from TopLevelDrawFunctionsForAlgebraicCurves
--R
--R
--RExamples of draw from TopLevelDrawFunctions
--R
--R
--RExamples of draw from TopLevelDrawFunctionsForPoints
--R
--E 18
--S 19 of 127
)d op repeating
--R
--R
--RThere is one exposed function called repeating :
--R   [1] List(D2) -> Stream(D2) from Stream(D2) if D2 has TYPE
--R
--RExamples of repeating from Stream
--R
--Rm:=repeating([-1,0,1,2,3])
--R
--E 19
--S 20 of 127
)d op cons
--R
--R
--RThere are 2 exposed functions called cons :
--R   [1] (D1,List(D1)) -> List(D1) from List(D1) if D1 has TYPE
--R   [2] (D1,Stream(D1)) -> Stream(D1) from Stream(D1) if D1 has TYPE
--R
--RExamples of cons from List
--R
--R
--RExamples of cons from Stream
--R

--Rm:=[1,2,3]
--Rn:=repeating(m)
--Rcons(4,n)
--R
--E 20
--S 21 of 127
)d op map
--R
--R
--RThere are 86 exposed functions called map :
--R   [1] ((D2 -> D2),D) -> D from D
--R            if D has AMR(D2,D3) and D2 has RING and D3 has OAMON
--R   [2] (((D2,D2) -> D2),D,D,D2) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [3] (((D2,D2) -> D2),D,D) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [4] ((D2 -> D2),D) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [5] ((D4 -> D5),OneDimensionalArray(D4)) -> OneDimensionalArray(D5)
--R            from OneDimensionalArrayFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [6] ((D2 -> D2),ArrayStack(D2)) -> ArrayStack(D2) from ArrayStack(D2
--R            )
--R            if D2 has SETCAT
--R   [7] ((D6 -> D7),CartesianTensor(D4,D5,D6)) -> CartesianTensor(D4,D5,
--R            D7)
--R            from CartesianTensorFunctions2(D4,D5,D6,D7)
--R            if D4: INT and D5: NNI and D6 has COMRING and D7 has
--R            COMRING
--R   [8] ((D4 -> D5),Complex(D4)) -> Complex(D5) from ComplexFunctions2(
--R            D4,D5)
--R            if D4 has COMRING and D5 has COMRING
--R   [9] ((D2 -> D2),Dequeue(D2)) -> Dequeue(D2) from Dequeue(D2)
--R            if D2 has SETCAT
--R   [10] ((D5 -> D6),DirectProduct(D4,D5)) -> DirectProduct(D4,D6)
--R            from DirectProductFunctions2(D4,D5,D6)
--R            if D4: NNI and D5 has TYPE and D6 has TYPE
--R   [11] ((D4 -> D5),Equation(D4)) -> Equation(D5)
--R            from EquationFunctions2(D4,D5) if D4 has TYPE and D5 has
--R            TYPE
--R   [12] ((D2 -> D2),Equation(D2)) -> Equation(D2) from Equation(D2)
--R            if D2 has TYPE
--R   [13] ((D4 -> D1),Kernel(D4)) -> D1 from ExpressionSpaceFunctions2(D4
--R            ,D1)
--R            if D4 has ES and D1 has ES
--R   [14] ((D -> D),Kernel(D)) -> D from D if D has ES

--R   [15] ((D4 -> D5),Matrix(D4)) -> Matrix(D5)
--R            from ExpertSystemToolsPackage2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [16] ((D4 -> D5),Expression(D4)) -> Expression(D5)
--R            from ExpressionFunctions2(D4,D5)
--R            if D4 has ORDSET and D5 has ORDSET
--R   [17] ((D5 -> D6),D3) -> D1
--R            from FiniteAbelianMonoidRingFunctions2(D4,D5,D3,D6,D1)
--R            if D5 has RING and D6 has RING and D4 has OAMON and D1 has
--R            FAMR(D6,D4) and D3 has FAMR(D5,D4)
--R   [18] ((D7 -> D11),FiniteDivisor(D7,D8,D9,D10)) -> FiniteDivisor(D11,
--R            D1,D2,D3)
--R            from FiniteDivisorFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
--R            if D7 has FIELD and D8 has UPOLYC(D7) and D9 has UPOLYC(
--R            FRAC(D8)) and D10 has FFCAT(D7,D8,D9) and D11 has FIELD and
--R            D1 has UPOLYC(D11) and D2 has UPOLYC(FRAC(D1)) and D3 has
--R            FFCAT(D11,D1,D2)
--R   [19] ((D2 -> D2),D) -> D from D if D has FEVALAB(D2) and D2 has
--R            SETCAT
--R   [20] ((D5 -> D8),D4) -> D2
--R            from FunctionFieldCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,
--R            D2)
--R            if D5 has UFD and D8 has UFD and D6 has UPOLYC(D5) and D7
--R            has UPOLYC(FRAC(D6)) and D9 has UPOLYC(D8) and D2 has FFCAT
--R            (D8,D9,D1) and D4 has FFCAT(D5,D6,D7) and D1 has UPOLYC(
--R            FRAC(D9))
--R   [21] ((D4 -> D5),D3) -> D1 from FiniteLinearAggregateFunctions2(D4,
--R            D3,D5,D1)
--R            if D4 has TYPE and D5 has TYPE and D1 has FLAGG(D5) and D3
--R            has FLAGG(D4)
--R   [22] ((D2 -> D2),D) -> D from D
--R            if D has FMCAT(D2,D3) and D2 has RING and D3 has SETCAT
--R   [23] ((D4 -> D5),Factored(D4)) -> Factored(D5)
--R            from FactoredFunctions2(D4,D5)
--R            if D4 has INTDOM and D5 has INTDOM
--R   [24] ((D4 -> D5),Fraction(D4)) -> Fraction(D5)
--R            from FractionFunctions2(D4,D5)
--R            if D4 has INTDOM and D5 has INTDOM
--R   [25] ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal(
--R            D11,D1,D2,D3)
--R            from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3)
--R            if D7 has EUCDOM and D8 has QFCAT(D7) and D9 has UPOLYC(D8)
--R            and D10 has Join(FramedAlgebra(D8,D9),RetractableTo(D8))
--R            and D11 has EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC(
--R            D1) and D3 has Join(FramedAlgebra(D1,D2),RetractableTo(D1))
--R
--R   [26] ((D4 -> D5),D3) -> D1
--R            from FramedNonAssociativeAlgebraFunctions2(D3,D4,D1,D5)
--R            if D4 has COMRING and D5 has COMRING and D1 has FRNAALG(D5)
--R            and D3 has FRNAALG(D4)

--R   [27] ((D2 -> D2),Factored(D2)) -> Factored(D2) from Factored(D2)
--R            if D2 has INTDOM
--R   [28] ((D4 -> D5),D3) -> D1 from FunctionSpaceFunctions2(D4,D3,D5,D1)
--R            if D4 has Join(Ring,OrderedSet) and D5 has Join(Ring,
--R            OrderedSet) and D1 has FS(D5) and D3 has FS(D4)
--R   [29] ((D4 -> D5),D3) -> D1 from FiniteSetAggregateFunctions2(D4,D3,
--R            D5,D1)
--R            if D4 has SETCAT and D5 has SETCAT and D1 has FSAGG(D5) and
--R            D3 has FSAGG(D4)
--R   [30] ((D2 -> D2),Heap(D2)) -> Heap(D2) from Heap(D2) if D2 has
--R            ORDSET
--R   [31] ((D2 -> D2),D) -> D from D if D has HOAGG(D2) and D2 has TYPE
--R
--R   [32] ((D2 -> D2),D) -> D from D
--R            if D has IDPC(D2,D3) and D2 has SETCAT and D3 has ORDSET
--R
--R   [33] ((D4 -> D5),IntegrationResult(D4)) -> IntegrationResult(D5)
--R            from IntegrationResultFunctions2(D4,D5)
--R            if D4 has FIELD and D5 has FIELD
--R   [34] ((D4 -> D5),Union(Record(ratpart: D4,coeff: D4),"failed")) ->
--R            Union(Record(ratpart: D5,coeff: D5),"failed")
--R            from IntegrationResultFunctions2(D4,D5)
--R            if D4 has FIELD and D5 has FIELD
--R   [35] ((D4 -> D1),Union(D4,"failed")) -> Union(D1,"failed")
--R            from IntegrationResultFunctions2(D4,D1)
--R            if D4 has FIELD and D1 has FIELD
--R   [36] ((D4 -> D5),Union(Record(mainpart: D4,limitedlogs: List(Record(
--R            coeff: D4,logand: D4))),"failed")) -> Union(Record(mainpart: D5,
--R            limitedlogs: List(Record(coeff: D5,logand: D5))),"failed")
--R            from IntegrationResultFunctions2(D4,D5)
--R            if D4 has FIELD and D5 has FIELD
--R   [37] ((D4 -> D5),InfiniteTuple(D4)) -> InfiniteTuple(D5)
--R            from InfiniteTupleFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [38] (((D5,D6) -> D7),InfiniteTuple(D5),InfiniteTuple(D6)) ->
--R            InfiniteTuple(D7)
--R            from InfiniteTupleFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [39] (((D5,D6) -> D7),Stream(D5),InfiniteTuple(D6)) -> Stream(D7)
--R            from InfiniteTupleFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [40] (((D5,D6) -> D7),InfiniteTuple(D5),Stream(D6)) -> Stream(D7)
--R            from InfiniteTupleFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [41] ((D2 -> D2),InfiniteTuple(D2)) -> InfiniteTuple(D2)
--R            from InfiniteTuple(D2) if D2 has TYPE
--R   [42] ((D4 -> D5),List(D4)) -> List(D5) from ListFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [43] (((D5,D6) -> D7),List(D5),List(D6)) -> List(D7)
--R            from ListFunctions3(D5,D6,D7)

--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [44] (((D2,D2) -> D2),D,D) -> D from D if D has LNAGG(D2) and D2 has
--R            TYPE
--R   [45] ((D5 -> D8),D4) -> D2
--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
--R            if D5 has RING and D8 has RING and D6 has FLAGG(D5) and D7
--R            has FLAGG(D5) and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT
--R            (D5,D6,D7) and D9 has FLAGG(D8) and D1 has FLAGG(D8)
--R   [46] ((D5 -> Union(D8,"failed")),D4) -> Union(D2,"failed")
--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D8,D9,D1,D2)
--R            if D5 has RING and D8 has RING and D6 has FLAGG(D5) and D7
--R            has FLAGG(D5) and D2 has MATCAT(D8,D9,D1) and D4 has MATCAT
--R            (D5,D6,D7) and D9 has FLAGG(D8) and D1 has FLAGG(D8)
--R   [47] ((D7 -> D8),D3) -> D1 from MPolyCatFunctions2(D4,D5,D6,D7,D8,D3
--R            ,D1)
--R            if D7 has RING and D8 has RING and D4 has ORDSET and D5 has
--R            OAMONS and D1 has POLYCAT(D8,D6,D4) and D6 has OAMONS and
--R            D3 has POLYCAT(D7,D5,D4)
--R   [48] ((D4 -> D5),MonoidRing(D4,D6)) -> MonoidRing(D5,D6)
--R            from MonoidRingFunctions2(D4,D5,D6)
--R            if D4 has RING and D5 has RING and D6 has MONOID
--R   [49] ((D4 -> D5),D3) -> D1 from OctonionCategoryFunctions2(D3,D4,D1,
--R            D5)
--R            if D4 has COMRING and D5 has COMRING and D1 has OC(D5) and
--R            D3 has OC(D4)
--R   [50] ((D4 -> D5),OnePointCompletion(D4)) -> OnePointCompletion(D5)
--R            from OnePointCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [51] ((D4 -> D5),OnePointCompletion(D4),OnePointCompletion(D5)) ->
--R            OnePointCompletion(D5)
--R            from OnePointCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [52] ((D4 -> D5),OrderedCompletion(D4)) -> OrderedCompletion(D5)
--R            from OrderedCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [53] ((D4 -> D5),OrderedCompletion(D4),OrderedCompletion(D5),
--R            OrderedCompletion(D5)) -> OrderedCompletion(D5)
--R            from OrderedCompletionFunctions2(D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [54] ((D4 -> D5),ParametricPlaneCurve(D4)) -> ParametricPlaneCurve(
--R            D5)
--R            from ParametricPlaneCurveFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [55] ((D4 -> D5),ParametricSpaceCurve(D4)) -> ParametricSpaceCurve(
--R            D5)
--R            from ParametricSpaceCurveFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [56] ((D4 -> D5),ParametricSurface(D4)) -> ParametricSurface(D5)
--R            from ParametricSurfaceFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE

--R   [57] ((D5 -> D6),PatternMatchResult(D4,D5)) -> PatternMatchResult(D4
--R            ,D6)
--R            from PatternMatchResultFunctions2(D4,D5,D6)
--R            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
--R   [58] ((D4 -> D5),Pattern(D4)) -> Pattern(D5) from PatternFunctions2(
--R            D4,D5)
--R            if D4 has SETCAT and D5 has SETCAT
--R   [59] ((D4 -> D5),Polynomial(D4)) -> Polynomial(D5)
--R            from PolynomialFunctions2(D4,D5) if D4 has RING and D5 has
--R            RING
--R   [60] ((D4 -> D5),PrimitiveArray(D4)) -> PrimitiveArray(D5)
--R            from PrimitiveArrayFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [61] ((D4 -> D5),Point(D4)) -> Point(D5) from PointFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [62] ((D4 -> D5),D3) -> D1 from QuotientFieldCategoryFunctions2(D4,
--R            D5,D3,D1)
--R            if D4 has INTDOM and D5 has INTDOM and D1 has QFCAT(D5) and
--R            D3 has QFCAT(D4)
--R   [63] ((D4 -> D5),D3) -> D1 from QuaternionCategoryFunctions2(D3,D4,
--R            D1,D5)
--R            if D4 has COMRING and D5 has COMRING and D1 has QUATCAT(D5)
--R            and D3 has QUATCAT(D4)
--R   [64] ((D2 -> D2),Queue(D2)) -> Queue(D2) from Queue(D2) if D2 has
--R            SETCAT
--R   [65] (((D4,D4) -> D4),D,D) -> D from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R   [66] ((D4 -> D4),D) -> D from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R   [67] ((D9 -> D1),D6) -> D4
--R            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
--R            D6,D1,D2,D3,D4)
--R            if D9 has RING and D1 has RING and D7: NNI and D8: NNI and
--R            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D4
--R            has RMATCAT(D7,D8,D1,D2,D3) and D6 has RMATCAT(D7,D8,D9,D10
--R            ,D11) and D2 has DIRPCAT(D8,D1) and D3 has DIRPCAT(D7,D1)
--R
--R   [68] ((D4 -> D5),Segment(D4)) -> Segment(D5) from SegmentFunctions2(
--R            D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [69] ((D4 -> D5),Segment(D4)) -> List(D5) from SegmentFunctions2(D4,
--R            D5)
--R            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
--R   [70] ((D4 -> D5),SegmentBinding(D4)) -> SegmentBinding(D5)
--R            from SegmentBindingFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [71] ((D3 -> D3),D) -> D1 from D
--R            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG

--R            (D3)
--R   [72] ((D2 -> D2),Stack(D2)) -> Stack(D2) from Stack(D2) if D2 has
--R            SETCAT
--R   [73] ((D4 -> D5),Stream(D4)) -> Stream(D5) from StreamFunctions2(D4,
--R            D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [74] (((D5,D6) -> D7),Stream(D5),Stream(D6)) -> Stream(D7)
--R            from StreamFunctions3(D5,D6,D7)
--R            if D5 has TYPE and D6 has TYPE and D7 has TYPE
--R   [75] ((D4 -> D5),SparseUnivariatePolynomial(D4)) ->
--R            SparseUnivariatePolynomial(D5)
--R            from SparseUnivariatePolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [76] (((D3,D3) -> D3),D,D) -> D from D
--R            if D has TBAGG(D2,D3) and D2 has SETCAT and D3 has SETCAT
--R
--R   [77] ((D5 -> D6),UnivariateLaurentSeries(D5,D7,D9)) ->
--R            UnivariateLaurentSeries(D6,D8,D1)
--R            from UnivariateLaurentSeriesFunctions2(D5,D6,D7,D8,D9,D1)
--R            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5
--R            and D1: D6 and D8: SYMBOL
--R   [78] ((D4 -> D5),UniversalSegment(D4)) -> UniversalSegment(D5)
--R            from UniversalSegmentFunctions2(D4,D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [79] ((D4 -> D5),UniversalSegment(D4)) -> Stream(D5)
--R            from UniversalSegmentFunctions2(D4,D5)
--R            if D4 has ORDRING and D4 has TYPE and D5 has TYPE
--R   [80] ((D5 -> D7),UnivariatePolynomial(D4,D5)) ->
--R            UnivariatePolynomial(D6,D7)
--R            from UnivariatePolynomialFunctions2(D4,D5,D6,D7)
--R            if D4: SYMBOL and D5 has RING and D7 has RING and D6:
--R            SYMBOL
--R   [81] ((D4 -> D5),D3) -> D1
--R            from UnivariatePolynomialCategoryFunctions2(D4,D3,D5,D1)
--R            if D4 has RING and D5 has RING and D1 has UPOLYC(D5) and D3
--R            has UPOLYC(D4)
--R   [82] ((D5 -> D6),UnivariatePuiseuxSeries(D5,D7,D9)) ->
--R            UnivariatePuiseuxSeries(D6,D8,D1)
--R            from UnivariatePuiseuxSeriesFunctions2(D5,D6,D7,D8,D9,D1)
--R            if D5 has RING and D6 has RING and D7: SYMBOL and D9: D5
--R            and D1: D6 and D8: SYMBOL
--R   [83] ((D4 -> D5),D3) -> D1
--R            from UnivariateTaylorSeriesFunctions2(D4,D5,D3,D1)
--R            if D4 has RING and D5 has RING and D1 has UTSCAT(D5) and D3
--R            has UTSCAT(D4)
--R   [84] ((D4 -> D5),Vector(D4)) -> Vector(D5) from VectorFunctions2(D4,
--R            D5)
--R            if D4 has TYPE and D5 has TYPE
--R   [85] ((D4 -> Union(D5,"failed")),Vector(D4)) -> Union(Vector(D5),
--R            "failed")

--R            from VectorFunctions2(D4,D5) if D4 has TYPE and D5 has TYPE
--R
--R   [86] ((D3 -> D3),D) -> D from D
--R            if D has XFALG(D2,D3) and D2 has ORDSET and D3 has RING
--R
--RThere are 10 unexposed functions called map :
--R   [1] ((D2 -> D2),AntiSymm(D2,D3)) -> AntiSymm(D2,D3) from AntiSymm(D2
--R            ,D3)
--R            if D2 has RING and D3: LIST(SYMBOL)
--R   [2] ((Expression(D2) -> Expression(D2)),DeRhamComplex(D2,D3)) ->
--R            DeRhamComplex(D2,D3)
--R            from DeRhamComplex(D2,D3)
--R            if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL)
--R   [3] ((D5 -> D1),String,Kernel(D5)) -> D1
--R            from ExpressionSpaceFunctions1(D5,D1)
--R            if D5 has ES and D1 has TYPE
--R   [4] ((D4 -> D6),D3) -> D1 from MultipleMap(D4,D5,D3,D6,D7,D1)
--R            if D4 has INTDOM and D6 has INTDOM and D5 has UPOLYC(D4)
--R            and D1 has UPOLYC(FRAC(D7)) and D3 has UPOLYC(FRAC(D5)) and
--R            D7 has UPOLYC(D6)
--R   [5] ((D4 -> D5),D3) -> D1 from MPolyCatFunctions3(D4,D5,D6,D7,D8,D3,
--R            D1)
--R            if D4 has ORDSET and D5 has ORDSET and D6 has OAMONS and D8
--R            has RING and D1 has POLYCAT(D8,D7,D5) and D7 has OAMONS and
--R            D3 has POLYCAT(D8,D6,D4)
--R   [6] ((D2 -> D2),MonoidRing(D2,D3)) -> MonoidRing(D2,D3)
--R            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
--R   [7] ((D4 -> D5),NewSparseUnivariatePolynomial(D4)) ->
--R            NewSparseUnivariatePolynomial(D5)
--R            from NewSparseUnivariatePolynomialFunctions2(D4,D5)
--R            if D4 has RING and D5 has RING
--R   [8] ((D7 -> D2),(D8 -> D2),D5) -> D2
--R            from PolynomialCategoryLifting(D6,D7,D8,D5,D2)
--R            if D7 has ORDSET and D8 has RING and D6 has OAMONS and D2
--R            has SetCategory with
--R               ?+? : (%,%) -> %
--R               ?*? : (%,%) -> %
--R               D : (%,NonNegativeInteger) -> %and D5 has POLYCAT(D8
--R            ,D6,D7)
--R   [9] ((Polynomial(D3) -> D1),D1) -> D1 from PushVariables(D3,D4,D5,D1
--R            )
--R            if D3 has RING and D1 has POLYCAT(POLY(D3),D4,D5) and D4
--R            has OAMONS and D5 has OrderedSet with
--R               convert : % -> Symbol
--R               variable : Symbol -> Union(%,"failed")
--R   [10] ((D2 -> D2),XPolynomialRing(D2,D3)) -> XPolynomialRing(D2,D3)
--R            from XPolynomialRing(D2,D3) if D2 has RING and D3 has
--R            ORDMON
--R
--RExamples of map from AbelianMonoidRing

--R
--R
--RExamples of map from AntiSymm
--R
--R
--RExamples of map from TwoDimensionalArrayCategory
--R
--Radder(a:Integer,b:Integer):Integer == a+b
--Rarr1 : ARRAY2 INT := new(5,4,10)
--Rarr2 : ARRAY2 INT := new(3,3,10)
--Rmap(adder,arr1,arr2,17)
--R
--Radder(a:Integer,b:Integer):Integer == a+b
--Rarr : ARRAY2 INT := new(5,4,10)
--Rmap(adder,arr,arr)
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rmap(-,arr)
--Rmap((x +-> x + x),arr)
--R
--R
--RExamples of map from OneDimensionalArrayFunctions2
--R
--RT1:=OneDimensionalArrayFunctions2(Integer,Integer)
--Rmap(x+->x+2,[i for i in 1..10])$T1
--R
--R
--RExamples of map from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5]
--Rmap(x+->x+10,a)
--Ra
--R
--R
--RExamples of map from CartesianTensorFunctions2
--R
--R
--RExamples of map from ComplexFunctions2
--R
--R
--RExamples of map from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5]
--Rmap(x+->x+10,a)
--Ra
--R
--R
--RExamples of map from DeRhamComplex
--R
--R

--RExamples of map from DirectProductFunctions2
--R
--R
--RExamples of map from EquationFunctions2
--R
--R
--RExamples of map from Equation
--R
--R
--RExamples of map from ExpressionSpaceFunctions1
--R
--R
--RExamples of map from ExpressionSpaceFunctions2
--R
--R
--RExamples of map from ExpressionSpace
--R
--R
--RExamples of map from ExpertSystemToolsPackage2
--R
--R
--RExamples of map from ExpressionFunctions2
--R
--R
--RExamples of map from FiniteAbelianMonoidRingFunctions2
--R
--R
--RExamples of map from FiniteDivisorFunctions2
--R
--R
--RExamples of map from FullyEvalableOver
--R
--R
--RExamples of map from FunctionFieldCategoryFunctions2
--R
--R
--RExamples of map from FiniteLinearAggregateFunctions2
--R
--R
--RExamples of map from FreeModuleCat
--R
--R
--RExamples of map from FactoredFunctions2
--R
--R
--RExamples of map from FractionFunctions2
--R
--R
--RExamples of map from FractionalIdealFunctions2
--R

--R
--RExamples of map from FramedNonAssociativeAlgebraFunctions2
--R
--R
--RExamples of map from Factored
--R
--Rm(a:Factored Polynomial Integer):Factored Polynomial Integer == a^2
--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4
--Rmap(m,f)
--Rg:=makeFR(z,factorList f)
--Rmap(m,g)
--R
--R
--RExamples of map from FunctionSpaceFunctions2
--R
--R
--RExamples of map from FiniteSetAggregateFunctions2
--R
--R
--RExamples of map from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5]
--Rmap(x+->x+10,a)
--Ra
--R
--R
--RExamples of map from HomogeneousAggregate
--R
--R
--RExamples of map from IndexedDirectProductCategory
--R
--R
--RExamples of map from IntegrationResultFunctions2
--R
--R
--RExamples of map from InfiniteTupleFunctions2
--R
--R
--RExamples of map from InfiniteTupleFunctions3
--R
--R
--RExamples of map from InfiniteTuple
--R
--R
--RExamples of map from ListFunctions2
--R
--R
--RExamples of map from ListFunctions3
--R
--R

--RExamples of map from LinearAggregate
--R
--R
--RExamples of map from MatrixCategoryFunctions2
--R
--R
--RExamples of map from MultipleMap
--R
--R
--RExamples of map from MPolyCatFunctions2
--R
--R
--RExamples of map from MPolyCatFunctions3
--R
--R
--RExamples of map from MonoidRingFunctions2
--R
--R
--RExamples of map from MonoidRing
--R
--R
--RExamples of map from NewSparseUnivariatePolynomialFunctions2
--R
--R
--RExamples of map from OctonionCategoryFunctions2
--R
--R
--RExamples of map from OnePointCompletionFunctions2
--R
--R
--RExamples of map from OrderedCompletionFunctions2
--R
--R
--RExamples of map from ParametricPlaneCurveFunctions2
--R
--R
--RExamples of map from ParametricSpaceCurveFunctions2
--R
--R
--RExamples of map from ParametricSurfaceFunctions2
--R
--R
--RExamples of map from PatternMatchResultFunctions2
--R
--R
--RExamples of map from PatternFunctions2
--R
--R
--RExamples of map from PolynomialFunctions2
--R

--R
--RExamples of map from PolynomialCategoryLifting
--R
--R
--RExamples of map from PrimitiveArrayFunctions2
--R
--RT1:=PrimitiveArrayFunctions2(Integer,Integer)
--Rmap(x+->x+2,[i for i in 1..10])$T1
--R
--R
--RExamples of map from PointFunctions2
--R
--R
--RExamples of map from PushVariables
--R
--R
--RExamples of map from QuotientFieldCategoryFunctions2
--R
--R
--RExamples of map from QuaternionCategoryFunctions2
--R
--Rf(a:FRAC(INT)):COMPLEX(FRAC(INT)) == a::COMPLEX(FRAC(INT))
--Rq:=quatern(2/11,-8,3/4,1)
--Rmap(f,q)
--R
--R
--RExamples of map from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5]
--Rmap(x+->x+10,a)
--Ra
--R
--R
--RExamples of map from RectangularMatrixCategory
--R
--R
--RExamples of map from RectangularMatrixCategoryFunctions2
--R
--R
--RExamples of map from SegmentFunctions2
--R
--R
--RExamples of map from SegmentBindingFunctions2
--R
--R
--RExamples of map from SegmentExpansionCategory
--R
--R
--RExamples of map from Stack
--R

--Ra:Stack INT:= stack [1,2,3,4,5]
--Rmap(x+->x+10,a)
--Ra
--R
--R
--RExamples of map from StreamFunctions2
--R
--Rm:=[i for i in 1..]
--Rf(i:PositiveInteger):PositiveInteger==i**2
--Rmap(f,m)
--R
--R
--RExamples of map from StreamFunctions3
--R
--Rm:=[i for i in 1..]::Stream(Integer)
--Rn:=[i for i in 1..]::Stream(Integer)
--Rf(i:Integer,j:Integer):Integer == i+j
--Rmap(f,m,n)
--R
--R
--RExamples of map from SparseUnivariatePolynomialFunctions2
--R
--R
--RExamples of map from TableAggregate
--R
--R
--RExamples of map from UnivariateLaurentSeriesFunctions2
--R
--R
--RExamples of map from UniversalSegmentFunctions2
--R
--R
--RExamples of map from UnivariatePolynomialFunctions2
--R
--R
--RExamples of map from UnivariatePolynomialCategoryFunctions2
--R
--R
--RExamples of map from UnivariatePuiseuxSeriesFunctions2
--R
--R
--RExamples of map from UnivariateTaylorSeriesFunctions2
--R
--R
--RExamples of map from VectorFunctions2
--R
--R
--RExamples of map from XFreeAlgebra
--R
--R

--RExamples of map from XPolynomialRing
--R
--E 21
--S 22 of 127
)d op complete
--R
--R
--RThere are 5 exposed functions called complete :
--R   [1] ContinuedFraction(D1) -> ContinuedFraction(D1)
--R            from ContinuedFraction(D1) if D1 has EUCDOM
--R   [2] Integer -> SymmetricPolynomial(Fraction(Integer)) from
--R            CycleIndicators
--R   [3] D -> D from D if D has LZSTAGG(D1) and D1 has TYPE
--R   [4] D -> D from D if D has PADICCT(D1)
--R   [5] D -> D from D
--R            if D has PSCAT(D1,D2,D3) and D1 has RING and D2 has OAMON
--R            and D3 has ORDSET
--R
--RExamples of complete from ContinuedFraction
--R
--R
--RExamples of complete from CycleIndicators
--R
--R
--RExamples of complete from LazyStreamAggregate
--R
--Rm:=[i for i in 1..]
--Rn:=filterUntil(i+->i>100,m)
--RnumberOfComputedEntries n
--Rcomplete n
--RnumberOfComputedEntries n
--R
--R
--RExamples of complete from PAdicIntegerCategory
--R
--R
--RExamples of complete from PowerSeriesCategory
--R
--E 22
--S 23 of 127
)d op cyclicEqual?
--R
--R
--RThere is one exposed function called cyclicEqual? :
--R   [1] (Tree(D2),Tree(D2)) -> Boolean from Tree(D2) if D2 has SETCAT
--R
--R
--RExamples of cyclicEqual? from Tree

--R
--Rt1:=tree [1,2,3,4]
--Rt2:=tree [1,2,3,4]
--RcyclicEqual?(t1,t2)
--R
--E 23
--S 24 of 127
)d op ncols
--R
--R
--RThere are 2 exposed functions called ncols :
--R   [1] D -> NonNegativeInteger from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] D -> NonNegativeInteger from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of ncols from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rncols(arr)
--R
--R
--RExamples of ncols from RectangularMatrixCategory
--R
--E 24
--S 25 of 127
)d op inverseIntegralMatrixAtInfinity
--R
--R
--RThere is one exposed function called inverseIntegralMatrixAtInfinity :
--R   [1]  -> Matrix(Fraction(D3)) from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RExamples of inverseIntegralMatrixAtInfinity from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RinverseIntegralMatrixAtInfinity()$R
--R
--E 25
--S 26 of 127
)d op generalizedContinuumHypothesisAssumed
--R

--R
--RThere is one exposed function called generalizedContinuumHypothesisAssumed :
--R   [1] Boolean -> Boolean from CardinalNumber
--R
--RExamples of generalizedContinuumHypothesisAssumed from CardinalNumber
--R
--RgeneralizedContinuumHypothesisAssumed true
--Ra:=Aleph 0
--Rc:=2**a
--Rf:=2**c
--R
--E 26
--S 27 of 127
)d op cyclic?
--R
--R
--RThere are 2 exposed functions called cyclic? :
--R   [1] D -> Boolean from D if D has RCAGG(D2) and D2 has TYPE
--R   [2] Tree(D2) -> Boolean from Tree(D2) if D2 has SETCAT
--R
--RExamples of cyclic? from RecursiveAggregate
--R
--R
--RExamples of cyclic? from Tree
--R
--Rt1:=tree [1,2,3,4]
--Rcyclic? t1
--R
--E 27
--S 28 of 127
)d op nilFactor
--R
--R
--RThere is one exposed function called nilFactor :
--R   [1] (D1,Integer) -> Factored(D1) from Factored(D1) if D1 has INTDOM
--R
--R
--RExamples of nilFactor from Factored
--R
--RnilFactor(24,2)
--RnilFactor(x-y,3)
--R
--E 28
--S 29 of 127
)d op quote
--R
--R

--RThere is one exposed function called quote :
--R   [1]  -> Character from Character
--R
--RThere is one unexposed function called quote :
--R   [1] OutputForm -> OutputForm from OutputForm
--R
--RExamples of quote from Character
--R
--Rquote()
--R
--R
--RExamples of quote from OutputForm
--R
--E 29
--S 30 of 127
)d op balancedBinaryTree
--R
--R
--RThere is one exposed function called balancedBinaryTree :
--R   [1] (NonNegativeInteger,D2) -> BalancedBinaryTree(D2)
--R            from BalancedBinaryTree(D2) if D2 has SETCAT
--R
--RExamples of balancedBinaryTree from BalancedBinaryTree
--R
--RbalancedBinaryTree(4, 0)
--R
--E 30
--S 31 of 127
)d op integralBasisAtInfinity
--R
--R
--RThere is one exposed function called integralBasisAtInfinity :
--R   [1]  -> Vector(D) from D
--R            if D2 has UFD and D3 has UPOLYC(D2) and D4 has UPOLYC(FRAC(
--R            D3)) and D has FFCAT(D2,D3,D4)
--R
--RExamples of integralBasisAtInfinity from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RintegralBasisAtInfinity()$R
--R
--E 31
--S 32 of 127
)d op branchPointAtInfinity?
--R

--R
--RThere is one exposed function called branchPointAtInfinity? :
--R   [1]  -> Boolean from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RExamples of branchPointAtInfinity? from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RbranchPointAtInfinity?()$R
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
--RbranchPointAtInfinity?()$R
--R
--E 32
--S 33 of 127
)d op transpose
--R
--R
--RThere are 4 exposed functions called transpose :
--R   [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
--R            D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [2] CartesianTensor(D1,D2,D3) -> CartesianTensor(D1,D2,D3)
--R            from CartesianTensor(D1,D2,D3)
--R            if D1: INT and D2: NNI and D3 has COMRING
--R   [3] D -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [4] D1 -> D from D
--R            if D2 has RING and D has MATCAT(D2,D1,D3) and D1 has FLAGG(
--R            D2) and D3 has FLAGG(D2)
--R
--RThere is one unexposed function called transpose :
--R   [1] SquareMatrix(D1,D2) -> SquareMatrix(D1,D2) from SquareMatrix(D1,
--R            D2)
--R            if D1: NNI and D2 has RING
--R
--RExamples of transpose from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
--Rtm:CartesianTensor(1,2,Integer):=m
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm]
--Rtranspose(tn,1,2)
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
--RTm:CartesianTensor(1,2,Integer):=m

--Rtranspose(Tm)
--R
--R
--RExamples of transpose from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rtranspose m
--R
--Rtranspose([1,2,3])@Matrix(INT)
--R
--R
--RExamples of transpose from SquareMatrix
--R
--E 33
--S 34 of 127
)d op setrest!
--R
--R
--RThere are 2 exposed functions called setrest! :
--R   [1] (Stream(D2),Integer,Stream(D2)) -> Stream(D2) from Stream(D2)
--R            if D2 has TYPE
--R   [2] (D,D) -> D from D
--R            if D has shallowlyMutable and D has URAGG(D1) and D1 has
--R            TYPE
--R
--RExamples of setrest! from Stream
--R
--Rp:=[i for i in 1..]
--Rq:=[i for i in 9..]
--Rsetrest!(p,4,q)
--Rp
--R
--R
--RExamples of setrest! from UnaryRecursiveAggregate
--R
--E 34
--S 35 of 127
)d op **
--R
--R
--RThere are 22 exposed functions called ** :
--R   [1] (CardinalNumber,CardinalNumber) -> CardinalNumber from
--R            CardinalNumber
--R   [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat
--R   [3] (D,Integer) -> D from D if D has DIVRING
--R   [4] (D,D) -> D from D if D has ELEMFUN
--R   [5] (Float,Float) -> Float from Float
--R   [6] (D,NonNegativeInteger) -> D from D

--R            if D has FS(D2) and D2 has ORDSET and D2 has SGROUP
--R   [7] (D,Integer) -> D from D if D has GROUP
--R   [8] (PolynomialIdeals(D2,D3,D4,D5),NonNegativeInteger) ->
--R            PolynomialIdeals(D2,D3,D4,D5)
--R            from PolynomialIdeals(D2,D3,D4,D5)
--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5
--R            has POLYCAT(D2,D3,D4)
--R   [9] ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from
--R            MappingPackage1(D3)
--R            if D3 has SETCAT
--R   [10] (D,Integer) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG(
--R            D2) and D4 has FLAGG(D2) and D2 has FIELD
--R   [11] (D,NonNegativeInteger) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG(
--R            D2) and D4 has FLAGG(D2)
--R   [12] (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3)
--R            from ModuleOperator(D2,D3) if D2 has RING and D3 has
--R            LMODULE(D2)
--R   [13] (BasicOperator,Integer) -> ModuleOperator(D3,D4)
--R            from ModuleOperator(D3,D4) if D3 has RING and D4 has
--R            LMODULE(D3)
--R   [14] (D,PositiveInteger) -> D from D if D has MONAD
--R   [15] (D,NonNegativeInteger) -> D from D if D has MONADWU
--R   [16] (D,NonNegativeInteger) -> D from D if D has MONOID
--R   [17] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
--R            )
--R            from MyExpression(D1,D2)
--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [18] (D,Fraction(Integer)) -> D from D if D has RADCAT
--R   [19] (StochasticDifferential(D2),PositiveInteger) ->
--R            StochasticDifferential(D2)
--R            from StochasticDifferential(D2)
--R            if D2 has Join(OrderedSet,IntegralDomain)
--R   [20] (D,PositiveInteger) -> D from D if D has SGROUP
--R   [21] (D,Integer) -> D from D
--R            if D has SMATCAT(D2,D3,D4,D5) and D3 has RING and D4 has
--R            DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) and D3 has FIELD
--R
--R   [22] (D,D1) -> D from D
--R            if D has UTSCAT(D1) and D1 has RING and D1 has FIELD
--R
--RThere are 18 unexposed functions called ** :
--R   [1] (D1,Fraction(Integer)) -> D1 from AlgebraicFunction(D3,D1)
--R            if D3 has RETRACT(INT) and D3 has Join(OrderedSet,
--R            IntegralDomain) and D1 has FS(D3)
--R   [2] (D1,D1) -> D1 from CombinatorialFunction(D2,D1)
--R            if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2)
--R

--R   [3] (D1,Fraction(Integer)) -> D1
--R            from ElementaryFunctionsUnivariateLaurentSeries(D3,D4,D1)
--R            if D3 has FIELD and D3 has ALGEBRA(FRAC(INT)) and D4 has
--R            UTSCAT(D3) and D1 has ULSCCAT(D3,D4)
--R   [4] (D1,Fraction(Integer)) -> D1
--R            from ElementaryFunctionsUnivariatePuiseuxSeries(D3,D4,D1,D5
--R            )
--R            if D3 has FIELD and D3 has ALGEBRA(FRAC(INT)) and D4 has
--R            ULSCAT(D3) and D1 has UPXSCCA(D3,D4) and D5 has PTRANFN(D4)
--R
--R   [5] (D1,Integer) -> FreeGroup(D1) from FreeGroup(D1) if D1 has
--R            SETCAT
--R   [6] (D1,NonNegativeInteger) -> FreeMonoid(D1) from FreeMonoid(D1)
--R            if D1 has SETCAT
--R   [7] (Vector(D3),Integer) -> Vector(D3)
--R            from InnerNormalBasisFieldFunctions(D3) if D3 has FFIELDC
--R
--R   [8] (InputForm,Integer) -> InputForm from InputForm
--R   [9] (InputForm,NonNegativeInteger) -> InputForm from InputForm
--R   [10] (Matrix(D3),NonNegativeInteger) -> Matrix(D3)
--R            from StorageEfficientMatrixOperations(D3) if D3 has RING
--R
--R   [11] (D1,NonNegativeInteger) -> OrderedFreeMonoid(D1)
--R            from OrderedFreeMonoid(D1) if D1 has ORDSET
--R   [12] (Operator(D2),Integer) -> Operator(D2) from Operator(D2) if D2
--R            has RING
--R   [13] (BasicOperator,Integer) -> Operator(D3) from Operator(D3) if D3
--R            has RING
--R   [14] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [15] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1)
--R            if D1 has SETCAT
--R   [16] (Pattern(D2),NonNegativeInteger) -> Pattern(D2) from Pattern(D2
--R            )
--R            if D2 has SETCAT
--R   [17] (Stream(D2),Stream(D2)) -> Stream(D2)
--R            from StreamTranscendentalFunctionsNonCommutative(D2)
--R            if D2 has ALGEBRA(FRAC(INT))
--R   [18] (Stream(D2),Stream(D2)) -> Stream(D2)
--R            from StreamTranscendentalFunctions(D2)
--R            if D2 has ALGEBRA(FRAC(INT))
--R
--RExamples of ** from AlgebraicFunction
--R
--R
--RExamples of ** from CardinalNumber
--R
--Rc2:=2::CardinalNumber
--Rc2**c2
--RA1:=Aleph 1
--RA1**c2

--RgeneralizedContinuumHypothesisAssumed true
--RA1**A1
--R
--R
--RExamples of ** from CombinatorialFunction
--R
--R
--RExamples of ** from DoubleFloat
--R
--R
--RExamples of ** from DivisionRing
--R
--R
--RExamples of ** from ElementaryFunctionsUnivariateLaurentSeries
--R
--R
--RExamples of ** from ElementaryFunctionsUnivariatePuiseuxSeries
--R
--R
--RExamples of ** from ElementaryFunctionCategory
--R
--R
--RExamples of ** from FreeGroup
--R
--R
--RExamples of ** from Float
--R
--R
--RExamples of ** from FreeMonoid
--R
--R
--RExamples of ** from FunctionSpace
--R
--R
--RExamples of ** from Group
--R
--R
--RExamples of ** from PolynomialIdeals
--R
--R
--RExamples of ** from InnerNormalBasisFieldFunctions
--R
--R
--RExamples of ** from InputForm
--R
--R
--RExamples of ** from MappingPackage1
--R
--R
--RExamples of ** from MatrixCategory

--R
--R(matrix [[j**i for i in 0..4] for j in 1..5]) ** 2
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rm**3
--R
--R
--RExamples of ** from StorageEfficientMatrixOperations
--R
--R
--RExamples of ** from ModuleOperator
--R
--R
--RExamples of ** from Monad
--R
--R
--RExamples of ** from MonadWithUnit
--R
--R
--RExamples of ** from Monoid
--R
--R
--RExamples of ** from MyExpression
--R
--R
--RExamples of ** from OrderedFreeMonoid
--R
--Rm1:=(y**3)$OFMONOID(Symbol)
--R
--R
--RExamples of ** from Operator
--R
--R
--RExamples of ** from OutputForm
--R
--R
--RExamples of ** from Pattern
--R
--R
--RExamples of ** from RadicalCategory
--R
--R
--RExamples of ** from StochasticDifferential
--R
--R
--RExamples of ** from SemiGroup
--R
--R
--RExamples of ** from SquareMatrixCategory
--R

--R
--RExamples of ** from StreamTranscendentalFunctionsNonCommutative
--R
--R
--RExamples of ** from StreamTranscendentalFunctions
--R
--R
--RExamples of ** from UnivariateTaylorSeriesCategory
--R
--E 35
--S 36 of 127
)d op plot
--R
--R
--RThere are 12 unexposed functions called plot :
--R   [1] (D2,Symbol,Segment(DoubleFloat)) -> Plot from PlotFunctions1(D2)
--R            if D2 has KONVERT(INFORM)
--R   [2] (D2,D2,Symbol,Segment(DoubleFloat)) -> Plot from PlotFunctions1(
--R            D2)
--R            if D2 has KONVERT(INFORM)
--R   [3] (Plot3D,Segment(DoubleFloat)) -> Plot3D from Plot3D
--R   [4] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
--R            DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment(
--R            DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat),Segment(
--R            DoubleFloat)) -> Plot3D
--R            from Plot3D
--R   [5] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),(
--R            DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),Segment(
--R            DoubleFloat)) -> Plot3D
--R            from Plot3D
--R   [6] (Plot,Segment(DoubleFloat)) -> Plot from Plot
--R   [7] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
--R            Segment(DoubleFloat),Segment(DoubleFloat),Segment(DoubleFloat))
--R             -> Plot
--R            from Plot
--R   [8] ((DoubleFloat -> DoubleFloat),(DoubleFloat -> DoubleFloat),
--R            Segment(DoubleFloat)) -> Plot
--R            from Plot
--R   [9] (List((DoubleFloat -> DoubleFloat)),Segment(DoubleFloat),Segment
--R            (DoubleFloat)) -> Plot
--R            from Plot
--R   [10] (List((DoubleFloat -> DoubleFloat)),Segment(DoubleFloat)) ->
--R            Plot
--R            from Plot
--R   [11] ((DoubleFloat -> DoubleFloat),Segment(DoubleFloat),Segment(
--R            DoubleFloat)) -> Plot
--R            from Plot
--R   [12] ((DoubleFloat -> DoubleFloat),Segment(DoubleFloat)) -> Plot
--R            from Plot

--R
--RExamples of plot from PlotFunctions1
--R
--R
--RExamples of plot from Plot3D
--R
--R
--RExamples of plot from Plot
--R
--Rfp:=(t:DFLOAT):DFLOAT +-> sin(t)
--Rplot(fp,-1.0..1.0)$PLOT
--R
--E 36
--S 37 of 127
)d op factorList
--R
--R
--RThere is one exposed function called factorList :
--R   [1] Factored(D2) -> List(Record(flg: Union("nil","sqfr","irred",
--R            "prime"),fctr: D2,xpnt: Integer))
--R            from Factored(D2) if D2 has INTDOM
--R
--RThere is one unexposed function called factorList :
--R   [1] (D2,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger)
--R             -> List(SparseUnivariatePolynomial(D2))
--R            from ChineseRemainderToolsForIntegralBases(D2,D4,D5)
--R            if D2 has FFIELDC and D4 has UPOLYC(D2) and D5 has UPOLYC(
--R            D4)
--R
--RExamples of factorList from Factored
--R
--Rf:=nilFactor(x-y,3)
--RfactorList f
--R
--R
--RExamples of factorList from ChineseRemainderToolsForIntegralBases
--R
--E 37
--S 38 of 127
)d op physicalLength
--R
--R
--RThere is one exposed function called physicalLength :
--R   [1] FlexibleArray(D2) -> NonNegativeInteger from FlexibleArray(D2)
--R            if D2 has TYPE
--R
--RThere is one unexposed function called physicalLength :
--R   [1] IndexedFlexibleArray(D2,D3) -> NonNegativeInteger

--R            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
--R
--R
--RExamples of physicalLength from FlexibleArray
--R
--R
--RExamples of physicalLength from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20)
--Rt2:=flexibleArray([i for i in 1..10])$T1
--RphysicalLength t2
--R
--E 38
--S 39 of 127
)d op absolutelyIrreducible?
--R
--R
--RThere is one exposed function called absolutelyIrreducible? :
--R   [1]  -> Boolean from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RThere is one unexposed function called absolutelyIrreducible? :
--R   [1]  -> Boolean from FunctionFieldCategory&(D2,D3,D4,D5)
--R            if D3 has UFD and D4 has UPOLYC(D3) and D5 has UPOLYC(FRAC(
--R            D4)) and D2 has FFCAT(D3,D4,D5)
--R
--RExamples of absolutelyIrreducible? from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
--RabsolutelyIrreducible?()$R2
--R
--R
--RExamples of absolutelyIrreducible? from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4)
--RabsolutelyIrreducible?()$R2
--R
--E 39
--S 40 of 127
)d op repeating?
--R
--R
--RThere is one exposed function called repeating? :

--R   [1] (List(D3),Stream(D3)) -> Boolean from Stream(D3)
--R            if D3 has SETCAT and D3 has TYPE
--R
--RExamples of repeating? from Stream
--R
--Rm:=[1,2,3]
--Rn:=repeating(m)
--Rrepeating?(m,n)
--R
--E 40
--S 41 of 127
)d op lazy?
--R
--R
--RThere is one exposed function called lazy? :
--R   [1] D -> Boolean from D if D has LZSTAGG(D2) and D2 has TYPE
--R
--RExamples of lazy? from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--Rlazy? m
--R
--E 41
--S 42 of 127
)d op ord
--R
--R
--RThere is one exposed function called ord :
--R   [1] Character -> Integer from Character
--R
--RExamples of ord from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[ord c for c in chars]
--R
--E 42
--S 43 of 127
)d op setColumn!
--R
--R
--RThere is one exposed function called setColumn! :
--R   [1] (D,Integer,D2) -> D from D
--R            if D has ARR2CAT(D3,D4,D2) and D3 has TYPE and D4 has FLAGG
--R            (D3) and D2 has FLAGG(D3)
--R
--RExamples of setColumn! from TwoDimensionalArrayCategory
--R

--RT1:=TwoDimensionalArray Integer
--Rarr:T1:= new(5,4,0)
--RT2:=OneDimensionalArray Integer
--Racol:=construct([1,2,3,4,5]::List(INT))$T2
--RsetColumn!(arr,1,acol)$T1
--R
--E 43
--S 44 of 127
)d op lowerCase?
--R
--R
--RThere is one exposed function called lowerCase? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of lowerCase? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[lowerCase? c for c in chars]
--R
--E 44
--S 45 of 127
)d op physicalLength!
--R
--R
--RThere is one exposed function called physicalLength! :
--R   [1] (FlexibleArray(D2),Integer) -> FlexibleArray(D2) from
--R            FlexibleArray(D2)
--R            if D2 has TYPE
--R
--RThere is one unexposed function called physicalLength! :
--R   [1] (IndexedFlexibleArray(D2,D3),Integer) -> IndexedFlexibleArray(D2
--R            ,D3)
--R            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
--R
--R
--RExamples of physicalLength! from FlexibleArray
--R
--R
--RExamples of physicalLength! from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20)
--Rt2:=flexibleArray([i for i in 1..10])$T1
--RphysicalLength!(t2,15)
--R
--E 45
--S 46 of 127
)d op countable?

--R
--R
--RThere is one exposed function called countable? :
--R   [1] CardinalNumber -> Boolean from CardinalNumber
--R
--RExamples of countable? from CardinalNumber
--R
--Rc2:=2::CardinalNumber
--Rcountable? c2
--RA0:=Aleph 0
--Rcountable? A0
--RA1:=Aleph 1
--Rcountable? A1
--R
--E 46
--S 47 of 127
)d op extend
--R
--R
--RThere are 11 exposed functions called extend :
--R   [1] (ContinuedFraction(D2),Integer) -> ContinuedFraction(D2)
--R            from ContinuedFraction(D2) if D2 has EUCDOM
--R   [2] (D,Integer) -> D from D if D has LZSTAGG(D2) and D2 has TYPE
--R   [3] (D,NonNegativeInteger) -> D from D
--R            if D has MTSCAT(D2,D3) and D2 has RING and D3 has ORDSET
--R
--R   [4] (D,Integer) -> D from D if D has PADICCT(D2)
--R   [5] (D,List(D2)) -> D from D if D has PTCAT(D2) and D2 has RING
--R   [6] (List(D6),List(D)) -> List(D) from D
--R            if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 has
--R            OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5)
--R   [7] (List(D6),D) -> List(D) from D
--R            if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has
--R            OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6)
--R   [8] (D2,List(D)) -> List(D) from D
--R            if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 has
--R            OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5)
--R   [9] (D2,D) -> List(D) from D
--R            if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and D2
--R            has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2)
--R   [10] (D,D1) -> D from D
--R            if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 has
--R            OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4)
--R   [11] (D,D1) -> D from D
--R            if D has UPSCAT(D2,D1) and D2 has RING and D1 has OAMON
--R
--RExamples of extend from ContinuedFraction
--R
--R

--RExamples of extend from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--RnumberOfComputedEntries m
--Rextend(m,20)
--RnumberOfComputedEntries m
--R
--R
--RExamples of extend from MultivariateTaylorSeriesCategory
--R
--R
--RExamples of extend from PAdicIntegerCategory
--R
--R
--RExamples of extend from PointCategory
--R
--R
--RExamples of extend from RegularTriangularSetCategory
--R
--R
--RExamples of extend from TriangularSetCategory
--R
--R
--RExamples of extend from UnivariatePowerSeriesCategory
--R
--E 47
--S 48 of 127
)d op length
--R
--R
--RThere are 5 exposed functions called length :
--R   [1] Dequeue(D2) -> NonNegativeInteger from Dequeue(D2) if D2 has
--R            SETCAT
--R   [2] D -> D from D if D has INS
--R   [3] D -> NonNegativeInteger from D if D has QUAGG(D2) and D2 has
--R            TYPE
--R   [4] Queue(D2) -> NonNegativeInteger from Queue(D2) if D2 has SETCAT
--R
--R   [5] D -> D1 from D
--R            if D has VECTCAT(D1) and D1 has TYPE and D1 has RADCAT and
--R            D1 has RING
--R
--RThere are 6 unexposed functions called length :
--R   [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1)
--R            if D3 has RING and D1 has Join(FloatingPointSystem,
--R            RetractableTo(D3),Field,TranscendentalFunctionCategory,
--R            ElementaryFunctionCategory) and D2 has UPOLYC(D3)
--R   [2] LyndonWord(D2) -> PositiveInteger from LyndonWord(D2) if D2 has
--R            ORDSET

--R   [3] Magma(D2) -> PositiveInteger from Magma(D2) if D2 has ORDSET
--R   [4] OrderedFreeMonoid(D2) -> NonNegativeInteger from
--R            OrderedFreeMonoid(D2)
--R            if D2 has ORDSET
--R   [5] PoincareBirkhoffWittLyndonBasis(D2) -> NonNegativeInteger
--R            from PoincareBirkhoffWittLyndonBasis(D2) if D2 has ORDSET
--R
--R   [6] Tuple(D2) -> NonNegativeInteger from Tuple(D2) if D2 has TYPE
--R
--R
--RExamples of length from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5]
--Rlength a
--R
--R
--RExamples of length from GaloisGroupFactorizationUtilities
--R
--R
--RExamples of length from IntegerNumberSystem
--R
--R
--RExamples of length from LyndonWord
--R
--R
--RExamples of length from Magma
--R
--R
--RExamples of length from OrderedFreeMonoid
--R
--Rm1:=(x*y*y*z)$OFMONOID(Symbol)
--Rlength m1
--R
--R
--RExamples of length from PoincareBirkhoffWittLyndonBasis
--R
--R
--RExamples of length from QueueAggregate
--R
--R
--RExamples of length from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5]
--Rlength a
--R
--R
--RExamples of length from Tuple
--R
--Rt1:PrimitiveArray(Integer):= [i for i in 1..10]
--Rt2:=coerce(t1)$Tuple(Integer)

--Rlength(t2)
--R
--R
--RExamples of length from VectorCategory
--R
--E 48
--S 49 of 127
)d op viewPosDefault
--R
--R
--RThere are 2 exposed functions called viewPosDefault :
--R   [1]  -> List(NonNegativeInteger) from ViewDefaultsPackage
--R   [2] List(NonNegativeInteger) -> List(NonNegativeInteger)
--R            from ViewDefaultsPackage
--R
--RExamples of viewPosDefault from ViewDefaultsPackage
--R
--E 49
--S 50 of 127
)d op groebner
--R
--R
--RThere are 5 exposed functions called groebner :
--R   [1] List(D5) -> List(D5) from GroebnerPackage(D2,D3,D4,D5)
--R            if D5 has POLYCAT(D2,D3,D4) and D2 has GCDDOM and D3 has
--R            OAMONS and D4 has ORDSET
--R   [2] (List(D6),String) -> List(D6) from GroebnerPackage(D3,D4,D5,D6)
--R            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has
--R            OAMONS and D5 has ORDSET
--R   [3] (List(D6),String,String) -> List(D6) from GroebnerPackage(D3,D4,
--R            D5,D6)
--R            if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has
--R            OAMONS and D5 has ORDSET
--R   [4] PolynomialIdeals(D1,D2,D3,D4) -> PolynomialIdeals(D1,D2,D3,D4)
--R            from PolynomialIdeals(D1,D2,D3,D4)
--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4
--R            has POLYCAT(D1,D2,D3)
--R   [5] List(D6) -> List(D6) from InterfaceGroebnerPackage(D2,D3,D4,D5,
--R            D6)
--R            if D6 has POLYCAT(D2,D4,D5) and D2 has FIELD and D4 has
--R            OAMONS and D5 has ORDSET and D3: LIST(SYMBOL)
--R
--RThere are 2 unexposed functions called groebner :
--R   [1] List(Polynomial(D2)) -> List(Polynomial(D2))
--R            from FGLMIfCanPackage(D2,D3) if D2 has GCDDOM and D3: LIST(
--R            SYMBOL)
--R   [2] List(NewSparseMultivariatePolynomial(D2,OrderedVariableList(D3))
--R            ) -> List(NewSparseMultivariatePolynomial(D2,OrderedVariableList(

--R            D3)))
--R            from LexTriangularPackage(D2,D3)
--R            if D2 has GCDDOM and D3: LIST(SYMBOL)
--R
--RExamples of groebner from FGLMIfCanPackage
--R
--R
--RExamples of groebner from GroebnerPackage
--R
--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
--Rsn7:=[s1,s2,s3,s4,s5,s6,s7]
--Rgroebner(sn7,"info","redcrit")
--R
--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
--Rsn7:=[s1,s2,s3,s4,s5,s6,s7]
--Rgroebner(sn7,"info")
--Rgroebner(sn7,"redcrit")
--R
--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36
--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s
--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2
--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s
--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3
--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2
--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000
--Rsn7:=[s1,s2,s3,s4,s5,s6,s7]
--Rgroebner(sn7)
--R
--R
--RExamples of groebner from PolynomialIdeals
--R
--R
--RExamples of groebner from InterfaceGroebnerPackage
--R
--R
--RExamples of groebner from LexTriangularPackage
--R
--E 50

--S 51 of 127
)d op primeFactor
--R
--R
--RThere is one exposed function called primeFactor :
--R   [1] (D1,Integer) -> Factored(D1) from Factored(D1) if D1 has INTDOM
--R
--R
--RExamples of primeFactor from Factored
--R
--Ra:=primeFactor(3,4)
--RnthFlag(a,1)
--R
--E 51
--S 52 of 127
)d op map!
--R
--R
--RThere are 7 exposed functions called map! :
--R   [1] ((D2 -> D2),D) -> D from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] ((D2 -> D2),ArrayStack(D2)) -> ArrayStack(D2) from ArrayStack(D2
--R            )
--R            if $ has shallowlyMutable and D2 has SETCAT
--R   [3] ((D2 -> D2),Dequeue(D2)) -> Dequeue(D2) from Dequeue(D2)
--R            if $ has shallowlyMutable and D2 has SETCAT
--R   [4] ((D2 -> D2),Heap(D2)) -> Heap(D2) from Heap(D2)
--R            if $ has shallowlyMutable and D2 has ORDSET
--R   [5] ((D2 -> D2),D) -> D from D
--R            if D has shallowlyMutable and D has HOAGG(D2) and D2 has
--R            TYPE
--R   [6] ((D2 -> D2),Queue(D2)) -> Queue(D2) from Queue(D2)
--R            if $ has shallowlyMutable and D2 has SETCAT
--R   [7] ((D2 -> D2),Stack(D2)) -> Stack(D2) from Stack(D2)
--R            if $ has shallowlyMutable and D2 has SETCAT
--R
--RExamples of map! from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rmap!(-,arr)
--R
--R
--RExamples of map! from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5]
--Rmap!(x+->x+10,a)
--Ra

--R
--R
--RExamples of map! from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5]
--Rmap!(x+->x+10,a)
--Ra
--R
--R
--RExamples of map! from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5]
--Rmap!(x+->x+10,a)
--Ra
--R
--R
--RExamples of map! from HomogeneousAggregate
--R
--R
--RExamples of map! from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5]
--Rmap!(x+->x+10,a)
--Ra
--R
--R
--RExamples of map! from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5]
--Rmap!(x+->x+10,a)
--Ra
--R
--E 52
--S 53 of 127
)d op setleaves!
--R
--R
--RThere is one exposed function called setleaves! :
--R   [1] (BalancedBinaryTree(D2),List(D2)) -> BalancedBinaryTree(D2)
--R            from BalancedBinaryTree(D2) if D2 has SETCAT
--R
--RExamples of setleaves! from BalancedBinaryTree
--R
--Rt1:=balancedBinaryTree(4, 0)
--Rsetleaves!(t1,[1,2,3,4])
--R
--E 53
--S 54 of 127

)d op scan
--R
--R
--RThere are 8 exposed functions called scan :
--R   [1] (((D5,D4) -> D4),OneDimensionalArray(D5),D4) ->
--R            OneDimensionalArray(D4)
--R            from OneDimensionalArrayFunctions2(D5,D4)
--R            if D5 has TYPE and D4 has TYPE
--R   [2] (((D6,D4) -> D4),DirectProduct(D5,D6),D4) -> DirectProduct(D5,D4
--R            )
--R            from DirectProductFunctions2(D5,D6,D4)
--R            if D5: NNI and D6 has TYPE and D4 has TYPE
--R   [3] (((D5,D4) -> D4),D3,D4) -> D1
--R            from FiniteLinearAggregateFunctions2(D5,D3,D4,D1)
--R            if D5 has TYPE and D4 has TYPE and D1 has FLAGG(D4) and D3
--R            has FLAGG(D5)
--R   [4] (((D5,D4) -> D4),D3,D4) -> D1
--R            from FiniteSetAggregateFunctions2(D5,D3,D4,D1)
--R            if D5 has SETCAT and D4 has SETCAT and D1 has FSAGG(D4) and
--R            D3 has FSAGG(D5)
--R   [5] (((D5,D4) -> D4),List(D5),D4) -> List(D4) from ListFunctions2(D5
--R            ,D4)
--R            if D5 has TYPE and D4 has TYPE
--R   [6] (((D5,D4) -> D4),PrimitiveArray(D5),D4) -> PrimitiveArray(D4)
--R            from PrimitiveArrayFunctions2(D5,D4)
--R            if D5 has TYPE and D4 has TYPE
--R   [7] (D2,((D5,D2) -> D2),Stream(D5)) -> Stream(D2)
--R            from StreamFunctions2(D5,D2) if D5 has TYPE and D2 has TYPE
--R
--R   [8] (((D5,D4) -> D4),Vector(D5),D4) -> Vector(D4)
--R            from VectorFunctions2(D5,D4) if D5 has TYPE and D4 has TYPE
--R
--R
--RExamples of scan from OneDimensionalArrayFunctions2
--R
--RT1:=OneDimensionalArrayFunctions2(Integer,Integer)
--Radder(a:Integer,b:Integer):Integer == a+b
--Rscan(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of scan from DirectProductFunctions2
--R
--R
--RExamples of scan from FiniteLinearAggregateFunctions2
--R
--R
--RExamples of scan from FiniteSetAggregateFunctions2
--R
--R
--RExamples of scan from ListFunctions2

--R
--R
--RExamples of scan from PrimitiveArrayFunctions2
--R
--RT1:=PrimitiveArrayFunctions2(Integer,Integer)
--Radder(a:Integer,b:Integer):Integer == a+b
--Rscan(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of scan from StreamFunctions2
--R
--Rm:=[i for i in 1..]::Stream(Integer)
--Rf(i:Integer,j:Integer):Integer==i+j
--Rscan(1,f,m)
--R
--R
--RExamples of scan from VectorFunctions2
--R
--E 54
--S 55 of 127
)d op alphabetic?
--R
--R
--RThere is one exposed function called alphabetic? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of alphabetic? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[alphabetic? c for c in chars]
--R
--E 55
--S 56 of 127
)d op +
--R
--R
--RThere are 15 exposed functions called + :
--R   [1] (D,D) -> D from D if D has ABELSG
--R   [2] (Color,Color) -> Color from Color
--R   [3] (Database(D1),Database(D1)) -> Database(D1) from Database(D1)
--R            if D1 has OrderedSet with
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [4] (Equation(D1),D1) -> Equation(D1) from Equation(D1)
--R            if D1 has ABELSG and D1 has TYPE
--R   [5] (D1,Equation(D1)) -> Equation(D1) from Equation(D1)
--R            if D1 has ABELSG and D1 has TYPE

--R   [6] (D1,D) -> D from D
--R            if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON
--R
--R   [7] (D1,FullPartialFractionExpansion(D2,D1)) ->
--R            FullPartialFractionExpansion(D2,D1)
--R            from FullPartialFractionExpansion(D2,D1)
--R            if D2 has Join(Field,CharacteristicZero) and D1 has UPOLYC(
--R            D2)
--R   [8] (D,D) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R
--R   [9] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
--R             -> PolynomialIdeals(D1,D2,D3,D4)
--R            from PolynomialIdeals(D1,D2,D3,D4)
--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4
--R            has POLYCAT(D1,D2,D3)
--R   [10] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
--R            D3)
--R            if D2 has SETCAT and D3 has RING
--R   [11] (D,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [12] (D,Divisor(D)) -> Divisor(D) from D
--R            if D has PLACESC(D2,D3) and D2 has FIELD and D3 has LOCPOWC
--R            (D2)
--R   [13] (Divisor(D),D) -> Divisor(D) from D
--R            if D has PLACESC(D2,D3) and D2 has FIELD and D3 has LOCPOWC
--R            (D2)
--R   [14] (D,D) -> Divisor(D) from D
--R            if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC(D2
--R            ,D3)
--R   [15] (D,D) -> D from D
--R            if D has VECTCAT(D1) and D1 has TYPE and D1 has ABELSG
--R
--RThere are 5 unexposed functions called + :
--R   [1] (InputForm,InputForm) -> InputForm from InputForm
--R   [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [3] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1)
--R            if D1 has SETCAT
--R   [4] (Stream(D2),Stream(D2)) -> Stream(D2)
--R            from StreamTaylorSeriesOperations(D2) if D2 has RING
--R   [5] (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat)
--R            from TubePlotTools
--R
--RExamples of + from AbelianSemiGroup
--R
--R
--RExamples of + from Color
--R
--R

--RExamples of + from Database
--R
--R
--RExamples of + from Equation
--R
--R
--RExamples of + from FreeAbelianMonoidCategory
--R
--R
--RExamples of + from FullPartialFractionExpansion
--R
--R
--RExamples of + from GradedModule
--R
--R
--RExamples of + from PolynomialIdeals
--R
--R
--RExamples of + from InputForm
--R
--R
--RExamples of + from MappingPackage4
--R
--Rf:=(x:INT):INT +-> 3*x
--Rg:=(x:INT):INT +-> 2*x+3
--R(f+g)(4)
--R
--R
--RExamples of + from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rm+m
--R
--R
--RExamples of + from OutputForm
--R
--R
--RExamples of + from Pattern
--R
--R
--RExamples of + from PlacesCategory
--R
--R
--RExamples of + from StreamTaylorSeriesOperations
--R
--R
--RExamples of + from TubePlotTools
--R
--R
--RExamples of + from VectorCategory

--S 57 of 127
)d op -
--R
--R
--RThere are 17 exposed functions called - :
--R   [1] (D,D) -> D from D if D has ABELGRP
--R   [2] D -> D from D if D has ABELGRP
--R   [3] (CardinalNumber,CardinalNumber) -> Union(CardinalNumber,"failed"
--R            )
--R            from CardinalNumber
--R   [4] (Database(D1),Database(D1)) -> Database(D1) from Database(D1)
--R            if D1 has OrderedSet with
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [5] (Equation(D1),D1) -> Equation(D1) from Equation(D1)
--R            if D1 has ABELGRP and D1 has TYPE
--R   [6] (D1,Equation(D1)) -> Equation(D1) from Equation(D1)
--R            if D1 has ABELGRP and D1 has TYPE
--R   [7] (D,D) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R
--R   [8] D -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R
--R   [9] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,D3
--R            )
--R            if D2 has SETCAT and D3 has RING
--R   [10] D -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [11] (D,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [12] D -> Divisor(D) from D
--R            if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC(D2
--R            ,D3)
--R   [13] (D,Divisor(D)) -> Divisor(D) from D
--R            if D has PLACESC(D2,D3) and D2 has FIELD and D3 has LOCPOWC
--R            (D2)
--R   [14] (Divisor(D),D) -> Divisor(D) from D
--R            if D has PLACESC(D2,D3) and D2 has FIELD and D3 has LOCPOWC
--R            (D2)
--R   [15] (D,D) -> Divisor(D) from D
--R            if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC(D2
--R            ,D3)
--R   [16] (D,D) -> D from D

--R            if D has VECTCAT(D1) and D1 has TYPE and D1 has ABELGRP
--R   [17] D -> D from D
--R            if D has VECTCAT(D1) and D1 has TYPE and D1 has ABELGRP
--R
--RThere are 5 unexposed functions called - :
--R   [1] OutputForm -> OutputForm from OutputForm
--R   [2] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [3] (Stream(D2),Stream(D2)) -> Stream(D2)
--R            from StreamTaylorSeriesOperations(D2) if D2 has RING
--R   [4] Stream(D2) -> Stream(D2) from StreamTaylorSeriesOperations(D2)
--R            if D2 has RING
--R   [5] (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat)
--R            from TubePlotTools
--R
--RExamples of - from AbelianGroup
--R
--R
--RExamples of - from CardinalNumber
--R
--Rc2:=2::CardinalNumber
--Rc2-c2
--RA1:=Aleph 1
--RA1-c2
--R
--R
--RExamples of - from Database
--R
--R
--RExamples of - from Equation
--R
--R
--RExamples of - from GradedModule
--R
--R
--RExamples of - from MappingPackage4
--R
--Rf:=(x:INT):INT +-> 3*x
--Rg:=(x:INT):INT +-> 2*x+3
--R(f-g)(4)
--R
--R
--RExamples of - from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--R-m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rm-m
--R
--R

--RExamples of - from OutputForm
--R
--R
--RExamples of - from PlacesCategory
--R
--R
--RExamples of - from StreamTaylorSeriesOperations
--R
--R
--RExamples of - from TubePlotTools
--R
--R
--RExamples of - from VectorCategory
--R
--E 57
--S 58 of 127
)d op /
--R
--R
--RThere are 15 exposed functions called / :
--R   [1] (D,D1) -> D from D
--R            if D has AMR(D1,D2) and D1 has RING and D2 has OAMON and D1
--R            has FIELD
--R   [2] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
--R   [3] (D,D) -> D from D
--R            if D = EQ(D1) and D1 has FIELD and D1 has TYPE or D = EQ(D1
--R            ) and D1 has GROUP and D1 has TYPE
--R   [4] (D,D) -> D from D if D has FIELD
--R   [5] (Float,Integer) -> Float from Float
--R   [6] (SparseMultivariatePolynomial(D2,Kernel(D)),
--R            SparseMultivariatePolynomial(D2,Kernel(D))) -> D
--R            from D if D2 has INTDOM and D2 has ORDSET and D has FS(D2)
--R
--R   [7] (D,D) -> D from D if D has GROUP
--R   [8] (D,D1) -> D from D
--R            if D has LIECAT(D1) and D1 has COMRING and D1 has FIELD
--R   [9] ((D2 -> Expression(Integer)),(D2 -> Expression(Integer))) -> (D2
--R             -> Expression(Integer))
--R            from MappingPackage4(D2,D3) if D2 has SETCAT and D3 has
--R            RING
--R   [10] (D,D1) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1) and D1 has FIELD
--R   [11] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
--R            )
--R            from MyExpression(D1,D2)
--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [12] (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM

--R   [13] (D,D1) -> D from D
--R            if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has RING and D4 has
--R            DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1) and D1 has FIELD
--R
--R   [14] (StochasticDifferential(D2),Expression(D2)) ->
--R            StochasticDifferential(D2)
--R            from StochasticDifferential(D2)
--R            if D2 has Join(OrderedSet,IntegralDomain)
--R   [15] (D,D1) -> D from D if D has VSPACE(D1) and D1 has FIELD
--R
--RThere are 12 unexposed functions called / :
--R   [1] (Vector(D2),Vector(D2)) -> Vector(D2)
--R            from InnerNormalBasisFieldFunctions(D2) if D2 has FFIELDC
--R
--R   [2] (InputForm,InputForm) -> InputForm from InputForm
--R   [3] (D1,D2) -> LocalAlgebra(D1,D3,D2) from LocalAlgebra(D1,D3,D2)
--R            if D3 has COMRING and D1 has ALGEBRA(D3) and D2 has
--R            SubsetCategory(Monoid,D3)
--R   [4] (LocalAlgebra(D2,D3,D1),D1) -> LocalAlgebra(D2,D3,D1)
--R            from LocalAlgebra(D2,D3,D1)
--R            if D3 has COMRING and D2 has ALGEBRA(D3) and D1 has
--R            SubsetCategory(Monoid,D3)
--R   [5] (D1,D2) -> Localize(D1,D3,D2) from Localize(D1,D3,D2)
--R            if D3 has COMRING and D1 has MODULE(D3) and D2 has
--R            SubsetCategory(Monoid,D3)
--R   [6] (Localize(D2,D3,D1),D1) -> Localize(D2,D3,D1) from Localize(D2,
--R            D3,D1)
--R            if D3 has COMRING and D2 has MODULE(D3) and D1 has
--R            SubsetCategory(Monoid,D3)
--R   [7] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [8] (OrdinaryWeightedPolynomials(D1,D2,D3,D4),
--R            OrdinaryWeightedPolynomials(D1,D2,D3,D4)) -> Union(
--R            OrdinaryWeightedPolynomials(D1,D2,D3,D4),"failed")
--R            from OrdinaryWeightedPolynomials(D1,D2,D3,D4)
--R            if D1 has FIELD and D1 has RING and D2: LIST(SYMBOL) and D3
--R            : LIST(NNI) and D4: NNI
--R   [9] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1)
--R            if D1 has SETCAT
--R   [10] (Stream(D2),Stream(D2)) -> Stream(D2)
--R            from StreamTaylorSeriesOperations(D2) if D2 has RING
--R   [11] (WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7),WeightedPolynomials(
--R            D1,D2,D3,D4,D5,D6,D7)) -> Union(WeightedPolynomials(D1,D2,D3,D4,
--R            D5,D6,D7),"failed")
--R            from WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7)
--R            if D1 has FIELD and D1 has RING and D2 has ORDSET and D3
--R            has OAMONS and D5: LIST(D2) and D4 has POLYCAT(D1,D3,D2)
--R            and D6: LIST(NNI) and D7: NNI
--R   [12] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
--R            from XPolynomialRing(D1,D2)
--R            if D1 has FIELD and D1 has RING and D2 has ORDMON

--R
--RExamples of / from AbelianMonoidRing
--R
--R
--RExamples of / from DoubleFloat
--R
--R
--RExamples of / from Equation
--R
--R
--RExamples of / from Field
--R
--R
--RExamples of / from Float
--R
--R
--RExamples of / from FunctionSpace
--R
--R
--RExamples of / from Group
--R
--R
--RExamples of / from InnerNormalBasisFieldFunctions
--R
--R
--RExamples of / from InputForm
--R
--R
--RExamples of / from LocalAlgebra
--R
--R
--RExamples of / from LieAlgebra
--R
--R
--RExamples of / from Localize
--R
--R
--RExamples of / from MappingPackage4
--R
--Rp:=(x:EXPR(INT)):EXPR(INT)+->3*x
--Rq:=(x:EXPR(INT)):EXPR(INT)+->2*x+3
--R(p/q)(4)
--R(p/q)(x)
--R
--R
--RExamples of / from MatrixCategory
--R
--Rm:=matrix [[2**i for i in 2..4] for j in 1..5]
--Rm/4
--R

--R
--RExamples of / from MyExpression
--R
--R
--RExamples of / from OutputForm
--R
--R
--RExamples of / from OrdinaryWeightedPolynomials
--R
--R
--RExamples of / from Pattern
--R
--R
--RExamples of / from QuotientFieldCategory
--R
--R
--RExamples of / from RectangularMatrixCategory
--R
--R
--RExamples of / from StochasticDifferential
--R
--R
--RExamples of / from StreamTaylorSeriesOperations
--R
--R
--RExamples of / from VectorSpace
--R
--R
--RExamples of / from WeightedPolynomials
--R
--R
--RExamples of / from XPolynomialRing
--R
--E 58
--S 59 of 127
)d op integralBasis
--R
--R
--RThere is one exposed function called integralBasis :
--R   [1]  -> Vector(D) from D
--R            if D2 has UFD and D3 has UPOLYC(D2) and D4 has UPOLYC(FRAC(
--R            D3)) and D has FFCAT(D2,D3,D4)
--R
--RThere are 4 unexposed functions called integralBasis :
--R   [1]  -> Record(basis: Matrix(D2),basisDen: D2,basisInv: Matrix(D2))
--R            from FunctionFieldIntegralBasis(D2,D3,D4)
--R            if D2 has EuclideanDomain with
--R               squareFree : % -> Factored(%)and D3 has UPOLYC(D2)
--R            and D4 has FRAMALG(D2,D3)

--R   [2]  -> Record(basis: Matrix(Integer),basisDen: Integer,basisInv:
--R            Matrix(Integer))
--R            from NumberFieldIntegralBasis(D2,D3)
--R            if D2 has UPOLYC(INT) and D3 has FRAMALG(INT,D2)
--R   [3]  -> Record(basis: Matrix(D3),basisDen: D3,basisInv: Matrix(D3))
--R            from PAdicWildFunctionFieldIntegralBasis(D2,D3,D4,D5)
--R            if D2 has FFIELDC and D3 has UPOLYC(D2) and D4 has UPOLYC(
--R            D3) and D5 has MONOGEN(D3,D4)
--R   [4]  -> Record(basis: Matrix(D3),basisDen: D3,basisInv: Matrix(D3))
--R            from WildFunctionFieldIntegralBasis(D2,D3,D4,D5)
--R            if D2 has FFIELDC and D3 has UPOLYC(D2) and D4 has UPOLYC(
--R            D3) and D5 has FRAMALG(D3,D4)
--R
--RExamples of integralBasis from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RintegralBasis()$R
--R
--R
--RExamples of integralBasis from FunctionFieldIntegralBasis
--R
--R
--RExamples of integralBasis from NumberFieldIntegralBasis
--R
--R
--RExamples of integralBasis from PAdicWildFunctionFieldIntegralBasis
--R
--R
--RExamples of integralBasis from WildFunctionFieldIntegralBasis
--R
--E 59
--S 60 of 127
)d op split
--R
--R
--RThere are 9 exposed functions called split :
--R   [1] D2 -> Factored(D2) from AlgFactor(D2) if D2 has UPOLYC(AN)
--R   [2] (D2,BinarySearchTree(D2)) -> Record(less: BinarySearchTree(D2),
--R            greater: BinarySearchTree(D2))
--R            from BinarySearchTree(D2) if D2 has ORDSET
--R   [3] D -> List(D) from D if D2 has SETCAT and D has DIVCAT(D2)
--R   [4] IntegrationResult(D3) -> IntegrationResult(D3)
--R            from IntegrationResultToFunction(D2,D3)
--R            if D3 has Join(AlgebraicallyClosedFunctionSpace(D2),
--R            TranscendentalFunctionCategory) and D2 has Join(GcdDomain,
--R            RetractableTo(Integer),OrderedSet,LinearlyExplicitRingOver(
--R            Integer))

--R   [5] IntegrationResult(Fraction(Polynomial(D2))) -> IntegrationResult
--R            (Fraction(Polynomial(D2)))
--R            from IntegrationResultRFToFunction(D2)
--R            if D2 has Join(GcdDomain,RetractableTo(Integer),OrderedSet,
--R            LinearlyExplicitRingOver(Integer))
--R   [6] (List(Matrix(D4)),Vector(D4)) -> List(List(Matrix(D4)))
--R            from RepresentationPackage2(D4) if D4 has FIELD and D4 has
--R            RING
--R   [7] (List(Matrix(D4)),Vector(Vector(D4))) -> List(List(Matrix(D4)))
--R            from RepresentationPackage2(D4) if D4 has FIELD and D4 has
--R            RING
--R   [8] (D,CharacterClass) -> List(D) from D if D has SRAGG
--R   [9] (D,Character) -> List(D) from D if D has SRAGG
--R
--RThere is one unexposed function called split :
--R   [1] (D2,(D2 -> D2)) -> Record(normal: D2,special: D2)
--R            from MonomialExtensionTools(D4,D2)
--R            if D2 has UPOLYC(D4) and D4 has FIELD
--R
--RExamples of split from AlgFactor
--R
--R
--RExamples of split from BinarySearchTree
--R
--Rt1:=binarySearchTree [1,2,3,4]
--Rsplit(3,t1)
--R
--R
--RExamples of split from DivisorCategory
--R
--R
--RExamples of split from IntegrationResultToFunction
--R
--R
--RExamples of split from IntegrationResultRFToFunction
--R
--R
--RExamples of split from MonomialExtensionTools
--R
--R
--RExamples of split from RepresentationPackage2
--R
--R
--RExamples of split from StringAggregate
--R
--E 60
--S 61 of 127
)d op qelt
--R

--R
--RThere are 3 exposed functions called qelt :
--R   [1] (D,Integer,Integer) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG(D1) and D4 has
--R            FLAGG(D1) and D1 has TYPE
--R   [2] (D,D2) -> D1 from D
--R            if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
--R
--R   [3] (D,Integer,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1)
--R            and D6 has DIRPCAT(D3,D1) and D1 has RING
--R
--RExamples of qelt from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rqelt(arr,1,1)
--R
--R
--RExamples of qelt from EltableAggregate
--R
--R
--RExamples of qelt from RectangularMatrixCategory
--R
--E 61
--S 62 of 127
)d op mapUp!
--R
--R
--RThere are 2 exposed functions called mapUp! :
--R   [1] (BalancedBinaryTree(D2),BalancedBinaryTree(D2),((D2,D2,D2,D2)
--R             -> D2)) -> BalancedBinaryTree(D2)
--R            from BalancedBinaryTree(D2) if D2 has SETCAT
--R   [2] (BalancedBinaryTree(D1),((D1,D1) -> D1)) -> D1
--R            from BalancedBinaryTree(D1) if D1 has SETCAT
--R
--RExamples of mapUp! from BalancedBinaryTree
--R
--RT1:=BalancedBinaryTree Integer
--Rt2:=balancedBinaryTree(4, 0)$T1
--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
--Radder4(i:INT,j:INT,k:INT,l:INT):INT == i+j+k+l
--RmapUp!(t2,t2,adder4)
--Rt2
--R
--RT1:=BalancedBinaryTree Integer
--Rt2:=balancedBinaryTree(4, 0)$T1
--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
--Radder(a:Integer,b:Integer):Integer == a+b
--RmapUp!(t2,adder)

--Rt2
--R
--E 62
--S 63 of 127
)d op reindex
--R
--R
--RThere is one exposed function called reindex :
--R   [1] (CartesianTensor(D2,D3,D4),List(Integer)) -> CartesianTensor(D2,
--R            D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R
--RExamples of reindex from CartesianTensor
--R
--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]]
--Rtn:CartesianTensor(1,2,Integer):=n
--Rp:=product(tn,tn)
--Rreindex(p,[4,3,2,1])
--R
--E 63
--S 64 of 127
)d op mapDown!
--R
--R
--RThere are 2 exposed functions called mapDown! :
--R   [1] (BalancedBinaryTree(D1),D1,((D1,D1,D1) -> List(D1))) ->
--R            BalancedBinaryTree(D1)
--R            from BalancedBinaryTree(D1) if D1 has SETCAT
--R   [2] (BalancedBinaryTree(D1),D1,((D1,D1) -> D1)) ->
--R            BalancedBinaryTree(D1)
--R            from BalancedBinaryTree(D1) if D1 has SETCAT
--R
--RExamples of mapDown! from BalancedBinaryTree
--R
--RT1:=BalancedBinaryTree Integer
--Rt2:=balancedBinaryTree(4, 0)$T1
--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
--Radder3(i:Integer,j:Integer,k:Integer):List Integer == [i+j,j+k]
--RmapDown!(t2,4::INT,adder3)
--Rt2
--R
--RT1:=BalancedBinaryTree Integer
--Rt2:=balancedBinaryTree(4, 0)$T1
--Rsetleaves!(t2,[1,2,3,4]::List(Integer))
--Radder(i:Integer,j:Integer):Integer == i+j
--RmapDown!(t2,4::INT,adder)
--Rt2

--S 65 of 127
)d op nrows
--R
--R
--RThere are 2 exposed functions called nrows :
--R   [1] D -> NonNegativeInteger from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] D -> NonNegativeInteger from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of nrows from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rnrows(arr)
--R
--R
--RExamples of nrows from RectangularMatrixCategory
--R
--E 65
--S 66 of 127
)d op row
--R
--R
--RThere are 2 exposed functions called row :
--R   [1] (D,Integer) -> D1 from D
--R            if D has ARR2CAT(D3,D1,D4) and D3 has TYPE and D4 has FLAGG
--R            (D3) and D1 has FLAGG(D3)
--R   [2] (D,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D5,D1,D6) and D5 has RING and D6 has
--R            DIRPCAT(D3,D5) and D1 has DIRPCAT(D4,D5)
--R
--RExamples of row from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rrow(arr,1)
--R
--R
--RExamples of row from RectangularMatrixCategory
--R
--E 66
--S 67 of 127
)d op ravel
--R

--R
--RThere is one exposed function called ravel :
--R   [1] CartesianTensor(D2,D3,D4) -> List(D4) from CartesianTensor(D2,D3
--R            ,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R
--RExamples of ravel from CartesianTensor
--R
--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]]
--Rtn:CartesianTensor(1,2,Integer):=n
--Rravel tn
--R
--E 67
--S 68 of 127
)d op inverseIntegralMatrix
--R
--R
--RThere is one exposed function called inverseIntegralMatrix :
--R   [1]  -> Matrix(Fraction(D3)) from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RExamples of inverseIntegralMatrix from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RinverseIntegralMatrix()$R
--R
--E 68
--S 69 of 127
)d op coerce
--R
--R
--RThere are 194 exposed functions called coerce :
--R   [1] List D2 -> D from D if D2 has FIELD and D has AFSPCAT D2
--R   [2] D -> List D2 from D if D has AFSPCAT D2 and D2 has FIELD
--R   [3] D1 -> D from D if D has ALGEBRA D1 and D1 has COMRING
--R   [4] Vector D2 -> AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
--R            from AlgebraGivenByStructuralConstants(D2,D3,D4,D5)
--R            if D2 has FIELD and D5: VECTOR MATRIX D2 and D3: PI and D4
--R            : LIST SYMBOL
--R   [5] SparseMultivariatePolynomial(Integer,Kernel AlgebraicNumber) ->
--R            AlgebraicNumber
--R            from AlgebraicNumber
--R   [6] D2 -> Any from AnyFunctions1 D2 if D2 has TYPE
--R   [7] Vector FortranExpression([construct,QUOTEJINT,QUOTEX,QUOTEELAM],
--R            [construct],MachineFloat) -> Asp10 D2

--R            from Asp10 D2 if D2: SYMBOL
--R   [8] Vector FortranExpression([construct],[construct,QUOTEXC],
--R            MachineFloat) -> Asp19 D2
--R            from Asp19 D2 if D2: SYMBOL
--R   [9] FortranExpression([construct,QUOTEX],[construct],MachineFloat)
--R             -> Asp1 D2
--R            from Asp1 D2 if D2: SYMBOL
--R   [10] Matrix FortranExpression([construct],[construct,QUOTEX,QUOTE
--R            HESS],MachineFloat) -> Asp20 D2
--R            from Asp20 D2 if D2: SYMBOL
--R   [11] FortranExpression([construct],[construct,QUOTEXC],MachineFloat)
--R             -> Asp24 D2
--R            from Asp24 D2 if D2: SYMBOL
--R   [12] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
--R            MachineFloat) -> Asp31 D2
--R            from Asp31 D2 if D2: SYMBOL
--R   [13] Vector FortranExpression([construct],[construct,QUOTEX],
--R            MachineFloat) -> Asp35 D2
--R            from Asp35 D2 if D2: SYMBOL
--R   [14] Vector FortranExpression([construct,QUOTEX,QUOTEEPS],[construct
--R            ,QUOTEY],MachineFloat) -> Asp41(D2,D3,D4)
--R            from Asp41(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4:
--R            SYMBOL
--R   [15] Vector FortranExpression([construct,QUOTEEPS],[construct,QUOTE
--R            YA,QUOTEYB],MachineFloat) -> Asp42(D2,D3,D4)
--R            from Asp42(D2,D3,D4) if D2: SYMBOL and D3: SYMBOL and D4:
--R            SYMBOL
--R   [16] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
--R             -> Asp49 D2
--R            from Asp49 D2 if D2: SYMBOL
--R   [17] FortranExpression([construct],[construct,QUOTEX],MachineFloat)
--R             -> Asp4 D2
--R            from Asp4 D2 if D2: SYMBOL
--R   [18] Vector FortranExpression([construct],[construct,QUOTEXC],
--R            MachineFloat) -> Asp50 D2
--R            from Asp50 D2 if D2: SYMBOL
--R   [19] Vector FortranExpression([construct],[construct,QUOTEX],
--R            MachineFloat) -> Asp55 D2
--R            from Asp55 D2 if D2: SYMBOL
--R   [20] Vector FortranExpression([construct],[construct,QUOTEX],
--R            MachineFloat) -> Asp6 D2
--R            from Asp6 D2 if D2: SYMBOL
--R   [21] Vector FortranExpression([construct,QUOTEX,QUOTEY],[construct],
--R            MachineFloat) -> Asp73 D2
--R            from Asp73 D2 if D2: SYMBOL
--R   [22] Matrix FortranExpression([construct,QUOTEX,QUOTEY],[construct],
--R            MachineFloat) -> Asp74 D2
--R            from Asp74 D2 if D2: SYMBOL
--R   [23] Matrix FortranExpression([construct,QUOTEX],[construct],
--R            MachineFloat) -> Asp77 D2

--R            from Asp77 D2 if D2: SYMBOL
--R   [24] Vector FortranExpression([construct,QUOTEX],[construct],
--R            MachineFloat) -> Asp78 D2
--R            from Asp78 D2 if D2: SYMBOL
--R   [25] Vector FortranExpression([construct,QUOTEX],[construct,QUOTEY],
--R            MachineFloat) -> Asp7 D2
--R            from Asp7 D2 if D2: SYMBOL
--R   [26] Matrix FortranExpression([construct,QUOTEXL,QUOTEXR,QUOTEELAM],
--R            [construct],MachineFloat) -> Asp80 D2
--R            from Asp80 D2 if D2: SYMBOL
--R   [27] FortranExpression([construct,QUOTEX],[construct,QUOTEY],
--R            MachineFloat) -> Asp9 D2
--R            from Asp9 D2 if D2: SYMBOL
--R   [28] ArrayStack D2 -> OutputForm from ArrayStack D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [29] BinaryExpansion -> RadixExpansion 2 from BinaryExpansion
--R   [30] BinaryExpansion -> Fraction Integer from BinaryExpansion
--R   [31] List Integer -> D from D if D has BLMETCT
--R   [32] List CartesianTensor(D2,D3,D4) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [33] List D4 -> CartesianTensor(D2,D3,D4) from CartesianTensor(D2,D3
--R            ,D4)
--R            if D4 has COMRING and D2: INT and D3: NNI
--R   [34] SquareMatrix(D3,D4) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D3: NNI and D4 has COMRING and D2: INT
--R   [35] DirectProduct(D3,D4) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D3: NNI and D4 has COMRING and D2: INT
--R   [36] List D2 -> Database D2 from Database D2
--R            if D2 has OrderedSet with
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [37] DecimalExpansion -> RadixExpansion 10 from DecimalExpansion
--R   [38] DecimalExpansion -> Fraction Integer from DecimalExpansion
--R   [39] Dequeue D2 -> OutputForm from Dequeue D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [40] DirichletRing D2 -> Stream D2 from DirichletRing D2 if D2 has
--R            RING
--R   [41] Stream D2 -> DirichletRing D2 from DirichletRing D2 if D2 has
--R            RING
--R   [42] DirichletRing D2 -> (PositiveInteger -> D2) from DirichletRing
--R            D2
--R            if D2 has RING
--R   [43] (PositiveInteger -> D2) -> DirichletRing D2 from DirichletRing
--R            D2
--R            if D2 has RING
--R   [44] DataList D2 -> List D2 from DataList D2 if D2 has ORDSET

--R   [45] List D2 -> DataList D2 from DataList D2 if D2 has ORDSET
--R   [46] SegmentBinding Expression D3 -> SegmentBinding Float
--R            from DrawNumericHack D3
--R            if D3 has Join(OrderedSet,IntegralDomain,ConvertibleTo
--R            Float)
--R   [47] D1 -> D from D if D has DVARCAT D1 and D1 has ORDSET
--R   [48] FortranCode -> OutputForm from FortranCode
--R   [49] FortranExpression(D2,D3,D4) -> Expression D4
--R            from FortranExpression(D2,D3,D4)
--R            if D2: LIST SYMBOL and D3: LIST SYMBOL and D4 has FMTC
--R   [50] D2 -> D1 from FiniteFieldHomomorphisms(D2,D3,D1)
--R            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
--R   [51] D2 -> D1 from FiniteFieldHomomorphisms(D1,D3,D2)
--R            if D3 has FFIELDC and D1 has FAXF D3 and D2 has FAXF D3
--R   [52] D -> XRecursivePolynomial(D2,D3) from D
--R            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
--R
--R   [53] D -> XDistributedPolynomial(D2,D3) from D
--R            if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING
--R
--R   [54] D1 -> D from D
--R            if D has FLALG(D1,D2) and D1 has ORDSET and D2 has COMRING
--R
--R   [55] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
--R            from D
--R            if D has FMC
--R   [56] FortranCode -> D from D if D has FMC
--R   [57] List FortranCode -> D from D if D has FMC
--R   [58] Matrix MachineFloat -> D from D if D has FMC
--R   [59] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
--R            from D
--R            if D has FMFUN
--R   [60] FortranCode -> D from D if D has FMFUN
--R   [61] List FortranCode -> D from D if D has FMFUN
--R   [62] D -> String from D if D has FNCAT
--R   [63] String -> D from D if D has FNCAT
--R   [64] D2 -> ScriptFormulaFormat from ScriptFormulaFormat1 D2 if D2
--R            has SETCAT
--R   [65] OutputForm -> ScriptFormulaFormat from ScriptFormulaFormat
--R   [66] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
--R            from D
--R            if D has FORTFN
--R   [67] FortranCode -> D from D if D has FORTFN
--R   [68] List FortranCode -> D from D if D has FORTFN
--R   [69] Equation Expression Complex Float -> FortranProgram(D2,D3,D4,D5
--R            )
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [70] Equation Expression Float -> FortranProgram(D2,D3,D4,D5)

--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [71] Equation Expression Integer -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [72] Expression Complex Float -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [73] Expression Float -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [74] Expression Integer -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [75] Equation Expression MachineComplex -> FortranProgram(D2,D3,D4,
--R            D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [76] Equation Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [77] Equation Expression MachineInteger -> FortranProgram(D2,D3,D4,
--R            D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [78] Expression MachineComplex -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [79] Expression MachineFloat -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [80] Expression MachineInteger -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [81] Record(localSymbols: SymbolTable,code: List FortranCode) ->
--R            FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB

--R   [82] List FortranCode -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [83] FortranCode -> FortranProgram(D2,D3,D4,D5)
--R            from FortranProgram(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3: Union(fst: FortranScalarType,void:
--R            void) and D4: LIST SYMBOL and D5: SYMTAB
--R   [84] FourierComponent D3 -> FourierSeries(D2,D3) from FourierSeries(
--R            D2,D3)
--R            if D3 has Join(OrderedSet,AbelianGroup) and D2 has Join(
--R            CommutativeRing,Algebra Fraction Integer)
--R   [85] D1 -> FourierSeries(D1,D2) from FourierSeries(D1,D2)
--R            if D1 has Join(CommutativeRing,Algebra Fraction Integer)
--R            and D2 has Join(OrderedSet,AbelianGroup)
--R   [86] Fraction Polynomial Fraction D2 -> D from D
--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R   [87] Polynomial Fraction D2 -> D from D
--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R   [88] Fraction D2 -> D from D
--R            if D2 has INTDOM and D2 has ORDSET and D has FS D2
--R   [89] SparseMultivariatePolynomial(D2,Kernel D) -> D from D
--R            if D2 has RING and D2 has ORDSET and D has FS D2
--R   [90] FortranScalarType -> SExpression from FortranScalarType
--R   [91] FortranScalarType -> Symbol from FortranScalarType
--R   [92] Symbol -> FortranScalarType from FortranScalarType
--R   [93] String -> FortranScalarType from FortranScalarType
--R   [94] FortranScalarType -> FortranType from FortranType
--R   [95] FortranType -> OutputForm from FortranType
--R   [96] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
--R            from D
--R            if D has FVC
--R   [97] FortranCode -> D from D if D has FVC
--R   [98] List FortranCode -> D from D if D has FVC
--R   [99] Vector MachineFloat -> D from D if D has FVC
--R   [100] Record(localSymbols: SymbolTable,code: List FortranCode) -> D
--R            from D
--R            if D has FVFUN
--R   [101] FortranCode -> D from D if D has FVFUN
--R   [102] List FortranCode -> D from D if D has FVFUN
--R   [103] UnivariatePuiseuxSeries(D2,D3,D4) ->
--R            GeneralUnivariatePowerSeries(D2,D3,D4)
--R            from GeneralUnivariatePowerSeries(D2,D3,D4)
--R            if D2 has RING and D3: SYMBOL and D4: D2
--R   [104] Variable D3 -> GeneralUnivariatePowerSeries(D2,D3,D4)
--R            from GeneralUnivariatePowerSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [105] Heap D2 -> OutputForm from Heap D2 if D2 has SETCAT and D2 has
--R            ORDSET
--R   [106] HexadecimalExpansion -> RadixExpansion 16 from

--R            HexadecimalExpansion
--R   [107] HexadecimalExpansion -> Fraction Integer from
--R            HexadecimalExpansion
--R   [108] OutputForm -> String from HTMLFormat
--R   [109] String -> IndexCard from IndexCard
--R   [110] List D5 -> PolynomialIdeals(D2,D3,D4,D5)
--R            from PolynomialIdeals(D2,D3,D4,D5)
--R            if D5 has POLYCAT(D2,D3,D4) and D2 has FIELD and D3 has
--R            OAMONS and D4 has ORDSET
--R   [111] D1 -> AssociatedJordanAlgebra(D2,D1)
--R            from AssociatedJordanAlgebra(D2,D1)
--R            if D2 has COMRING and D1 has NAALG D2
--R   [112] D -> D1 from D if D has KOERCE D1 and D1 has TYPE
--R   [113] D1 -> D from D if D has LALG D1 and D1 has RING
--R   [114] D1 -> AssociatedLieAlgebra(D2,D1) from AssociatedLieAlgebra(D2
--R            ,D1)
--R            if D2 has COMRING and D1 has NAALG D2
--R   [115] D -> Stream Record(k: Integer,c: D2) from D
--R            if D has LOCPOWC D2 and D2 has FIELD
--R   [116] Stream Record(k: Integer,c: D2) -> D from D
--R            if D2 has FIELD and D has LOCPOWC D2
--R   [117] ThreeDimensionalMatrix D2 -> PrimitiveArray PrimitiveArray
--R            PrimitiveArray D2
--R            from ThreeDimensionalMatrix D2 if D2 has SETCAT
--R   [118] PrimitiveArray PrimitiveArray PrimitiveArray D2 ->
--R            ThreeDimensionalMatrix D2
--R            from ThreeDimensionalMatrix D2 if D2 has SETCAT
--R   [119] D2 -> (() -> D2) from MappingPackage1 D2 if D2 has SETCAT
--R   [120] D1 -> D from D
--R            if D2 has RING and D has MATCAT(D2,D3,D1) and D3 has FLAGG
--R            D2 and D1 has FLAGG D2
--R   [121] MachineComplex -> Complex Float from MachineComplex
--R   [122] Complex MachineInteger -> MachineComplex from MachineComplex
--R
--R   [123] Complex MachineFloat -> MachineComplex from MachineComplex
--R   [124] Complex Integer -> MachineComplex from MachineComplex
--R   [125] Complex Float -> MachineComplex from MachineComplex
--R   [126] MachineInteger -> MachineFloat from MachineFloat
--R   [127] MachineFloat -> Float from MachineFloat
--R   [128] Expression Integer -> Expression MachineInteger from
--R            MachineInteger
--R   [129] OutputForm -> String from MathMLFormat
--R   [130] Fraction MyUnivariatePolynomial(D2,D3) -> MyExpression(D2,D3)
--R            from MyExpression(D2,D3)
--R            if D2: SYMBOL and D3 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [131] Polynomial D3 -> MyUnivariatePolynomial(D2,D3)
--R            from MyUnivariatePolynomial(D2,D3) if D3 has RING and D2:
--R            SYMBOL
--R   [132] Variable D2 -> MyUnivariatePolynomial(D2,D3)

--R            from MyUnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
--R            RING
--R   [133] D1 -> MyUnivariatePolynomial(D2,D1) from
--R            MyUnivariatePolynomial(D2,D1)
--R            if D2: SYMBOL and D1 has RING
--R   [134] Integer -> D from D if D has NASRING
--R   [135] Union(nia: Record(var: Symbol,fn: Expression DoubleFloat,range
--R            : Segment OrderedCompletion DoubleFloat,abserr: DoubleFloat,
--R            relerr: DoubleFloat),mdnia: Record(fn: Expression DoubleFloat,
--R            range: List Segment OrderedCompletion DoubleFloat,abserr:
--R            DoubleFloat,relerr: DoubleFloat)) -> NumericalIntegrationProblem
--R            from NumericalIntegrationProblem
--R   [136] Record(fn: Expression DoubleFloat,range: List Segment
--R            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr:
--R            DoubleFloat) -> NumericalIntegrationProblem
--R            from NumericalIntegrationProblem
--R   [137] Record(var: Symbol,fn: Expression DoubleFloat,range: Segment
--R            OrderedCompletion DoubleFloat,abserr: DoubleFloat,relerr:
--R            DoubleFloat) -> NumericalIntegrationProblem
--R            from NumericalIntegrationProblem
--R   [138] NumericalIntegrationProblem -> OutputForm
--R            from NumericalIntegrationProblem
--R   [139] D2 -> None from NoneFunctions1 D2 if D2 has TYPE
--R   [140] Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector
--R            Expression DoubleFloat,yinit: List DoubleFloat,intvals: List
--R            DoubleFloat,g: Expression DoubleFloat,abserr: DoubleFloat,relerr
--R            : DoubleFloat) -> NumericalODEProblem
--R            from NumericalODEProblem
--R   [141] NumericalODEProblem -> OutputForm from NumericalODEProblem
--R   [142] OrdinaryDifferentialRing(D2,D1,D3) -> D1
--R            from OrdinaryDifferentialRing(D2,D1,D3)
--R            if D1 has PDRING D2 and D2 has SETCAT and D3: D2
--R   [143] D1 -> OrdinaryDifferentialRing(D2,D1,D3)
--R            from OrdinaryDifferentialRing(D2,D1,D3)
--R            if D2 has SETCAT and D3: D2 and D1 has PDRING D2
--R   [144] Symbol -> OpenMathErrorKind from OpenMathErrorKind
--R   [145] Union(noa: Record(fn: Expression DoubleFloat,init: List
--R            DoubleFloat,lb: List OrderedCompletion DoubleFloat,cf: List
--R            Expression DoubleFloat,ub: List OrderedCompletion DoubleFloat),
--R            lsa: Record(lfn: List Expression DoubleFloat,init: List
--R            DoubleFloat)) -> NumericalOptimizationProblem
--R            from NumericalOptimizationProblem
--R   [146] Record(lfn: List Expression DoubleFloat,init: List DoubleFloat
--R            ) -> NumericalOptimizationProblem
--R            from NumericalOptimizationProblem
--R   [147] Record(fn: Expression DoubleFloat,init: List DoubleFloat,lb:
--R            List OrderedCompletion DoubleFloat,cf: List Expression
--R            DoubleFloat,ub: List OrderedCompletion DoubleFloat) ->
--R            NumericalOptimizationProblem
--R            from NumericalOptimizationProblem

--R   [148] NumericalOptimizationProblem -> OutputForm
--R            from NumericalOptimizationProblem
--R   [149] Integer -> OrdSetInts from OrdSetInts
--R   [150] Color -> Palette from Palette
--R   [151] Polynomial AlgebraicNumber -> Expression Integer
--R            from PolynomialAN2Expression
--R   [152] Fraction Polynomial AlgebraicNumber -> Expression Integer
--R            from PolynomialAN2Expression
--R   [153] Record(pde: List Expression DoubleFloat,constraints: List
--R            Record(start: DoubleFloat,finish: DoubleFloat,grid:
--R            NonNegativeInteger,boundaryType: Integer,dStart: Matrix
--R            DoubleFloat,dFinish: Matrix DoubleFloat),f: List List Expression
--R            DoubleFloat,st: String,tol: DoubleFloat) -> NumericalPDEProblem
--R            from NumericalPDEProblem
--R   [154] NumericalPDEProblem -> OutputForm from NumericalPDEProblem
--R   [155] PendantTree D2 -> Tree D2 from PendantTree D2 if D2 has SETCAT
--R
--R   [156] List Permutation D2 -> PermutationGroup D2 from
--R            PermutationGroup D2
--R            if D2 has SETCAT
--R   [157] PermutationGroup D2 -> List Permutation D2 from
--R            PermutationGroup D2
--R            if D2 has SETCAT
--R   [158] List D2 -> Permutation D2 from Permutation D2 if D2 has SETCAT
--R
--R   [159] List List D2 -> Permutation D2 from Permutation D2 if D2 has
--R            SETCAT
--R   [160] Fraction Factored D2 -> PartialFraction D2 from
--R            PartialFraction D2
--R            if D2 has EUCDOM
--R   [161] PartialFraction D2 -> Fraction D2 from PartialFraction D2
--R            if D2 has EUCDOM
--R   [162] Pi -> Expression D3 from PiCoercions D3
--R            if D3 has Join(OrderedSet,IntegralDomain)
--R   [163] List D2 -> D from D if D2 has FIELD and D has PRSPCAT D2
--R   [164] D -> List D2 from D if D has PRSPCAT D2 and D2 has FIELD
--R   [165] Queue D2 -> OutputForm from Queue D2
--R            if D2 has SETCAT and D2 has SETCAT
--R   [166] RadixExpansion D2 -> Fraction Integer from RadixExpansion D2
--R            if D2: INT
--R   [167] D2 -> Void from ResolveLatticeCompletion D2 if D2 has TYPE
--R   [168] Exit -> D1 from ResolveLatticeCompletion D1 if D1 has TYPE
--R   [169] D1 -> D from D if D has RETRACT D1 and D1 has TYPE
--R   [170] D2 -> Fraction Polynomial D2 from RationalFunction D2 if D2
--R            has INTDOM
--R   [171] Integer -> D from D if D has RING
--R   [172] D -> OutputForm from D if D has SPACEC D2 and D2 has RING
--R   [173] Character -> D from D if D has SRAGG
--R   [174] Stack D2 -> OutputForm from Stack D2
--R            if D2 has SETCAT and D2 has SETCAT

--R   [175] List D2 -> Stream D2 from Stream D2 if D2 has TYPE
--R   [176] Symbol -> Switch from Switch
--R   [177] String -> Symbol from Symbol
--R   [178] SymbolTable -> Table(Symbol,FortranType) from SymbolTable
--R   [179] Tableau D2 -> OutputForm from Tableau D2 if D2 has SETCAT
--R   [180] D2 -> TexFormat from TexFormat1 D2 if D2 has SETCAT
--R   [181] OutputForm -> TexFormat from TexFormat
--R   [182] Polynomial D2 -> TaylorSeries D2 from TaylorSeries D2 if D2
--R            has RING
--R   [183] Symbol -> TaylorSeries D2 from TaylorSeries D2 if D2 has RING
--R
--R   [184] Variable QUOTE x -> UnivariateFormalPowerSeries D2
--R            from UnivariateFormalPowerSeries D2 if D2 has RING
--R   [185] UnivariatePolynomial(QUOTE x,D2) ->
--R            UnivariateFormalPowerSeries D2
--R            from UnivariateFormalPowerSeries D2 if D2 has RING
--R   [186] D1 -> D from D
--R            if D2 has RING and D has ULSCCAT(D2,D1) and D1 has UTSCAT
--R            D2
--R   [187] Segment D2 -> UniversalSegment D2 from UniversalSegment D2
--R            if D2 has TYPE
--R   [188] Variable D2 -> UnivariatePolynomial(D2,D3)
--R            from UnivariatePolynomial(D2,D3) if D2: SYMBOL and D3 has
--R            RING
--R   [189] D1 -> D from D
--R            if D2 has RING and D has UPXSCCA(D2,D1) and D1 has ULSCAT
--R            D2
--R   [190] Variable D3 -> UnivariateTaylorSeriesCZero(D2,D3)
--R            from UnivariateTaylorSeriesCZero(D2,D3)
--R            if D3: SYMBOL and D2 has RING
--R   [191] UnivariatePolynomial(D3,D2) -> UnivariateTaylorSeriesCZero(D2,
--R            D3)
--R            from UnivariateTaylorSeriesCZero(D2,D3)
--R            if D2 has RING and D3: SYMBOL
--R   [192] Void -> OutputForm from Void
--R   [193] D1 -> D from D if D has XALG D1 and D1 has RING
--R   [194] D1 -> D from D
--R            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
--R
--RThere are 50 unexposed functions called coerce :
--R   [1] Vector Matrix D3 -> Vector Matrix Fraction Polynomial D3
--R            from CoerceVectorMatrixPackage D3 if D3 has COMRING
--R   [2] List Integer -> ExtAlgBasis from ExtAlgBasis
--R   [3] EuclideanModularRing(D2,D1,D3,D4,D5,D6) -> D1
--R            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
--R            if D1 has UPOLYC D2 and D2 has COMRING and D3 has ABELMON
--R            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
--R            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
--R   [4] UnivariatePuiseuxSeries(D3,D4,D5) -> ExponentialExpansion(D2,D3,
--R            D4,D5)

--R            from ExponentialExpansion(D2,D3,D4,D5)
--R            if D3 has Join(AlgebraicallyClosedField,
--R            TranscendentalFunctionCategory,FunctionSpace D2) and D4:
--R            SYMBOL and D5: D3 and D2 has Join(OrderedSet,RetractableTo
--R            Integer,LinearlyExplicitRingOver Integer,GcdDomain)
--R   [5] Vector Fraction Polynomial D2 -> GenericNonAssociativeAlgebra(D2
--R            ,D3,D4,D5)
--R            from GenericNonAssociativeAlgebra(D2,D3,D4,D5)
--R            if D2 has COMRING and D5: VECTOR MATRIX D2 and D3: PI and
--R            D4: LIST SYMBOL
--R   [6] List List Point DoubleFloat -> GraphImage from GraphImage
--R   [7] GraphImage -> OutputForm from GraphImage
--R   [8] SparseMultivariatePolynomial(Integer,Kernel InnerAlgebraicNumber
--R            ) -> InnerAlgebraicNumber
--R            from InnerAlgebraicNumber
--R   [9] LieExponentials(D2,D3,D4) -> XPBWPolynomial(D2,D3)
--R            from LieExponentials(D2,D3,D4)
--R            if D2 has ORDSET and D3 has Join(CommutativeRing,Module
--R            Fraction Integer) and D4: PI
--R   [10] LieExponentials(D2,D3,D4) -> XDistributedPolynomial(D2,D3)
--R            from LieExponentials(D2,D3,D4)
--R            if D2 has ORDSET and D3 has Join(CommutativeRing,Module
--R            Fraction Integer) and D4: PI
--R   [11] LyndonWord D2 -> Magma D2 from LyndonWord D2 if D2 has ORDSET
--R
--R   [12] LyndonWord D2 -> OrderedFreeMonoid D2 from LyndonWord D2
--R            if D2 has ORDSET
--R   [13] Magma D2 -> OrderedFreeMonoid D2 from Magma D2 if D2 has ORDSET
--R
--R   [14] D1 -> MakeCachableSet D1 from MakeCachableSet D1 if D1 has
--R            SETCAT
--R   [15] ModularField(D1,D2,D3,D4,D5) -> D1 from ModularField(D1,D2,D3,
--R            D4,D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [16] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
--R            if D2 has RING and D1 has UPOLYC D2
--R   [17] ModuleMonomial(D2,D3,D4) -> Record(index: D2,exponent: D3)
--R            from ModuleMonomial(D2,D3,D4)
--R            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index:
--R            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
--R            )
--R   [18] Record(index: D2,exponent: D3) -> ModuleMonomial(D2,D3,D4)
--R            from ModuleMonomial(D2,D3,D4)
--R            if D2 has ORDSET and D3 has SETCAT and D4: ((Record(index:
--R            D2,exponent: D3),Record(index: D2,exponent: D3)) -> Boolean
--R            )
--R   [19] ModularRing(D1,D2,D3,D4,D5) -> D1 from ModularRing(D1,D2,D3,D4,
--R            D5)

--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [20] List Record(coef: D2,monom: D3) -> MonoidRing(D2,D3)
--R            from MonoidRing(D2,D3) if D2 has RING and D3 has MONOID
--R   [21] Variable D2 -> UnivariateSkewPolynomial(D2,D3,D4,D5)
--R            from UnivariateSkewPolynomial(D2,D3,D4,D5)
--R            if D2: SYMBOL and D3 has RING and D4: AUTOMOR D3 and D5: (
--R            D3 -> D3)
--R   [22] Polynomial D2 -> OrdinaryWeightedPolynomials(D2,D3,D4,D5)
--R            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
--R            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
--R            : NNI
--R   [23] OrdinaryWeightedPolynomials(D2,D3,D4,D5) -> Polynomial D2
--R            from OrdinaryWeightedPolynomials(D2,D3,D4,D5)
--R            if D2 has RING and D3: LIST SYMBOL and D4: LIST NNI and D5
--R            : NNI
--R   [24] D1 -> PoincareBirkhoffWittLyndonBasis D1
--R            from PoincareBirkhoffWittLyndonBasis D1 if D1 has ORDSET
--R
--R   [25] PoincareBirkhoffWittLyndonBasis D2 -> OrderedFreeMonoid D2
--R            from PoincareBirkhoffWittLyndonBasis D2 if D2 has ORDSET
--R
--R   [26] Partition -> List Integer from Partition
--R   [27] D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
--R            D5)
--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1
--R            has POLYCAT(D2,D3,D4) and D5: LIST D1
--R   [28] RectangularMatrix(D2,D3,D4) -> Matrix D4
--R            from RectangularMatrix(D2,D3,D4)
--R            if D2: NNI and D3: NNI and D4 has RING
--R   [29] D1 -> SparseMultivariateTaylorSeries(D2,D3,D1)
--R            from SparseMultivariateTaylorSeries(D2,D3,D1)
--R            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
--R            D3,D3)
--R   [30] D1 -> SparseMultivariateTaylorSeries(D2,D1,D3)
--R            from SparseMultivariateTaylorSeries(D2,D1,D3)
--R            if D2 has RING and D1 has ORDSET and D3 has POLYCAT(D2,INDE
--R            D1,D1)
--R   [31] SquareMatrix(D2,D3) -> Matrix D3 from SquareMatrix(D2,D3)
--R            if D2: NNI and D3 has RING
--R   [32] D2 -> Stream D2 from StreamTaylorSeriesOperations D2 if D2 has
--R            RING
--R   [33] Variable D3 -> SparseUnivariateLaurentSeries(D2,D3,D4)
--R            from SparseUnivariateLaurentSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [34] Variable D3 -> SparseUnivariatePuiseuxSeries(D2,D3,D4)
--R            from SparseUnivariatePuiseuxSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [35] Variable D3 -> SparseUnivariateTaylorSeries(D2,D3,D4)

--R            from SparseUnivariateTaylorSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [36] UnivariatePolynomial(D3,D2) -> SparseUnivariateTaylorSeries(D2,
--R            D3,D4)
--R            from SparseUnivariateTaylorSeries(D2,D3,D4)
--R            if D2 has RING and D3: SYMBOL and D4: D2
--R   [37] PrimitiveArray D2 -> Tuple D2 from Tuple D2 if D2 has TYPE
--R   [38] Variable D3 -> UnivariateLaurentSeries(D2,D3,D4)
--R            from UnivariateLaurentSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [39] Variable D3 -> UnivariatePuiseuxSeries(D2,D3,D4)
--R            from UnivariatePuiseuxSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [40] Variable D3 -> UnivariateTaylorSeries(D2,D3,D4)
--R            from UnivariateTaylorSeries(D2,D3,D4)
--R            if D3: SYMBOL and D2 has RING and D4: D2
--R   [41] UnivariatePolynomial(D3,D2) -> UnivariateTaylorSeries(D2,D3,D4)
--R            from UnivariateTaylorSeries(D2,D3,D4)
--R            if D2 has RING and D3: SYMBOL and D4: D2
--R   [42] Variable D2 -> Symbol from Variable D2 if D2: SYMBOL
--R   [43] TwoDimensionalViewport -> OutputForm from
--R            TwoDimensionalViewport
--R   [44] GraphImage -> TwoDimensionalViewport from ViewportPackage
--R   [45] D1 -> WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
--R            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
--R            if D2 has RING and D3 has ORDSET and D4 has OAMONS and D5:
--R            LIST D3 and D1 has POLYCAT(D2,D4,D3) and D6: LIST NNI and
--R            D7: NNI
--R   [46] WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7) -> D1
--R            from WeightedPolynomials(D2,D3,D4,D1,D5,D6,D7)
--R            if D1 has POLYCAT(D2,D4,D3) and D2 has RING and D3 has
--R            ORDSET and D4 has OAMONS and D5: LIST D3 and D6: LIST NNI
--R            and D7: NNI
--R   [47] XPBWPolynomial(D2,D3) -> XRecursivePolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
--R            COMRING
--R   [48] XPBWPolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
--R            COMRING
--R   [49] LiePolynomial(D2,D3) -> XPBWPolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
--R            COMRING
--R   [50] D1 -> XPolynomialRing(D2,D1) from XPolynomialRing(D2,D1)
--R            if D2 has RING and D1 has ORDMON
--R
--RExamples of coerce from AffineSpaceCategory
--R
--R
--RExamples of coerce from Algebra
--R

--R
--RExamples of coerce from AlgebraGivenByStructuralConstants
--R
--R
--RExamples of coerce from AlgebraicNumber
--R
--R
--RExamples of coerce from AnyFunctions1
--R
--R
--RExamples of coerce from Asp10
--R
--R
--RExamples of coerce from Asp19
--R
--R
--RExamples of coerce from Asp1
--R
--R
--RExamples of coerce from Asp20
--R
--R
--RExamples of coerce from Asp24
--R
--R
--RExamples of coerce from Asp31
--R
--R
--RExamples of coerce from Asp35
--R
--R
--RExamples of coerce from Asp41
--R
--R
--RExamples of coerce from Asp42
--R
--R
--RExamples of coerce from Asp49
--R
--R
--RExamples of coerce from Asp4
--R
--R
--RExamples of coerce from Asp50
--R
--R
--RExamples of coerce from Asp55
--R
--R
--RExamples of coerce from Asp6

--R
--R
--RExamples of coerce from Asp73
--R
--R
--RExamples of coerce from Asp74
--R
--R
--RExamples of coerce from Asp77
--R
--R
--RExamples of coerce from Asp78
--R
--R
--RExamples of coerce from Asp7
--R
--R
--RExamples of coerce from Asp80
--R
--R
--RExamples of coerce from Asp9
--R
--R
--RExamples of coerce from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5]
--Rcoerce a
--R
--R
--RExamples of coerce from BinaryExpansion
--R
--R
--RExamples of coerce from BlowUpMethodCategory
--R
--R
--RExamples of coerce from CartesianTensor
--R
--Rv:=[2,3]
--Rtv:CartesianTensor(1,2,Integer):=v
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
--R
--Rv:=[2,3]
--Rtv:CartesianTensor(1,2,Integer):=v
--R
--Rv:SquareMatrix(2,Integer):=[[1,2],[3,4]]
--Rtv:CartesianTensor(1,2,Integer):=v
--R
--Rv:DirectProduct(2,Integer):=directProduct [3,4]
--Rtv:CartesianTensor(1,2,Integer):=v
--R

--R
--RExamples of coerce from CoerceVectorMatrixPackage
--R
--R
--RExamples of coerce from Database
--R
--R
--RExamples of coerce from DecimalExpansion
--R
--R
--RExamples of coerce from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5]
--Rcoerce a
--R
--R
--RExamples of coerce from DirichletRing
--R
--R
--RExamples of coerce from DataList
--R
--R
--RExamples of coerce from DrawNumericHack
--R
--R
--RExamples of coerce from DifferentialVariableCategory
--R
--R
--RExamples of coerce from ExtAlgBasis
--R
--R
--RExamples of coerce from EuclideanModularRing
--R
--R
--RExamples of coerce from ExponentialExpansion
--R
--R
--RExamples of coerce from FortranCode
--R
--R
--RExamples of coerce from FortranExpression
--R
--R
--RExamples of coerce from FiniteFieldHomomorphisms
--R
--R
--RExamples of coerce from FreeLieAlgebra
--R
--R
--RExamples of coerce from FortranMatrixCategory

--R
--R
--RExamples of coerce from FortranMatrixFunctionCategory
--R
--R
--RExamples of coerce from FileNameCategory
--R
--R
--RExamples of coerce from ScriptFormulaFormat1
--R
--R
--RExamples of coerce from ScriptFormulaFormat
--R
--R
--RExamples of coerce from FortranFunctionCategory
--R
--R
--RExamples of coerce from FortranProgram
--R
--R
--RExamples of coerce from FourierSeries
--R
--R
--RExamples of coerce from FunctionSpace
--R
--R
--RExamples of coerce from FortranScalarType
--R
--R
--RExamples of coerce from FortranType
--R
--R
--RExamples of coerce from FortranVectorCategory
--R
--R
--RExamples of coerce from FortranVectorFunctionCategory
--R
--R
--RExamples of coerce from GenericNonAssociativeAlgebra
--R
--R
--RExamples of coerce from GraphImage
--R
--R
--RExamples of coerce from GeneralUnivariatePowerSeries
--R
--R
--RExamples of coerce from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5]

--Rcoerce a
--R
--R
--RExamples of coerce from HexadecimalExpansion
--R
--R
--RExamples of coerce from HTMLFormat
--R
--Rcoerce(sqrt(3+x)::OutputForm)$HTMLFORM
--R
--R
--RExamples of coerce from InnerAlgebraicNumber
--R
--R
--RExamples of coerce from IndexCard
--R
--R
--RExamples of coerce from PolynomialIdeals
--R
--R
--RExamples of coerce from AssociatedJordanAlgebra
--R
--R
--RExamples of coerce from CoercibleTo
--R
--R
--RExamples of coerce from LeftAlgebra
--R
--R
--RExamples of coerce from LieExponentials
--R
--R
--RExamples of coerce from AssociatedLieAlgebra
--R
--R
--RExamples of coerce from LocalPowerSeriesCategory
--R
--R
--RExamples of coerce from LyndonWord
--R
--R
--RExamples of coerce from ThreeDimensionalMatrix
--R
--R
--RExamples of coerce from Magma
--R
--R
--RExamples of coerce from MappingPackage1
--R
--R

--RExamples of coerce from MatrixCategory
--R
--Rcoerce([1,2,3])@Matrix(INT)
--R
--R
--RExamples of coerce from MachineComplex
--R
--R
--RExamples of coerce from MachineFloat
--R
--R
--RExamples of coerce from MachineInteger
--R
--R
--RExamples of coerce from MakeCachableSet
--R
--R
--RExamples of coerce from MathMLFormat
--R
--R
--RExamples of coerce from ModularField
--R
--R
--RExamples of coerce from ModMonic
--R
--R
--RExamples of coerce from ModuleMonomial
--R
--R
--RExamples of coerce from ModularRing
--R
--R
--RExamples of coerce from MonoidRing
--R
--R
--RExamples of coerce from MyExpression
--R
--R
--RExamples of coerce from MyUnivariatePolynomial
--R
--R
--RExamples of coerce from NonAssociativeRing
--R
--R
--RExamples of coerce from NumericalIntegrationProblem
--R
--R
--RExamples of coerce from NoneFunctions1
--R
--R

--RExamples of coerce from NumericalODEProblem
--R
--R
--RExamples of coerce from OrdinaryDifferentialRing
--R
--R
--RExamples of coerce from OpenMathErrorKind
--R
--R
--RExamples of coerce from NumericalOptimizationProblem
--R
--R
--RExamples of coerce from UnivariateSkewPolynomial
--R
--R
--RExamples of coerce from OrdSetInts
--R
--R
--RExamples of coerce from OrdinaryWeightedPolynomials
--R
--R
--RExamples of coerce from Palette
--R
--R
--RExamples of coerce from PolynomialAN2Expression
--R
--R
--RExamples of coerce from PoincareBirkhoffWittLyndonBasis
--R
--R
--RExamples of coerce from NumericalPDEProblem
--R
--R
--RExamples of coerce from PendantTree
--R
--Rt1:=ptree([1,2,3])
--Rt2:=ptree(t1,ptree([1,2,3]))
--Rt2::Tree List PositiveInteger
--R
--R
--RExamples of coerce from PermutationGroup
--R
--R
--RExamples of coerce from Permutation
--R
--R
--RExamples of coerce from PartialFraction
--R
--R(13/74)::PFR(INT)
--R

--Ra:=(13/74)::PFR(INT)
--Ra::FRAC(INT)
--R
--R
--RExamples of coerce from PiCoercions
--R
--R
--RExamples of coerce from ProjectiveSpaceCategory
--R
--R
--RExamples of coerce from Partition
--R
--R
--RExamples of coerce from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5]
--Rcoerce a
--R
--R
--RExamples of coerce from RadixExpansion
--R
--R
--RExamples of coerce from ResolveLatticeCompletion
--R
--R
--RExamples of coerce from ResidueRing
--R
--R
--RExamples of coerce from RetractableTo
--R
--R
--RExamples of coerce from RationalFunction
--R
--R
--RExamples of coerce from Ring
--R
--R
--RExamples of coerce from RectangularMatrix
--R
--R
--RExamples of coerce from SparseMultivariateTaylorSeries
--R
--R
--RExamples of coerce from ThreeSpaceCategory
--R
--R
--RExamples of coerce from SquareMatrix
--R
--R
--RExamples of coerce from StringAggregate

--R
--R
--RExamples of coerce from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5]
--Rcoerce a
--R
--R
--RExamples of coerce from Stream
--R
--Rm:=[1,2,3,4,5,6,7,8,9,10,11,12]
--Rcoerce(m)@Stream(Integer)
--Rm::Stream(Integer)
--R
--R
--RExamples of coerce from StreamTaylorSeriesOperations
--R
--R
--RExamples of coerce from SparseUnivariateLaurentSeries
--R
--R
--RExamples of coerce from SparseUnivariatePuiseuxSeries
--R
--R
--RExamples of coerce from SparseUnivariateTaylorSeries
--R
--R
--RExamples of coerce from Switch
--R
--R
--RExamples of coerce from Symbol
--R
--R
--RExamples of coerce from SymbolTable
--R
--R
--RExamples of coerce from Tableau
--R
--R
--RExamples of coerce from TexFormat1
--R
--R
--RExamples of coerce from TexFormat
--R
--R
--RExamples of coerce from TaylorSeries
--R
--R
--RExamples of coerce from Tuple
--R

--Rt1:PrimitiveArray(Integer):= [i for i in 1..10]
--Rt2:=coerce(t1)$Tuple(Integer)
--R
--R
--RExamples of coerce from UnivariateFormalPowerSeries
--R
--R
--RExamples of coerce from UnivariateLaurentSeriesConstructorCategory
--R
--R
--RExamples of coerce from UnivariateLaurentSeries
--R
--R
--RExamples of coerce from UniversalSegment
--R
--R
--RExamples of coerce from UnivariatePolynomial
--R
--R
--RExamples of coerce from UnivariatePuiseuxSeriesConstructorCategory
--R
--R
--RExamples of coerce from UnivariatePuiseuxSeries
--R
--R
--RExamples of coerce from UnivariateTaylorSeries
--R
--R
--RExamples of coerce from UnivariateTaylorSeriesCZero
--R
--R
--RExamples of coerce from Variable
--R
--R
--RExamples of coerce from TwoDimensionalViewport
--R
--R
--RExamples of coerce from ViewportPackage
--R
--R
--RExamples of coerce from Void
--R
--R
--RExamples of coerce from WeightedPolynomials
--R
--R
--RExamples of coerce from XAlgebra
--R
--R
--RExamples of coerce from XFreeAlgebra

--R
--R
--RExamples of coerce from XPBWPolynomial
--R
--R
--RExamples of coerce from XPolynomialRing
--R
--E 69
--S 70 of 127
)d op contract
--R
--R
--RThere are 3 exposed functions called contract :
--R   [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor(
--R            D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [2] (CartesianTensor(D2,D3,D4),Integer,CartesianTensor(D2,D3,D4),
--R            Integer) -> CartesianTensor(D2,D3,D4)
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [3] (PolynomialIdeals(Fraction(Integer),DirectProduct(D4,
--R            NonNegativeInteger),OrderedVariableList(D3),
--R            DistributedMultivariatePolynomial(D3,Fraction(Integer))),List(
--R            OrderedVariableList(D3))) -> PolynomialIdeals(Fraction(Integer),
--R            DirectProduct(D4,NonNegativeInteger),OrderedVariableList(D3),
--R            DistributedMultivariatePolynomial(D3,Fraction(Integer)))
--R            from IdealDecompositionPackage(D3,D4)
--R            if D3: LIST(SYMBOL) and D4: NNI
--R
--RExamples of contract from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
--RTm:CartesianTensor(1,2,Integer):=m
--Rv:DirectProduct(2,Integer):=directProduct [3,4]
--RTv:CartesianTensor(1,2,Integer):=v
--RTmv:=contract(Tm,2,1)
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
--RTm:CartesianTensor(1,2,Integer):=m
--Rv:DirectProduct(2,Integer):=directProduct [3,4]
--RTv:CartesianTensor(1,2,Integer):=v
--RTmv:=contract(Tm,2,Tv,1)
--R
--R
--RExamples of contract from IdealDecompositionPackage
--R
--E 70

--S 71 of 127
)d op irreducibleFactor
--R
--R
--RThere is one exposed function called irreducibleFactor :
--R   [1] (D1,Integer) -> Factored(D1) from Factored(D1) if D1 has INTDOM
--R
--R
--RExamples of irreducibleFactor from Factored
--R
--Ra:=irreducibleFactor(3,1)
--RnthFlag(a,1)
--R
--E 71
--S 72 of 127
)d op concat
--R
--R
--RThere are 11 exposed functions called concat :
--R   [1] (D,D) -> D from D if D has DIVCAT(D1) and D1 has SETCAT
--R   [2] (Result,Result) -> Result from ExpertSystemToolsPackage
--R   [3] List(Result) -> Result from ExpertSystemToolsPackage
--R   [4] List(D) -> D from D if D has LNAGG(D2) and D2 has TYPE
--R   [5] (D,D) -> D from D if D has LNAGG(D1) and D1 has TYPE
--R   [6] (D1,D) -> D from D if D has LNAGG(D1) and D1 has TYPE
--R   [7] (D,D1) -> D from D if D has LNAGG(D1) and D1 has TYPE
--R   [8] (RoutinesTable,RoutinesTable) -> RoutinesTable from
--R            RoutinesTable
--R   [9] Stream(Stream(D3)) -> Stream(D3) from StreamFunctions1(D3)
--R            if D3 has TYPE
--R   [10] (D1,D) -> D from D if D has URAGG(D1) and D1 has TYPE
--R   [11] (D,D) -> D from D if D has URAGG(D1) and D1 has TYPE
--R
--RExamples of concat from DivisorCategory
--R
--R
--RExamples of concat from ExpertSystemToolsPackage
--R
--R
--RExamples of concat from LinearAggregate
--R
--R
--RExamples of concat from RoutinesTable
--R
--R
--RExamples of concat from StreamFunctions1
--R
--Rm:=[i for i in 10..]
--Rn:=[j for j in 1.. | prime? j]

--Rp:=[m,n]::Stream(Stream(PositiveInteger))
--Rconcat(p)
--R
--R
--RExamples of concat from UnaryRecursiveAggregate
--R
--E 72
--S 73 of 127
)d op binaryTournament
--R
--R
--RThere is one exposed function called binaryTournament :
--R   [1] List(D2) -> BinaryTournament(D2) from BinaryTournament(D2)
--R            if D2 has ORDSET
--R
--RExamples of binaryTournament from BinaryTournament
--R
--RbinaryTournament [1,2,3,4]
--R
--E 73
--S 74 of 127
)d op upperCase
--R
--R
--RThere are 3 exposed functions called upperCase :
--R   [1]  -> CharacterClass from CharacterClass
--R   [2] Character -> Character from Character
--R   [3] D -> D from D if D has SRAGG
--R
--RExamples of upperCase from CharacterClass
--R
--R
--RExamples of upperCase from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[upperCase c for c in chars]
--R
--R
--RExamples of upperCase from StringAggregate
--R
--E 74
--S 75 of 127
)d op exponent
--R
--R
--RThere are 3 exposed functions called exponent :
--R   [1] D -> Integer from D if D has FPS

--R   [2] Factored(D2) -> Integer from Factored(D2) if D2 has INTDOM
--R   [3] MachineFloat -> Integer from MachineFloat
--R
--RThere are 2 unexposed functions called exponent :
--R   [1] ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) ->
--R            UnivariatePuiseuxSeries(D2,D3,D4)
--R            from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4)
--R            if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2
--R
--R   [2] ModuleMonomial(D2,D1,D3) -> D1 from ModuleMonomial(D2,D1,D3)
--R            if D1 has SETCAT and D2 has ORDSET and D3: ((Record(index:
--R            D2,exponent: D1),Record(index: D2,exponent: D1)) -> Boolean
--R            )
--R
--RExamples of exponent from ExponentialOfUnivariatePuiseuxSeries
--R
--R
--RExamples of exponent from FloatingPointSystem
--R
--R
--RExamples of exponent from Factored
--R
--Rf:=nilFactor(y-x,3)
--Rexponent(f)
--R
--R
--RExamples of exponent from MachineFloat
--R
--R
--RExamples of exponent from ModuleMonomial
--R
--E 75
--S 76 of 127
)d op setRow!
--R
--R
--RThere is one exposed function called setRow! :
--R   [1] (D,Integer,D2) -> D from D
--R            if D has ARR2CAT(D3,D2,D4) and D3 has TYPE and D2 has FLAGG
--R            (D3) and D4 has FLAGG(D3)
--R
--RExamples of setRow! from TwoDimensionalArrayCategory
--R
--RT1:=TwoDimensionalArray Integer
--Rarr:T1:= new(5,4,0)
--RT2:=OneDimensionalArray Integer
--Rarow:=construct([1,2,3,4]::List(INT))$T2
--RsetRow!(arr,1,arow)$T1
--R

--E 76
--S 77 of 127
)d op generate
--R
--R
--RThere are 4 exposed functions called generate :
--R   [1] (NonNegativeInteger,NonNegativeInteger) -> Vector(List(Integer))
--R            from HallBasis
--R   [2] ((D2 -> D2),D2) -> InfiniteTuple(D2) from InfiniteTuple(D2)
--R            if D2 has TYPE
--R   [3] ((D2 -> D2),D2) -> Stream(D2) from Stream(D2) if D2 has TYPE
--R   [4] (() -> D2) -> Stream(D2) from Stream(D2) if D2 has TYPE
--R
--RExamples of generate from HallBasis
--R
--R
--RExamples of generate from InfiniteTuple
--R
--R
--RExamples of generate from Stream
--R
--Rf(x:Integer):Integer == x+10
--Rgenerate(f,10)
--R
--Rf():Integer == 1
--Rgenerate(f)
--R
--E 77
--S 78 of 127
)d op gcd
--R
--R
--RThere are 8 exposed functions called gcd :
--R   [1] List(D) -> D from D if D has GCDDOM
--R   [2] (D,D) -> D from D if D has GCDDOM
--R   [3] (D1,D1,Integer) -> D1 from ModularDistinctDegreeFactorizer(D1)
--R            if D1 has UPOLYC(INT)
--R   [4] (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger
--R            from NonNegativeInteger
--R   [5] (PositiveInteger,PositiveInteger) -> PositiveInteger
--R            from PositiveInteger
--R   [6] (U32Vector,U32Vector,Integer) -> U32Vector
--R            from U32VectorPolynomialOperations
--R   [7] (PrimitiveArray(U32Vector),Integer,Integer,Integer) -> U32Vector
--R            from U32VectorPolynomialOperations
--R   [8] (D1,D) -> D1 from D
--R            if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has
--R            OAMONS and D3 has ORDSET and D1 has GCDDOM

--R
--RThere are 6 unexposed functions called gcd :
--R   [1] List(D1) -> D1 from HeuGcd(D1) if D1 has UPOLYC(INT)
--R   [2] (D1,D1) -> D1 from PolynomialGcdPackage(D2,D3,D4,D1)
--R            if D2 has OAMONS and D3 has ORDSET and D4 has EUCDOM and D1
--R            has POLYCAT(D4,D2,D3)
--R   [3] List(D1) -> D1 from PolynomialGcdPackage(D3,D4,D5,D1)
--R            if D1 has POLYCAT(D5,D3,D4) and D3 has OAMONS and D4 has
--R            ORDSET and D5 has EUCDOM
--R   [4] (SparseUnivariatePolynomial(D5),SparseUnivariatePolynomial(D5))
--R             -> SparseUnivariatePolynomial(D5)
--R            from PolynomialGcdPackage(D2,D3,D4,D5)
--R            if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has
--R            ORDSET and D4 has EUCDOM
--R   [5] List(SparseUnivariatePolynomial(D6)) ->
--R            SparseUnivariatePolynomial(D6)
--R            from PolynomialGcdPackage(D3,D4,D5,D6)
--R            if D3 has OAMONS and D4 has ORDSET and D5 has EUCDOM and D6
--R            has POLYCAT(D5,D3,D4)
--R   [6] (D1,D1) -> D1 from PseudoRemainderSequence(D2,D1)
--R            if D2 has GCDDOM and D2 has INTDOM and D1 has UPOLYC(D2)
--R
--R
--RExamples of gcd from GcdDomain
--R
--R
--RExamples of gcd from HeuGcd
--R
--Rgcd([671*671*x^2-1,671*671*x^2+2*671*x+1])
--Rgcd([7*x^2+1,(7*x^2+1)^2])
--R
--R
--RExamples of gcd from ModularDistinctDegreeFactorizer
--R
--R
--RExamples of gcd from NonNegativeInteger
--R
--R
--RExamples of gcd from PolynomialGcdPackage
--R
--R
--RExamples of gcd from PositiveInteger
--R
--R
--RExamples of gcd from U32VectorPolynomialOperations
--R
--R
--RExamples of gcd from PseudoRemainderSequence
--R
--R

--RExamples of gcd from RecursivePolynomialCategory
--R
--E 78
--S 79 of 127
)d op binary
--R
--R
--RThere is one exposed function called binary :
--R   [1] Fraction(Integer) -> BinaryExpansion from BinaryExpansion
--R
--RThere is one unexposed function called binary :
--R   [1] (InputForm,List(InputForm)) -> InputForm from InputForm
--R
--RExamples of binary from BinaryExpansion
--R
--Rbinary(22/7)
--R
--R
--RExamples of binary from InputForm
--R
--Ra:=[1,2,3]::List(InputForm)
--Rbinary(_+::InputForm,a)
--R
--E 79
--S 80 of 127
)d op expand
--R
--R
--RThere are 6 exposed functions called expand :
--R   [1] Factored(D1) -> D1 from Factored(D1) if D1 has INTDOM
--R   [2] IntegrationResult(D4) -> List(D4)
--R            from IntegrationResultToFunction(D3,D4)
--R            if D4 has Join(AlgebraicallyClosedFunctionSpace(D3),
--R            TranscendentalFunctionCategory) and D3 has Join(GcdDomain,
--R            RetractableTo(Integer),OrderedSet,LinearlyExplicitRingOver(
--R            Integer))
--R   [3] IntegrationResult(Fraction(Polynomial(D3))) -> List(Expression(
--R            D3))
--R            from IntegrationResultRFToFunction(D3)
--R            if D3 has Join(GcdDomain,RetractableTo(Integer),OrderedSet,
--R            LinearlyExplicitRingOver(Integer))
--R   [4] D -> D1 from D
--R            if D has SEGXCAT(D2,D1) and D2 has ORDRING and D1 has STAGG
--R            (D2)
--R   [5] List(D) -> D1 from D
--R            if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has STAGG
--R            (D3)
--R   [6] D1 -> D1 from TranscendentalManipulations(D2,D1)

--R            if D2 has Join(OrderedSet,GcdDomain) and D1 has Join(
--R            FunctionSpace(D2),TranscendentalFunctionCategory)
--R
--RThere are 3 unexposed functions called expand :
--R   [1] (Expression(D5),PositiveInteger) -> List(Expression(D5))
--R            from DegreeReductionPackage(D4,D5)
--R            if D5 has Join(IntegralDomain,OrderedSet) and D4 has RING
--R
--R   [2] XPolynomial(D2) -> XDistributedPolynomial(Symbol,D2)
--R            from XPolynomial(D2) if D2 has RING
--R   [3] XRecursivePolynomial(D2,D3) -> XDistributedPolynomial(D2,D3)
--R            from XRecursivePolynomial(D2,D3)
--R            if D2 has ORDSET and D3 has RING
--R
--RExamples of expand from DegreeReductionPackage
--R
--R
--RExamples of expand from Factored
--R
--Rf:=nilFactor(y-x,3)
--Rexpand(f)
--R
--R
--RExamples of expand from IntegrationResultToFunction
--R
--R
--RExamples of expand from IntegrationResultRFToFunction
--R
--R
--RExamples of expand from SegmentExpansionCategory
--R
--R
--RExamples of expand from TranscendentalManipulations
--R
--R
--RExamples of expand from XPolynomial
--R
--R
--RExamples of expand from XRecursivePolynomial
--R
--E 80
--S 81 of 127
)d op filterWhile
--R
--R
--RThere are 2 exposed functions called filterWhile :
--R   [1] ((D2 -> Boolean),InfiniteTuple(D2)) -> InfiniteTuple(D2)
--R            from InfiniteTuple(D2) if D2 has TYPE
--R   [2] ((D2 -> Boolean),Stream(D2)) -> Stream(D2) from Stream(D2)

--R            if D2 has TYPE
--R
--RExamples of filterWhile from InfiniteTuple
--R
--R
--RExamples of filterWhile from Stream
--R
--Rm:=[i for i in 1..]
--Rf(x:PositiveInteger):Boolean == x < 5
--RfilterWhile(f,m)
--R
--E 81
--S 82 of 127
)d op filterUntil
--R
--R
--RThere are 2 exposed functions called filterUntil :
--R   [1] ((D2 -> Boolean),InfiniteTuple(D2)) -> InfiniteTuple(D2)
--R            from InfiniteTuple(D2) if D2 has TYPE
--R   [2] ((D2 -> Boolean),Stream(D2)) -> Stream(D2) from Stream(D2)
--R            if D2 has TYPE
--R
--RExamples of filterUntil from InfiniteTuple
--R
--R
--RExamples of filterUntil from Stream
--R
--Rm:=[i for i in 1..]
--Rf(x:PositiveInteger):Boolean == x < 5
--RfilterUntil(f,m)
--R
--E 82
--S 83 of 127
)d op select
--R
--RThere are 4 exposed functions called select :
--R   [1] ((D2 -> Boolean),D) -> D from D
--R            if D has finiteAggregate and D has CLAGG(D2) and D2 has
--R            TYPE
--R   [2] ((D2 -> Boolean),InfiniteTuple(D2)) -> InfiniteTuple(D2)
--R            from InfiniteTuple(D2) if D2 has TYPE
--R   [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG(D2) and D2 has
--R            TYPE
--R   [4] (D,D2) -> Union(D1,"failed") from D
--R            if D has TSETCAT(D3,D4,D2,D1) and D3 has INTDOM and D4 has
--R            OAMONS and D2 has ORDSET and D1 has RPOLCAT(D3,D4,D2)
--R
--RThere is one unexposed function called select :

--R   [1] (Tuple(D1),NonNegativeInteger) -> D1 from Tuple(D1) if D1 has
--R            TYPE
--R
--RExamples of select from Collection
--R
--R
--RExamples of select from InfiniteTuple
--R
--R
--RExamples of select from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--Rselect(x+->prime? x,m)
--R
--R
--RExamples of select from TriangularSetCategory
--R
--R
--RExamples of select from Tuple
--R
--Rt1:PrimitiveArray(Integer):= [i for i in 1..10]
--Rt2:=coerce(t1)$Tuple(Integer)
--Rselect(t2,3)
--R
--E 83
--S 84 of 127
)d op nthFlag
--R
--R
--RThere is one exposed function called nthFlag :
--R   [1] (Factored(D3),Integer) -> Union("nil","sqfr","irred","prime")
--R            from Factored(D3) if D3 has INTDOM
--R
--RExamples of nthFlag from Factored
--R
--Ra:=factor 9720000
--RnthFlag(a,2)
--R
--E 84
--S 85 of 127
)d op makeFR
--R
--R
--RThere is one exposed function called makeFR :
--R   [1] (D1,List(Record(flg: Union("nil","sqfr","irred","prime"),fctr:
--R            D1,xpnt: Integer))) -> Factored(D1)
--R            from Factored(D1) if D1 has INTDOM
--R

--RThere is one unexposed function called makeFR :
--R   [1] Record(contp: Integer,factors: List(Record(irr: D3,pow: Integer)
--R            )) -> Factored(D3)
--R            from GaloisGroupFactorizer(D3) if D3 has UPOLYC(INT)
--R
--RExamples of makeFR from Factored
--R
--Rf:=nilFactor(x-y,3)
--Rg:=factorList f
--RmakeFR(z,g)
--R
--R
--RExamples of makeFR from GaloisGroupFactorizer
--R
--E 85
--S 86 of 127
)d op *
--R
--R
--RThere are 37 exposed functions called * :
--R   [1] (Integer,D) -> D from D if D has ABELGRP
--R   [2] (NonNegativeInteger,D) -> D from D if D has ABELMON
--R   [3] (PositiveInteger,D) -> D from D if D has ABELSG
--R   [4] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) ->
--R            CartesianTensor(D1,D2,D3)
--R            from CartesianTensor(D1,D2,D3)
--R            if D1: INT and D2: NNI and D3 has COMRING
--R   [5] (DoubleFloat,Color) -> Color from Color
--R   [6] (PositiveInteger,Color) -> Color from Color
--R   [7] (DenavitHartenbergMatrix(D2),Point(D2)) -> Point(D2)
--R            from DenavitHartenbergMatrix(D2)
--R            if D2 has Join(Field,TranscendentalFunctionCategory)
--R   [8] (D1,D) -> D from D
--R            if D has DIRPCAT(D2,D1) and D1 has TYPE and D1 has MONOID
--R
--R   [9] (D,D1) -> D from D
--R            if D has DIRPCAT(D2,D1) and D1 has TYPE and D1 has MONOID
--R
--R   [10] (D1,Equation(D1)) -> Equation(D1) from Equation(D1)
--R            if D1 has SGROUP and D1 has TYPE
--R   [11] (Equation(D1),D1) -> Equation(D1) from Equation(D1)
--R            if D1 has SGROUP and D1 has TYPE
--R   [12] (D1,D2) -> D from D
--R            if D has FAMONC(D2,D1) and D2 has SETCAT and D1 has CABMON
--R
--R   [13] (D1,D2) -> D from D
--R            if D has FMCAT(D1,D2) and D1 has RING and D2 has SETCAT
--R   [14] (D,D1) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON

--R
--R   [15] (D1,D) -> D from D
--R            if D has GRMOD(D1,D2) and D1 has COMRING and D2 has ABELMON
--R
--R   [16] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4))
--R             -> PolynomialIdeals(D1,D2,D3,D4)
--R            from PolynomialIdeals(D1,D2,D3,D4)
--R            if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4
--R            has POLYCAT(D1,D2,D3)
--R   [17] (D1,D) -> D from D if D has LMODULE(D1) and D1 has RNG
--R   [18] ((D5 -> D6),(D4 -> D5)) -> (D4 -> D6) from MappingPackage3(D4,
--R            D5,D6)
--R            if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT
--R   [19] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,
--R            D3)
--R            if D2 has SETCAT and D3 has RING
--R   [20] (D1,D) -> D1 from D
--R            if D has MATCAT(D2,D1,D3) and D2 has RING and D1 has FLAGG(
--R            D2) and D3 has FLAGG(D2)
--R   [21] (D,D1) -> D1 from D
--R            if D has MATCAT(D2,D3,D1) and D2 has RING and D3 has FLAGG(
--R            D2) and D1 has FLAGG(D2)
--R   [22] (Integer,D) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG(
--R            D2) and D4 has FLAGG(D2)
--R   [23] (D,D1) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [24] (D1,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [25] (D,D) -> D from D
--R            if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG(
--R            D1) and D3 has FLAGG(D1)
--R   [26] (D,D) -> D from D if D has MONAD
--R   [27] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2
--R            )
--R            from MyExpression(D1,D2)
--R            if D1: SYMBOL and D2 has Join(Ring,OrderedSet,
--R            IntegralDomain)
--R   [28] (Integer,D) -> Divisor(D) from D
--R            if D3 has FIELD and D4 has LOCPOWC(D3) and D has PLACESC(D3
--R            ,D4)
--R   [29] (D,D1) -> D from D if D has RMODULE(D1) and D1 has RNG
--R   [30] (D,D) -> D from D if D has SGROUP
--R   [31] (D1,D) -> D1 from D
--R            if D has SMATCAT(D2,D3,D1,D4) and D3 has RING and D1 has
--R            DIRPCAT(D2,D3) and D4 has DIRPCAT(D2,D3)
--R   [32] (D,D1) -> D1 from D
--R            if D has SMATCAT(D2,D3,D4,D1) and D3 has RING and D4 has

--R            DIRPCAT(D2,D3) and D1 has DIRPCAT(D2,D3)
--R   [33] (D,D1) -> D from D
--R            if D has VECTCAT(D1) and D1 has TYPE and D1 has MONOID
--R   [34] (D1,D) -> D from D
--R            if D has VECTCAT(D1) and D1 has TYPE and D1 has MONOID
--R   [35] (Integer,D) -> D from D
--R            if D has VECTCAT(D2) and D2 has TYPE and D2 has ABELGRP
--R   [36] (D1,D) -> D from D
--R            if D has XFALG(D1,D2) and D1 has ORDSET and D2 has RING
--R   [37] (D,D1) -> D from D
--R            if D has XFALG(D2,D1) and D2 has ORDSET and D1 has RING
--R
--RThere are 23 unexposed functions called * :
--R   [1] (FreeGroup(D1),D1) -> FreeGroup(D1) from FreeGroup(D1) if D1 has
--R            SETCAT
--R   [2] (D1,FreeGroup(D1)) -> FreeGroup(D1) from FreeGroup(D1) if D1 has
--R            SETCAT
--R   [3] (D1,D2) -> FreeModule1(D2,D1) from FreeModule1(D2,D1)
--R            if D2 has RING and D1 has ORDSET
--R   [4] (FreeMonoid(D1),D1) -> FreeMonoid(D1) from FreeMonoid(D1)
--R            if D1 has SETCAT
--R   [5] (D1,FreeMonoid(D1)) -> FreeMonoid(D1) from FreeMonoid(D1)
--R            if D1 has SETCAT
--R   [6] (D1,GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)) ->
--R            GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
--R            from GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)
--R            if D2: LIST(SYMBOL) and D3 has COMRING and D5 has DIRPCAT(#
--R            (D2),NNI) and D6: ((Record(index: D4,exponent: D5),Record(
--R            index: D4,exponent: D5)) -> Boolean) and D4 has ORDSET and
--R            D1 has POLYCAT(D3,D5,OVAR(D2))
--R   [7] (Vector(D2),Vector(D2)) -> Vector(D2)
--R            from InnerNormalBasisFieldFunctions(D2) if D2 has FFIELDC
--R
--R   [8] (InputForm,InputForm) -> InputForm from InputForm
--R   [9] (InnerTaylorSeries(D2),Integer) -> InnerTaylorSeries(D2)
--R            from InnerTaylorSeries(D2) if D2 has RING
--R   [10] (InnerTaylorSeries(D1),D1) -> InnerTaylorSeries(D1)
--R            from InnerTaylorSeries(D1) if D1 has RING
--R   [11] (D1,InnerTaylorSeries(D1)) -> InnerTaylorSeries(D1)
--R            from InnerTaylorSeries(D1) if D1 has RING
--R   [12] (Magma(D1),Magma(D1)) -> Magma(D1) from Magma(D1) if D1 has
--R            ORDSET
--R   [13] (OrderedFreeMonoid(D1),D1) -> OrderedFreeMonoid(D1)
--R            from OrderedFreeMonoid(D1) if D1 has ORDSET
--R   [14] (D1,OrderedFreeMonoid(D1)) -> OrderedFreeMonoid(D1)
--R            from OrderedFreeMonoid(D1) if D1 has ORDSET
--R   [15] (OutputForm,OutputForm) -> OutputForm from OutputForm
--R   [16] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1)
--R            if D1 has SETCAT
--R   [17] (D2,Vector(D3)) -> Vector(D3) from PseudoRemainderSequence(D2,

--R            D3)
--R            if D3 has UPOLYC(D2) and D2 has INTDOM
--R   [18] (D1,SparseMultivariateTaylorSeries(D2,D3,D1)) ->
--R            SparseMultivariateTaylorSeries(D2,D3,D1)
--R            from SparseMultivariateTaylorSeries(D2,D3,D1)
--R            if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2,INDE
--R            (D3),D3)
--R   [19] (Stream(D2),Stream(D2)) -> Stream(D2)
--R            from StreamTaylorSeriesOperations(D2) if D2 has RING
--R   [20] (D2,Stream(D2)) -> Stream(D2) from StreamTaylorSeriesOperations
--R            (D2)
--R            if D2 has RING
--R   [21] (Stream(D2),D2) -> Stream(D2) from StreamTaylorSeriesOperations
--R            (D2)
--R            if D2 has RING
--R   [22] (DoubleFloat,Point(DoubleFloat)) -> Point(DoubleFloat)
--R            from TubePlotTools
--R   [23] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2)
--R            from XPolynomialRing(D1,D2) if D1 has RING and D2 has
--R            ORDMON
--R
--RExamples of * from AbelianGroup
--R
--R
--RExamples of * from AbelianMonoid
--R
--R
--RExamples of * from AbelianSemiGroup
--R
--R
--RExamples of * from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
--RTm:CartesianTensor(1,2,Integer):=m
--Rv:DirectProduct(2,Integer):=directProduct [3,4]
--RTv:CartesianTensor(1,2,Integer):=v
--RTm*Tv
--R
--R
--RExamples of * from Color
--R
--R
--RExamples of * from DenavitHartenbergMatrix
--R
--R
--RExamples of * from DirectProductCategory
--R
--R
--RExamples of * from Equation
--R

--R
--RExamples of * from FreeAbelianMonoidCategory
--R
--R
--RExamples of * from FreeGroup
--R
--R
--RExamples of * from FreeModule1
--R
--R
--RExamples of * from FreeModuleCat
--R
--R
--RExamples of * from FreeMonoid
--R
--R
--RExamples of * from GeneralModulePolynomial
--R
--R
--RExamples of * from GradedModule
--R
--R
--RExamples of * from PolynomialIdeals
--R
--R
--RExamples of * from InnerNormalBasisFieldFunctions
--R
--R
--RExamples of * from InputForm
--R
--R
--RExamples of * from InnerTaylorSeries
--R
--R
--RExamples of * from LeftModule
--R
--R
--RExamples of * from Magma
--R
--R
--RExamples of * from MappingPackage3
--R
--R
--RExamples of * from MappingPackage4
--R
--Rf:=(x:INT):INT +-> 3*x
--Rg:=(x:INT):INT +-> 2*x+3
--R(f*g)(4)
--R
--R

--RExamples of * from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rr:=transpose([1,2,3,4,5])@Matrix(INT)
--Rr*m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rc:=coerce([1,2,3,4,5])@Matrix(INT)
--Rm*c
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--R3*m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rm*1/3
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--R1/3*m
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rm*m
--R
--R
--RExamples of * from Monad
--R
--R
--RExamples of * from MyExpression
--R
--R
--RExamples of * from OrderedFreeMonoid
--R
--Rm1:=(y**3)$OFMONOID(Symbol)
--Rm1*x
--R
--Rm1:=(x*y*y*z)$OFMONOID(Symbol)
--Rx*m1
--R
--R
--RExamples of * from OutputForm
--R
--R
--RExamples of * from Pattern
--R
--R
--RExamples of * from PlacesCategory
--R
--R
--RExamples of * from PseudoRemainderSequence
--R
--R

--RExamples of * from RightModule
--R
--R
--RExamples of * from SemiGroup
--R
--R
--RExamples of * from SquareMatrixCategory
--R
--R
--RExamples of * from SparseMultivariateTaylorSeries
--R
--R
--RExamples of * from StreamTaylorSeriesOperations
--R
--R
--RExamples of * from TubePlotTools
--R
--R
--RExamples of * from VectorCategory
--R
--R
--RExamples of * from XFreeAlgebra
--R
--R
--RExamples of * from XPolynomialRing
--R
--E 86
--S 87 of 127
)d op numberOfComponents
--R
--R
--RThere are 2 exposed functions called numberOfComponents :
--R   [1]  -> NonNegativeInteger from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R   [2] D -> NonNegativeInteger from D if D has SPACEC(D2) and D2 has
--R            RING
--R
--RThere is one unexposed function called numberOfComponents :
--R   [1]  -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5)
--R            if D3 has UFD and D4 has UPOLYC(D3) and D5 has UPOLYC(FRAC(
--R            D4)) and D2 has FFCAT(D3,D4,D5)
--R
--RExamples of numberOfComponents from FunctionFieldCategory&
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RnumberOfComponents()$R

--R
--R
--RExamples of numberOfComponents from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RnumberOfComponents()$R
--R
--R
--RExamples of numberOfComponents from ThreeSpaceCategory
--R
--E 87
--S 88 of 127
)d op tree
--R
--R
--RThere are 6 exposed functions called tree :
--R   [1] List(D2) -> D from D if D2 has SETCAT and D has DSTRCAT(D2)
--R   [2] D1 -> D from D if D has DSTRCAT(D1) and D1 has SETCAT
--R   [3] (D1,List(D)) -> D from D if D has DSTRCAT(D1) and D1 has SETCAT
--R
--R   [4] D1 -> Tree(D1) from Tree(D1) if D1 has SETCAT
--R   [5] List(D2) -> Tree(D2) from Tree(D2) if D2 has SETCAT
--R   [6] (D1,List(Tree(D1))) -> Tree(D1) from Tree(D1) if D1 has SETCAT
--R
--R
--RExamples of tree from DesingTreeCategory
--R
--R
--RExamples of tree from Tree
--R
--Rtree 6
--R
--Rtree [1,2,3,4]
--R
--Rt1:=tree [1,2,3,4]
--Rtree(5,[t1])
--R
--E 88
--S 89 of 127
)d op Aleph
--R
--R
--RThere is one exposed function called Aleph :
--R   [1] NonNegativeInteger -> CardinalNumber from CardinalNumber
--R
--RExamples of Aleph from CardinalNumber

--R
--RA0:=Aleph 0
--R
--E 89
--S 90 of 127
)d op unit
--R
--R
--RThere are 3 exposed functions called unit :
--R   [1] List(Float) -> DrawOption from DrawOption
--R   [2]  -> Union(D,"failed") from D
--R            if D has FINAALG(D1) and D1 has INTDOM and D1 has COMRING
--R
--R   [3] Factored(D1) -> D1 from Factored(D1) if D1 has INTDOM
--R
--RExamples of unit from DrawOption
--R
--R
--RExamples of unit from FiniteRankNonAssociativeAlgebra
--R
--R
--RExamples of unit from Factored
--R
--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4
--Runit f
--Rg:=makeFR(z,factorList f)
--Runit g
--R
--E 90
--S 91 of 127
)d op frst
--R
--R
--RThere is one exposed function called frst :
--R   [1] D -> D1 from D if D has LZSTAGG(D1) and D1 has TYPE
--R
--RExamples of frst from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--Rfrst m
--R
--E 91
--S 92 of 127
)d op product
--R
--R
--RThere are 4 exposed functions called product :

--R   [1] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) ->
--R            CartesianTensor(D1,D2,D3)
--R            from CartesianTensor(D1,D2,D3)
--R            if D1: INT and D2: NNI and D3 has COMRING
--R   [2] (D,SegmentBinding(D)) -> D from D if D has COMBOPC
--R   [3] (D,Symbol) -> D from D if D has COMBOPC
--R   [4] (D,D) -> D from D
--R            if D has GRALG(D1,D2) and D1 has COMRING and D2 has ABELMON
--R
--R
--RThere are 3 unexposed functions called product :
--R   [1] (D1,Symbol) -> D1 from CombinatorialFunction(D3,D1)
--R            if D3 has Join(OrderedSet,IntegralDomain) and D1 has FS(D3)
--R
--R   [2] (D1,SegmentBinding(D1)) -> D1 from CombinatorialFunction(D3,D1)
--R            if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain)
--R
--R   [3] (XPBWPolynomial(D2,D3),XPBWPolynomial(D2,D3),NonNegativeInteger)
--R             -> XPBWPolynomial(D2,D3)
--R            from XPBWPolynomial(D2,D3) if D2 has ORDSET and D3 has
--R            COMRING
--R
--RExamples of product from CartesianTensor
--R
--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]]
--RTm:CartesianTensor(1,2,Integer):=m
--Rn:SquareMatrix(2,Integer):=matrix [[2,3],[0,1]]
--RTn:CartesianTensor(1,2,Integer):=n
--RTmn:=product(Tm,Tn)
--R
--R
--RExamples of product from CombinatorialFunction
--R
--R
--RExamples of product from CombinatorialOpsCategory
--R
--R
--RExamples of product from GradedAlgebra
--R
--R
--RExamples of product from XPBWPolynomial
--R
--E 92
--S 93 of 127
)d op fill!
--R
--R
--RThere are 2 exposed functions called fill! :
--R   [1] (D,D1) -> D from D

--R            if D has ARR2CAT(D1,D2,D3) and D1 has TYPE and D2 has FLAGG
--R            (D1) and D3 has FLAGG(D1)
--R   [2] (D,D1) -> D from D
--R            if D has shallowlyMutable and D has IXAGG(D2,D1) and D2 has
--R            SETCAT and D1 has TYPE
--R
--RExamples of fill! from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0)
--Rfill!(arr,10)
--R
--R
--RExamples of fill! from IndexedAggregate
--R
--E 93
--S 94 of 127
)d op upperCase?
--R
--R
--RThere is one exposed function called upperCase? :
--R   [1] Character -> Boolean from Character
--R
--RExamples of upperCase? from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[upperCase? c for c in chars]
--R
--E 94
--S 95 of 127
)d op integralMatrixAtInfinity
--R
--R
--RThere is one exposed function called integralMatrixAtInfinity :
--R   [1]  -> Matrix(Fraction(D3)) from D
--R            if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC(
--R            D2) and D4 has UPOLYC(FRAC(D3))
--R
--RExamples of integralMatrixAtInfinity from FunctionFieldCategory
--R
--RP0 := UnivariatePolynomial(x, Integer)
--RP1 := UnivariatePolynomial(y, Fraction P0)
--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20)
--RintegralMatrixAtInfinity()$R
--R
--E 95
--S 96 of 127
)d op finite?

--R
--R
--RThere are 3 exposed functions called finite? :
--R   [1] CardinalNumber -> Boolean from CardinalNumber
--R   [2] OnePointCompletion(D2) -> Boolean from OnePointCompletion(D2)
--R            if D2 has SETCAT
--R   [3] OrderedCompletion(D2) -> Boolean from OrderedCompletion(D2)
--R            if D2 has SETCAT
--R
--RExamples of finite? from CardinalNumber
--R
--Rc2:=2::CardinalNumber
--Rfinite? c2
--RA0:=Aleph 0
--Rfinite? A0
--R
--R
--RExamples of finite? from OnePointCompletion
--R
--R
--RExamples of finite? from OrderedCompletion
--R
--E 96
--S 97 of 127
)d op rank
--R
--R
--RThere are 8 exposed functions called rank :
--R   [1] CartesianTensor(D2,D3,D4) -> NonNegativeInteger
--R            from CartesianTensor(D2,D3,D4)
--R            if D2: INT and D3: NNI and D4 has COMRING
--R   [2]  -> PositiveInteger from D if D has FINAALG(D2) and D2 has
--R            COMRING
--R   [3]  -> PositiveInteger from D
--R            if D has FINRALG(D2,D3) and D2 has COMRING and D3 has
--R            UPOLYC(D2)
--R   [4] (Matrix(D4),Vector(D4)) -> NonNegativeInteger
--R            from LinearSystemMatrixPackage1(D4) if D4 has FIELD
--R   [5] (D2,D3) -> NonNegativeInteger
--R            from LinearSystemMatrixPackage(D4,D5,D3,D2)
--R            if D4 has FIELD and D5 has FiniteLinearAggregate(D4) with
--R                 shallowlyMutableand D3 has FiniteLinearAggregate(D4)
--R            with
--R                 shallowlyMutableand D2 has MATCAT(D4,D5,D3)
--R   [6] D -> NonNegativeInteger from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG(
--R            D2) and D4 has FLAGG(D2) and D2 has INTDOM
--R   [7] D2 -> NonNegativeInteger from MatrixLinearAlgebraFunctions(D3,D4
--R            ,D5,D2)

--R            if D3 has INTDOM and D3 has COMRING and D4 has FLAGG(D3)
--R            and D5 has FLAGG(D3) and D2 has MATCAT(D3,D4,D5)
--R   [8] D -> NonNegativeInteger from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) and D4 has INTDOM
--R
--R
--RThere are 2 unexposed functions called rank :
--R   [1]  -> PositiveInteger from ComplexCategory&(D2,D3)
--R            if D3 has COMRING and D2 has COMPCAT(D3)
--R   [2] D2 -> NonNegativeInteger
--R            from InnerMatrixLinearAlgebraFunctions(D3,D4,D5,D2)
--R            if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3)
--R            and D2 has MATCAT(D3,D4,D5)
--R
--RExamples of rank from CartesianTensor
--R
--RCT:=CARTEN(1,2,Integer)
--Rt0:CT:=8
--Rrank t0
--R
--R
--RExamples of rank from ComplexCategory&
--R
--R
--RExamples of rank from FiniteRankNonAssociativeAlgebra
--R
--R
--RExamples of rank from FiniteRankAlgebra
--R
--R
--RExamples of rank from InnerMatrixLinearAlgebraFunctions
--R
--R
--RExamples of rank from LinearSystemMatrixPackage1
--R
--R
--RExamples of rank from LinearSystemMatrixPackage
--R
--R
--RExamples of rank from MatrixCategory
--R
--Rrank matrix [[1,2,3],[4,5,6],[7,8,9]]
--R
--R
--RExamples of rank from MatrixLinearAlgebraFunctions
--R
--R
--RExamples of rank from RectangularMatrixCategory
--R

--E 97
--S 98 of 127
)d op numberOfComputedEntries
--R
--R
--RThere is one exposed function called numberOfComputedEntries :
--R   [1] D -> NonNegativeInteger from D if D has LZSTAGG(D2) and D2 has
--R            TYPE
--R
--RExamples of numberOfComputedEntries from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--RnumberOfComputedEntries m
--R
--E 98
--S 99 of 127
)d op groebnerFactorize
--R
--R
--RThere are 4 exposed functions called groebnerFactorize :
--R   [1] (List(D6),List(D6)) -> List(List(D6))
--R            from GroebnerFactorizationPackage(D3,D4,D5,D6)
--R            if D3 has Join(EuclideanDomain,CharacteristicZero) and D4
--R            has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5)
--R
--R   [2] (List(D7),List(D7),Boolean) -> List(List(D7))
--R            from GroebnerFactorizationPackage(D4,D5,D6,D7)
--R            if D4 has Join(EuclideanDomain,CharacteristicZero) and D5
--R            has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6)
--R
--R   [3] List(D6) -> List(List(D6))
--R            from GroebnerFactorizationPackage(D3,D4,D5,D6)
--R            if D3 has Join(EuclideanDomain,CharacteristicZero) and D4
--R            has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5)
--R
--R   [4] (List(D7),Boolean) -> List(List(D7))
--R            from GroebnerFactorizationPackage(D4,D5,D6,D7)
--R            if D4 has Join(EuclideanDomain,CharacteristicZero) and D5
--R            has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6)
--R
--R
--RExamples of groebnerFactorize from GroebnerFactorizationPackage
--R
--Imfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := ++X [ [0,1,1,1,1,1], ...
--Req := determinant mfzn
--RgroebnerFactorize ++X [eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])]
--R
--E 99

--S 100 of 127
)d op lowerCase
--R
--R
--RThere are 3 exposed functions called lowerCase :
--R   [1]  -> CharacterClass from CharacterClass
--R   [2] Character -> Character from Character
--R   [3] D -> D from D if D has SRAGG
--R
--RExamples of lowerCase from CharacterClass
--R
--R
--RExamples of lowerCase from Character
--R
--Rchars := [char "a", char "A", char "X", char "8", char "+"]
--R[lowerCase c for c in chars]
--R
--R
--RExamples of lowerCase from StringAggregate
--R
--E 100
--S 101 of 127
)d op showAllElements
--R
--R
--RThere is one exposed function called showAllElements :
--R   [1] Stream(D2) -> OutputForm from Stream(D2)
--R            if D2 has SETCAT and D2 has TYPE
--R
--RExamples of showAllElements from Stream
--R
--Rm:=[1,2,3,4,5,6,7,8,9,10,11,12]
--Rn:=m::Stream(PositiveInteger)
--RshowAllElements n
--R
--E 101
--S 102 of 127
)d op maxColIndex
--R
--R
--RThere are 2 exposed functions called maxColIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)

--R
--RExamples of maxColIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--RmaxColIndex(arr)
--R
--R
--RExamples of maxColIndex from RectangularMatrixCategory
--R
--E 102
--S 103 of 127
)d op minRowIndex
--R
--R
--RThere are 2 exposed functions called minRowIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of minRowIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--RminRowIndex(arr)
--R
--R
--RExamples of minRowIndex from RectangularMatrixCategory
--R
--E 103
--S 104 of 127
)d op space
--R
--R
--RThere are 2 exposed functions called space :
--R   [1]  -> Character from Character
--R   [2] ThreeSpace(DoubleFloat) -> DrawOption from DrawOption
--R
--RThere is one unexposed function called space :
--R   [1] List(DrawOption) -> ThreeSpace(DoubleFloat) from
--R            DrawOptionFunctions0
--R
--RExamples of space from Character
--R
--Rspace()
--R
--R

--RExamples of space from DrawOptionFunctions0
--R
--R
--RExamples of space from DrawOption
--R
--E 104
--S 105 of 127
)d op remove
--R
--R
--RThere are 5 exposed functions called remove :
--R   [1] (D1,D) -> D from D
--R            if D has finiteAggregate and D has CLAGG(D1) and D1 has
--R            TYPE and D1 has SETCAT
--R   [2] ((D2 -> Boolean),D) -> D from D
--R            if D has finiteAggregate and D has CLAGG(D2) and D2 has
--R            TYPE
--R   [3] ((D2 -> Boolean),D) -> D from D if D has LZSTAGG(D2) and D2 has
--R            TYPE
--R   [4] ((D3 -> Boolean),Multiset(D3),Integer) -> Multiset(D3)
--R            from Multiset(D3) if D3 has SETCAT
--R   [5] (D1,Multiset(D1),Integer) -> Multiset(D1) from Multiset(D1)
--R            if D1 has SETCAT
--R
--RThere is one unexposed function called remove :
--R   [1] (SplittingNode(D2,D3),SplittingTree(D2,D3)) -> SplittingTree(D2,
--R            D3)
--R            from SplittingTree(D2,D3)
--R            if D2 has Join(SetCategory,Aggregate) and D3 has Join(
--R            SetCategory,Aggregate)
--R
--RExamples of remove from Collection
--R
--R
--RExamples of remove from LazyStreamAggregate
--R
--Rm:=[i for i in 1..]
--Rf(i:PositiveInteger):Boolean == even? i
--Rremove(f,m)
--R
--R
--RExamples of remove from Multiset
--R
--R
--RExamples of remove from SplittingTree
--R
--E 105
--S 106 of 127

)d op factors
--R
--R
--RThere is one exposed function called factors :
--R   [1] Factored(D2) -> List(Record(factor: D2,exponent: Integer))
--R            from Factored(D2) if D2 has INTDOM
--R
--RThere are 3 unexposed functions called factors :
--R   [1] FreeGroup(D2) -> List(Record(gen: D2,exp: Integer)) from
--R            FreeGroup(D2)
--R            if D2 has SETCAT
--R   [2] FreeMonoid(D2) -> List(Record(gen: D2,exp: NonNegativeInteger))
--R            from FreeMonoid(D2) if D2 has SETCAT
--R   [3] OrderedFreeMonoid(D2) -> List(Record(gen: D2,exp:
--R            NonNegativeInteger))
--R            from OrderedFreeMonoid(D2) if D2 has ORDSET
--R
--RExamples of factors from FreeGroup
--R
--R
--RExamples of factors from FreeMonoid
--R
--R
--RExamples of factors from Factored
--R
--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4
--Rfactors f
--Rg:=makeFR(z,factorList f)
--Rfactors g
--R
--R
--RExamples of factors from OrderedFreeMonoid
--R
--Rm1:=(x*y*y*z)$OFMONOID(Symbol)
--Rfactors m1
--R
--E 106
--S 107 of 127
)d op output
--R
--R
--RThere are 4 exposed functions called output :
--R   [1] String -> Void from OutputPackage
--R   [2] OutputForm -> Void from OutputPackage
--R   [3] (String,OutputForm) -> Void from OutputPackage
--R   [4] (Integer,Stream(D3)) -> Void from Stream(D3)
--R            if D3 has SETCAT and D3 has TYPE
--R
--RExamples of output from OutputPackage

--R
--R
--RExamples of output from Stream
--R
--Rm:=[1,2,3]
--Rn:=repeating(m)
--Routput(5,n)
--R
--E 107
--S 108 of 127
)d op binarySearchTree
--R
--R
--RThere is one exposed function called binarySearchTree :
--R   [1] List(D2) -> BinarySearchTree(D2) from BinarySearchTree(D2)
--R            if D2 has ORDSET
--R
--RExamples of binarySearchTree from BinarySearchTree
--R
--RbinarySearchTree [1,2,3,4]
--R
--E 108
--S 109 of 127
)d op char
--R
--R
--RThere are 2 exposed functions called char :
--R   [1] String -> Character from Character
--R   [2] Integer -> Character from Character
--R
--RExamples of char from Character
--R
--R[char c for c in ["a","A","X","8","+"]]
--R
--R[char c for c in [97,65,88,56,43]]
--R
--E 109
--S 110 of 127
)d op shrinkable
--R
--R
--RThere is one exposed function called shrinkable :
--R   [1] Boolean -> Boolean from FlexibleArray(D2) if D2 has TYPE
--R
--RThere is one unexposed function called shrinkable :
--R   [1] Boolean -> Boolean from IndexedFlexibleArray(D2,D3)
--R            if D2 has TYPE and D3: INT

--R
--RExamples of shrinkable from FlexibleArray
--R
--R
--RExamples of shrinkable from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20)
--Rshrinkable(false)$T1
--R
--E 110
--S 111 of 127
)d op rst
--R
--R
--RThere is one exposed function called rst :
--R   [1] D -> D from D if D has LZSTAGG(D1) and D1 has TYPE
--R
--RExamples of rst from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--Rrst m
--R
--E 111
--S 112 of 127
)d op flexibleArray
--R
--R
--RThere is one exposed function called flexibleArray :
--R   [1] List(D2) -> FlexibleArray(D2) from FlexibleArray(D2) if D2 has
--R            TYPE
--R
--RThere is one unexposed function called flexibleArray :
--R   [1] List(D2) -> IndexedFlexibleArray(D2,D3)
--R            from IndexedFlexibleArray(D2,D3) if D2 has TYPE and D3: INT
--R
--R
--RExamples of flexibleArray from FlexibleArray
--R
--R
--RExamples of flexibleArray from IndexedFlexibleArray
--R
--RT1:=IndexedFlexibleArray(Integer,20)
--RflexibleArray([i for i in 1..10])$T1
--R
--E 112
--S 113 of 127
)d op setelt

--R
--R
--RThere are 14 exposed functions called setelt :
--R   [1] (D,Integer,D1) -> D1 from D if D has AFSPCAT(D1) and D1 has
--R            FIELD
--R   [2] (D,Integer,Integer,D1) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
--R            (D1) and D4 has FLAGG(D1)
--R   [3] (D,right,D) -> D from D
--R            if D has shallowlyMutable and D has BRAGG(D2) and D2 has
--R            TYPE
--R   [4] (D,left,D) -> D from D
--R            if D has shallowlyMutable and D has BRAGG(D2) and D2 has
--R            TYPE
--R   [5] (D,D2,D1) -> D1 from D
--R            if D has shallowlyMutable and D has ELTAGG(D2,D1) and D2
--R            has SETCAT and D1 has TYPE
--R   [6] (Library,Symbol,Any) -> Any from Library
--R   [7] (D,UniversalSegment(Integer),D1) -> D1 from D
--R            if D has shallowlyMutable and D has LNAGG(D1) and D1 has
--R            TYPE
--R   [8] (D,List(Integer),List(Integer),D) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG(
--R            D2) and D4 has FLAGG(D2)
--R   [9] (D,Integer,D1) -> D1 from D if D has PRSPCAT(D1) and D1 has
--R            FIELD
--R   [10] (D,value,D1) -> D1 from D
--R            if D has shallowlyMutable and D has RCAGG(D1) and D1 has
--R            TYPE
--R   [11] (D,D2,D1) -> D1 from D
--R            if D has TBAGG(D2,D1) and D2 has SETCAT and D1 has SETCAT
--R
--R   [12] (D,last,D1) -> D1 from D
--R            if D has shallowlyMutable and D has URAGG(D1) and D1 has
--R            TYPE
--R   [13] (D,rest,D) -> D from D
--R            if D has shallowlyMutable and D has URAGG(D2) and D2 has
--R            TYPE
--R   [14] (D,first,D1) -> D1 from D
--R            if D has shallowlyMutable and D has URAGG(D1) and D1 has
--R            TYPE
--R
--RThere is one unexposed function called setelt :
--R   [1] (Reference(D1),D1) -> D1 from Reference(D1) if D1 has TYPE
--R
--RExamples of setelt from AffineSpaceCategory
--R
--R
--RExamples of setelt from TwoDimensionalArrayCategory
--R

--Rarr : ARRAY2 INT := new(5,4,0)
--Rsetelt(arr,1,1,17)
--R
--R
--RExamples of setelt from BinaryRecursiveAggregate
--R
--R
--RExamples of setelt from EltableAggregate
--R
--R
--RExamples of setelt from Library
--R
--R
--RExamples of setelt from LinearAggregate
--R
--R
--RExamples of setelt from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Rsetelt(m,3,3,10)
--R
--R
--RExamples of setelt from ProjectiveSpaceCategory
--R
--R
--RExamples of setelt from RecursiveAggregate
--R
--R
--RExamples of setelt from Reference
--R
--R
--RExamples of setelt from TableAggregate
--R
--R
--RExamples of setelt from UnaryRecursiveAggregate
--R
--E 113
--S 114 of 127
)d op cyclicParents
--R
--R
--RThere is one exposed function called cyclicParents :
--R   [1] Tree(D2) -> List(Tree(D2)) from Tree(D2) if D2 has SETCAT
--R
--RExamples of cyclicParents from Tree
--R
--Rt1:=tree [1,2,3,4]
--RcyclicParents t1
--R

--E 114
--S 115 of 127
)d op explicitEntries?
--R
--R
--RThere is one exposed function called explicitEntries? :
--R   [1] D -> Boolean from D if D has LZSTAGG(D2) and D2 has TYPE
--R
--RExamples of explicitEntries? from LazyStreamAggregate
--R
--Rm:=[i for i in 0..]
--RexplicitEntries? m
--R
--E 115
--S 116 of 127
)d op column
--R
--R
--RThere are 2 exposed functions called column :
--R   [1] (D,Integer) -> D1 from D
--R            if D has ARR2CAT(D3,D4,D1) and D3 has TYPE and D4 has FLAGG
--R            (D3) and D1 has FLAGG(D3)
--R   [2] (D,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D5,D6,D1) and D5 has RING and D6 has
--R            DIRPCAT(D4,D5) and D1 has DIRPCAT(D3,D5)
--R
--RExamples of column from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rcolumn(arr,1)
--R
--R
--RExamples of column from RectangularMatrixCategory
--R
--E 116
--S 117 of 127
)d op reduce
--R
--R
--RThere are 21 exposed functions called reduce :
--R   [1] AlgebraicNumber -> AlgebraicNumber from AlgebraicNumber
--R   [2] (((D4,D1) -> D1),OneDimensionalArray(D4),D1) -> D1
--R            from OneDimensionalArrayFunctions2(D4,D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [3] (((D1,D1) -> D1),D,D1,D1) -> D1 from D
--R            if D1 has SETCAT and D has finiteAggregate and D has CLAGG(
--R            D1) and D1 has TYPE

--R   [4] (((D1,D1) -> D1),D,D1) -> D1 from D
--R            if D has finiteAggregate and D has CLAGG(D1) and D1 has
--R            TYPE
--R   [5] (((D1,D1) -> D1),D) -> D1 from D
--R            if D has finiteAggregate and D has CLAGG(D1) and D1 has
--R            TYPE
--R   [6] (((D5,D1) -> D1),DirectProduct(D4,D5),D1) -> D1
--R            from DirectProductFunctions2(D4,D5,D1)
--R            if D4: NNI and D5 has TYPE and D1 has TYPE
--R   [7] Expression(D1) -> Expression(D1) from Expression(D1)
--R            if D1 has INTDOM and D1 has ORDSET
--R   [8] D -> D from D
--R            if D has FDIVCAT(D1,D2,D3,D4) and D1 has FIELD and D2 has
--R            UPOLYC(D1) and D3 has UPOLYC(FRAC(D2)) and D4 has FFCAT(D1,
--R            D2,D3)
--R   [9] (((D4,D1) -> D1),D3,D1) -> D1
--R            from FiniteLinearAggregateFunctions2(D4,D3,D1,D5)
--R            if D4 has TYPE and D1 has TYPE and D3 has FLAGG(D4) and D5
--R            has FLAGG(D1)
--R   [10] (((D4,D1) -> D1),D3,D1) -> D1
--R            from FiniteSetAggregateFunctions2(D4,D3,D1,D5)
--R            if D4 has SETCAT and D1 has SETCAT and D3 has FSAGG(D4) and
--R            D5 has FSAGG(D1)
--R   [11] (((D4,D1) -> D1),List(D4),D1) -> D1 from ListFunctions2(D4,D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [12] (((D5,D2) -> D2),D4,D2) -> D2
--R            from MatrixCategoryFunctions2(D5,D6,D7,D4,D2,D8,D9,D1)
--R            if D5 has RING and D2 has RING and D6 has FLAGG(D5) and D7
--R            has FLAGG(D5) and D8 has FLAGG(D2) and D9 has FLAGG(D2) and
--R            D4 has MATCAT(D5,D6,D7) and D1 has MATCAT(D2,D8,D9)
--R   [13] Fraction(D3) -> Union(D,"failed") from D
--R            if D3 has UPOLYC(D2) and D2 has FIELD and D2 has COMRING
--R            and D has MONOGEN(D2,D3)
--R   [14] D1 -> D from D
--R            if D2 has COMRING and D has MONOGEN(D2,D1) and D1 has
--R            UPOLYC(D2)
--R   [15] SparseUnivariatePolynomial(D) -> D from D if D has PACPERC
--R   [16] List(D) -> Divisor(D) from D
--R            if D has PLACESC(D3,D4) and D3 has FIELD and D4 has LOCPOWC
--R            (D3)
--R   [17] (((D4,D1) -> D1),PrimitiveArray(D4),D1) -> D1
--R            from PrimitiveArrayFunctions2(D4,D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [18] (((D9,D4) -> D4),D6,D4) -> D4
--R            from RectangularMatrixCategoryFunctions2(D7,D8,D9,D10,D11,
--R            D6,D4,D1,D2,D3)
--R            if D9 has RING and D4 has RING and D7: NNI and D8: NNI and
--R            D10 has DIRPCAT(D8,D9) and D11 has DIRPCAT(D7,D9) and D1
--R            has DIRPCAT(D8,D4) and D2 has DIRPCAT(D7,D4) and D6 has
--R            RMATCAT(D7,D8,D9,D10,D11) and D3 has RMATCAT(D7,D8,D4,D1,D2

--R            )
--R   [19] (D1,((D4,D1) -> D1),Stream(D4)) -> D1 from StreamFunctions2(D4,
--R            D1)
--R            if D4 has TYPE and D1 has TYPE
--R   [20] (D1,D,((D1,D1) -> D1),((D1,D1) -> Boolean)) -> D1 from D
--R            if D has TSETCAT(D4,D5,D6,D1) and D4 has INTDOM and D5 has
--R            OAMONS and D6 has ORDSET and D1 has RPOLCAT(D4,D5,D6)
--R   [21] (((D4,D1) -> D1),Vector(D4),D1) -> D1 from VectorFunctions2(D4,
--R            D1)
--R            if D4 has TYPE and D1 has TYPE
--R
--RThere are 7 unexposed functions called reduce :
--R   [1] SparseUnivariatePolynomial(D3) -> Record(pol:
--R            SparseUnivariatePolynomial(D3),deg: PositiveInteger)
--R            from DegreeReductionPackage(D3,D4)
--R            if D3 has RING and D4 has Join(IntegralDomain,OrderedSet)
--R
--R   [2] (D1,D2) -> EuclideanModularRing(D3,D1,D2,D4,D5,D6)
--R            from EuclideanModularRing(D3,D1,D2,D4,D5,D6)
--R            if D3 has COMRING and D1 has UPOLYC(D3) and D2 has ABELMON
--R            and D4: ((D1,D2) -> D1) and D5: ((D2,D2) -> Union(D2,
--R            "failed")) and D6: ((D1,D1,D2) -> Union(D1,"failed"))
--R   [3] InnerAlgebraicNumber -> InnerAlgebraicNumber from
--R            InnerAlgebraicNumber
--R   [4] (D1,D2) -> ModularField(D1,D2,D3,D4,D5)
--R            from ModularField(D1,D2,D3,D4,D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [5] D1 -> ModMonic(D2,D1) from ModMonic(D2,D1)
--R            if D2 has RING and D1 has UPOLYC(D2)
--R   [6] (D1,D2) -> ModularRing(D1,D2,D3,D4,D5) from ModularRing(D1,D2,D3
--R            ,D4,D5)
--R            if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> D1
--R            ) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1,
--R            D2) -> Union(D1,"failed"))
--R   [7] D1 -> ResidueRing(D2,D3,D4,D1,D5) from ResidueRing(D2,D3,D4,D1,
--R            D5)
--R            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D1
--R            has POLYCAT(D2,D3,D4) and D5: LIST(D1)
--R
--RExamples of reduce from AlgebraicNumber
--R
--R
--RExamples of reduce from OneDimensionalArrayFunctions2
--R
--RT1:=OneDimensionalArrayFunctions2(Integer,Integer)
--Radder(a:Integer,b:Integer):Integer == a+b
--Rreduce(adder,[i for i in 1..10],0)$T1
--R

--R
--RExamples of reduce from Collection
--R
--Rreduce(+,[C[i]*x**i for i in 1..5])
--R
--R
--RExamples of reduce from DegreeReductionPackage
--R
--R
--RExamples of reduce from DirectProductFunctions2
--R
--R
--RExamples of reduce from EuclideanModularRing
--R
--R
--RExamples of reduce from Expression
--R
--R
--RExamples of reduce from FiniteDivisorCategory
--R
--R
--RExamples of reduce from FiniteLinearAggregateFunctions2
--R
--R
--RExamples of reduce from FiniteSetAggregateFunctions2
--R
--R
--RExamples of reduce from InnerAlgebraicNumber
--R
--R
--RExamples of reduce from ListFunctions2
--R
--R
--RExamples of reduce from MatrixCategoryFunctions2
--R
--R
--RExamples of reduce from ModularField
--R
--R
--RExamples of reduce from ModMonic
--R
--R
--RExamples of reduce from ModularRing
--R
--R
--RExamples of reduce from MonogenicAlgebra
--R
--R
--RExamples of reduce from PseudoAlgebraicClosureOfPerfectFieldCategory
--R

--R
--RExamples of reduce from PlacesCategory
--R
--R
--RExamples of reduce from PrimitiveArrayFunctions2
--R
--RT1:=PrimitiveArrayFunctions2(Integer,Integer)
--Radder(a:Integer,b:Integer):Integer == a+b
--Rreduce(adder,[i for i in 1..10],0)$T1
--R
--R
--RExamples of reduce from ResidueRing
--R
--R
--RExamples of reduce from RectangularMatrixCategoryFunctions2
--R
--R
--RExamples of reduce from StreamFunctions2
--R
--Rm:=[i for i in 1..300]::Stream(Integer)
--Rf(i:Integer,j:Integer):Integer==i+j
--Rreduce(1,f,m)
--R
--R
--RExamples of reduce from TriangularSetCategory
--R
--R
--RExamples of reduce from VectorFunctions2
--R
--E 117
--S 118 of 127
)d op new
--R
--R
--RThere are 7 exposed functions called new :
--R   [1] (NonNegativeInteger,NonNegativeInteger,D2) -> D from D
--R            if D2 has TYPE and D has ARR2CAT(D2,D3,D4) and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] (String,String,String) -> D from D if D has FNCAT
--R   [3]  -> ScriptFormulaFormat from ScriptFormulaFormat
--R   [4] (NonNegativeInteger,D2) -> D from D if D has LNAGG(D2) and D2
--R            has TYPE
--R   [5] Symbol -> Symbol from Symbol
--R   [6]  -> Symbol from Symbol
--R   [7]  -> TexFormat from TexFormat
--R
--RThere are 4 unexposed functions called new :
--R   [1]  -> SubSpaceComponentProperty from SubSpaceComponentProperty
--R   [2]  -> PatternMatchListResult(D1,D2,D3)

--R            from PatternMatchListResult(D1,D2,D3)
--R            if D2 has SETCAT and D1 has SETCAT and D3 has LSAGG(D2)
--R   [3]  -> PatternMatchResult(D1,D2) from PatternMatchResult(D1,D2)
--R            if D1 has SETCAT and D2 has SETCAT
--R   [4]  -> SubSpace(D1,D2) from SubSpace(D1,D2) if D1: PI and D2 has
--R            RING
--R
--RExamples of new from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,0)
--R
--R
--RExamples of new from SubSpaceComponentProperty
--R
--R
--RExamples of new from FileNameCategory
--R
--R
--RExamples of new from ScriptFormulaFormat
--R
--R
--RExamples of new from LinearAggregate
--R
--R
--RExamples of new from PatternMatchListResult
--R
--R
--RExamples of new from PatternMatchResult
--R
--R
--RExamples of new from SubSpace
--R
--R
--RExamples of new from Symbol
--R
--R
--RExamples of new from TexFormat
--R
--E 118
--S 119 of 127
)d op insertRoot!
--R
--R
--RThere is one exposed function called insertRoot! :
--R   [1] (D1,BinarySearchTree(D1)) -> BinarySearchTree(D1)
--R            from BinarySearchTree(D1) if D1 has ORDSET
--R
--RExamples of insertRoot! from BinarySearchTree
--R

--Rt1:=binarySearchTree [1,2,3,4]
--RinsertRoot!(5,t1)
--R
--E 119
--S 120 of 127
)d op maxRowIndex
--R
--R
--RThere are 2 exposed functions called maxRowIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of maxRowIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--RmaxRowIndex(arr)
--R
--R
--RExamples of maxRowIndex from RectangularMatrixCategory
--R
--E 120
--S 121 of 127
)d op escape
--R
--R
--RThere is one exposed function called escape :
--R   [1]  -> Character from Character
--R
--RExamples of escape from Character
--R
--Rescape()
--R
--E 121
--S 122 of 127
)d op nthExponent
--R
--R
--RThere is one exposed function called nthExponent :
--R   [1] (Factored(D2),Integer) -> Integer from Factored(D2) if D2 has
--R            INTDOM
--R
--RExamples of nthExponent from Factored
--R

--Ra:=factor 9720000
--RnthExponent(a,2)
--R
--E 122
--S 123 of 127
)d op parts
--R
--R
--RThere are 7 exposed functions called parts :
--R   [1] D -> List(D2) from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] ArrayStack(D2) -> List(D2) from ArrayStack(D2)
--R            if $ has finiteAggregate and D2 has SETCAT
--R   [3] Dequeue(D2) -> List(D2) from Dequeue(D2)
--R            if $ has finiteAggregate and D2 has SETCAT
--R   [4] Heap(D2) -> List(D2) from Heap(D2)
--R            if $ has finiteAggregate and D2 has ORDSET
--R   [5] D -> List(D2) from D
--R            if D has finiteAggregate and D has HOAGG(D2) and D2 has
--R            TYPE
--R   [6] Queue(D2) -> List(D2) from Queue(D2)
--R            if $ has finiteAggregate and D2 has SETCAT
--R   [7] Stack(D2) -> List(D2) from Stack(D2)
--R            if $ has finiteAggregate and D2 has SETCAT
--R
--RExamples of parts from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Rparts(arr)
--R
--R
--RExamples of parts from ArrayStack
--R
--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5]
--Rparts a
--R
--R
--RExamples of parts from Dequeue
--R
--Ra:Dequeue INT:= dequeue [1,2,3,4,5]
--Rparts a
--R
--R
--RExamples of parts from Heap
--R
--Ra:Heap INT:= heap [1,2,3,4,5]
--Rparts a
--R

--R
--RExamples of parts from HomogeneousAggregate
--R
--R
--RExamples of parts from Queue
--R
--Ra:Queue INT:= queue [1,2,3,4,5]
--Rparts a
--R
--R
--RExamples of parts from Stack
--R
--Ra:Stack INT:= stack [1,2,3,4,5]
--Rparts a
--R
--E 123
--S 124 of 127
)d op elt
--R
--R
--RThere are 50 exposed functions called elt :
--R   [1] (D,Integer) -> D1 from D if D has AFSPCAT(D1) and D1 has FIELD
--R
--R   [2] (D,Integer,Integer,D1) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has FLAGG
--R            (D1) and D4 has FLAGG(D1)
--R   [3] (D,Integer,Integer) -> D1 from D
--R            if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG(D1) and D4 has
--R            FLAGG(D1) and D1 has TYPE
--R   [4] (D,right) -> D from D if D has BRAGG(D2) and D2 has TYPE
--R   [5] (D,left) -> D from D if D has BRAGG(D2) and D2 has TYPE
--R   [6] (CartesianTensor(D3,D4,D1),List(Integer)) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [7] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer,Integer) ->
--R            D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [8] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [9] (CartesianTensor(D3,D4,D1),Integer,Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [10] (CartesianTensor(D3,D4,D1),Integer) -> D1
--R            from CartesianTensor(D3,D4,D1)
--R            if D1 has COMRING and D3: INT and D4: NNI
--R   [11] CartesianTensor(D2,D3,D1) -> D1 from CartesianTensor(D2,D3,D1)
--R            if D1 has COMRING and D2: INT and D3: NNI

--R   [12] (Database(D3),Symbol) -> DataList(String) from Database(D3)
--R            if D3 has OrderedSet with
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [13] (Database(D2),QueryEquation) -> Database(D2) from Database(D2)
--R            if D2 has OrderedSet with
--R               ?.? : (%,Symbol) -> String
--R               display : % -> Void
--R               fullDisplay : % -> Void
--R   [14] (DataList(D3),count) -> NonNegativeInteger from DataList(D3)
--R            if D3 has ORDSET
--R   [15] (DataList(D2),sort) -> DataList(D2) from DataList(D2) if D2 has
--R            ORDSET
--R   [16] (DataList(D2),unique) -> DataList(D2) from DataList(D2) if D2
--R            has ORDSET
--R   [17] (D,D2) -> D1 from D
--R            if D has ELTAB(D2,D1) and D2 has SETCAT and D1 has TYPE
--R   [18] (D,D2,D1) -> D1 from D
--R            if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE
--R
--R   [19] (BasicOperator,List(D)) -> D from D if D has ES
--R   [20] (BasicOperator,D,D,D,D) -> D from D if D has ES
--R   [21] (BasicOperator,D,D,D) -> D from D if D has ES
--R   [22] (BasicOperator,D,D) -> D from D if D has ES
--R   [23] (BasicOperator,D) -> D from D if D has ES
--R   [24] (D,D1,D1) -> D1 from D
--R            if D has FFCAT(D1,D2,D3) and D1 has UFD and D2 has UPOLYC(
--R            D1) and D3 has UPOLYC(FRAC(D2))
--R   [25] (D,Integer) -> D1 from D if D has FRNAALG(D1) and D1 has
--R            COMRING
--R   [26] (IndexCard,Symbol) -> String from IndexCard
--R   [27] (Library,Symbol) -> Any from Library
--R   [28] (D,UniversalSegment(Integer)) -> D from D
--R            if D has LNAGG(D2) and D2 has TYPE
--R   [29] (ThreeDimensionalMatrix(D1),NonNegativeInteger,
--R            NonNegativeInteger,NonNegativeInteger) -> D1
--R            from ThreeDimensionalMatrix(D1) if D1 has SETCAT
--R   [30] (D,List(Integer),List(Integer)) -> D from D
--R            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG(
--R            D2) and D4 has FLAGG(D2)
--R   [31] (D,D1) -> D1 from D if D has PERMCAT(D1) and D1 has SETCAT
--R   [32] (PermutationGroup(D3),NonNegativeInteger) -> Permutation(D3)
--R            from PermutationGroup(D3) if D3 has SETCAT
--R   [33] (D,Integer) -> D1 from D
--R            if D has PLACESC(D1,D3) and D3 has LOCPOWC(D1) and D1 has
--R            FIELD
--R   [34] (D,Integer) -> D1 from D if D has PRSPCAT(D1) and D1 has FIELD
--R
--R   [35] (QuadraticForm(D3,D1),DirectProduct(D3,D1)) -> D1

--R            from QuadraticForm(D3,D1) if D3: PI and D1 has FIELD
--R   [36] (D,value) -> D1 from D if D has RCAGG(D1) and D1 has TYPE
--R   [37] (D,Integer,Integer,D1) -> D1 from D
--R            if D has RMATCAT(D3,D4,D1,D5,D6) and D1 has RING and D5 has
--R            DIRPCAT(D4,D1) and D6 has DIRPCAT(D3,D1)
--R   [38] (D,Integer,Integer) -> D1 from D
--R            if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1)
--R            and D6 has DIRPCAT(D3,D1) and D1 has RING
--R   [39] (RewriteRule(D3,D4,D1),D1,PositiveInteger) -> D1
--R            from RewriteRule(D3,D4,D1)
--R            if D3 has SETCAT and D4 has Join(Ring,PatternMatchable(D3),
--R            OrderedSet,ConvertibleTo(Pattern(D3))) and D1 has Join(
--R            FunctionSpace(D4),PatternMatchable(D3),ConvertibleTo(
--R            Pattern(D3)))
--R   [40] (Ruleset(D3,D4,D1),D1,PositiveInteger) -> D1 from Ruleset(D3,D4
--R            ,D1)
--R            if D3 has SETCAT and D4 has Join(Ring,PatternMatchable(D3),
--R            OrderedSet,ConvertibleTo(Pattern(D3))) and D1 has Join(
--R            FunctionSpace(D4),PatternMatchable(D3),ConvertibleTo(
--R            Pattern(D3)))
--R   [41] (D,List(Integer)) -> D from D
--R            if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3
--R            has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has
--R            SETCAT
--R   [42] (D,Integer) -> D from D
--R            if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3
--R            has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has
--R            SETCAT
--R   [43] (D,D) -> D from D if D has SRAGG
--R   [44] (Symbol,List(OutputForm)) -> Symbol from Symbol
--R   [45] (Fraction(D),D1) -> D1 from D
--R            if D has UPOLYC(D1) and D1 has RING and D1 has FIELD
--R   [46] (Fraction(D),Fraction(D)) -> Fraction(D) from D
--R            if D has UPOLYC(D2) and D2 has RING and D2 has INTDOM
--R   [47] (D,D2) -> D1 from D
--R            if D has UPSCAT(D1,D2) and D2 has OAMON and D1 has RING
--R   [48] (D,last) -> D1 from D if D has URAGG(D1) and D1 has TYPE
--R   [49] (D,rest) -> D from D if D has URAGG(D2) and D2 has TYPE
--R   [50] (D,first) -> D1 from D if D has URAGG(D1) and D1 has TYPE
--R
--RThere are 4 unexposed functions called elt :
--R   [1] (EuclideanModularRing(D2,D1,D3,D4,D5,D6),D1) -> D1
--R            from EuclideanModularRing(D2,D1,D3,D4,D5,D6)
--R            if D2 has COMRING and D1 has UPOLYC(D2) and D3 has ABELMON
--R            and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3,
--R            "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed"))
--R   [2] (OutputForm,List(OutputForm)) -> OutputForm from OutputForm
--R   [3] (BasicOperator,List(Pattern(D3))) -> Pattern(D3) from Pattern(D3
--R            )
--R            if D3 has SETCAT

--R   [4] Reference(D1) -> D1 from Reference(D1) if D1 has TYPE
--R
--RExamples of elt from AffineSpaceCategory
--R
--R
--RExamples of elt from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Relt(arr,1,1,6)
--Relt(arr,1,10,6)
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--Relt(arr,1,1)
--R
--R
--RExamples of elt from BinaryRecursiveAggregate
--R
--R
--RExamples of elt from CartesianTensor
--R
--Rv:=[2,3]
--Rtv:CartesianTensor(1,2,Integer):=v
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm]
--Rtp:CartesianTensor(1,2,Integer):=[tn,tn]
--Rtq:CartesianTensor(1,2,Integer):=[tp,tp]
--Relt(tq,[2,2,2,2,2])
--R
--Rv:=[2,3]
--Rtv:CartesianTensor(1,2,Integer):=v
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm]
--Rtp:CartesianTensor(1,2,Integer):=[tn,tn]
--Relt(tp,2,2,2,2)
--Rtp[2,2,2,2]
--R
--Rv:=[2,3]
--Rtv:CartesianTensor(1,2,Integer):=v
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
--Rtn:CartesianTensor(1,2,Integer):=[tm,tm]
--Relt(tn,2,2,2)
--Rtn[2,2,2]
--R
--Rv:=[2,3]
--Rtv:CartesianTensor(1,2,Integer):=v
--Rtm:CartesianTensor(1,2,Integer):=[tv,tv]
--Relt(tm,2,2)
--Rtm[2,2]
--R
--Rv:=[2,3]

--Rtv:CartesianTensor(1,2,Integer):=v
--Relt(tv,2)
--Rtv[2]
--R
--Rtv:CartesianTensor(1,2,Integer):=8
--Relt(tv)
--Rtv[]
--R
--R
--RExamples of elt from Database
--R
--R
--RExamples of elt from DataList
--R
--R
--RExamples of elt from Eltable
--R
--R
--RExamples of elt from EltableAggregate
--R
--R
--RExamples of elt from EuclideanModularRing
--R
--R
--RExamples of elt from ExpressionSpace
--R
--R
--RExamples of elt from FunctionFieldCategory
--R
--R
--RExamples of elt from FramedNonAssociativeAlgebra
--R
--R
--RExamples of elt from IndexCard
--R
--R
--RExamples of elt from Library
--R
--R
--RExamples of elt from LinearAggregate
--R
--R
--RExamples of elt from ThreeDimensionalMatrix
--R
--R
--RExamples of elt from MatrixCategory
--R
--Rm:=matrix [[j**i for i in 0..4] for j in 1..5]
--Relt(m,3,3)
--R

--R
--RExamples of elt from OutputForm
--R
--R
--RExamples of elt from Pattern
--R
--R
--RExamples of elt from PermutationCategory
--R
--R
--RExamples of elt from PermutationGroup
--R
--R
--RExamples of elt from PlacesCategory
--R
--R
--RExamples of elt from ProjectiveSpaceCategory
--R
--R
--RExamples of elt from QuadraticForm
--R
--R
--RExamples of elt from RecursiveAggregate
--R
--R
--RExamples of elt from Reference
--R
--R
--RExamples of elt from RectangularMatrixCategory
--R
--R
--RExamples of elt from RewriteRule
--R
--R
--RExamples of elt from Ruleset
--R
--R
--RExamples of elt from SExpressionCategory
--R
--R
--RExamples of elt from StringAggregate
--R
--R
--RExamples of elt from Symbol
--R
--R
--RExamples of elt from UnivariatePolynomialCategory
--R
--R
--RExamples of elt from UnivariatePowerSeriesCategory

--R
--R
--RExamples of elt from UnaryRecursiveAggregate
--R
--E 124
--S 125 of 127
)d op minColIndex
--R
--R
--RThere are 2 exposed functions called minColIndex :
--R   [1] D -> Integer from D
--R            if D has ARR2CAT(D2,D3,D4) and D2 has TYPE and D3 has FLAGG
--R            (D2) and D4 has FLAGG(D2)
--R   [2] D -> Integer from D
--R            if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 has
--R            DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4)
--R
--RExamples of minColIndex from TwoDimensionalArrayCategory
--R
--Rarr : ARRAY2 INT := new(5,4,10)
--RminColIndex(arr)
--R
--R
--RExamples of minColIndex from RectangularMatrixCategory
--R
--E 125
--S 126 of 127
)d op numberOfFactors
--R
--R
--RThere is one exposed function called numberOfFactors :
--R   [1] Factored(D2) -> NonNegativeInteger from Factored(D2) if D2 has
--R            INTDOM
--R
--RThere is one unexposed function called numberOfFactors :
--R   [1] List(Record(factor: D3,degree: Integer)) -> NonNegativeInteger
--R            from GaloisGroupFactorizer(D3) if D3 has UPOLYC(INT)
--R
--RExamples of numberOfFactors from Factored
--R
--Ra:=factor 9720000
--RnumberOfFactors a
--R
--R
--RExamples of numberOfFactors from GaloisGroupFactorizer
--R
--E 126

--S 127 of 127
)d op cyclicCopy
--R
--R
--RThere is one exposed function called cyclicCopy :
--R   [1] Tree(D1) -> Tree(D1) from Tree(D1) if D1 has SETCAT
--R
--RExamples of cyclicCopy from Tree
--R
--Rt1:=tree [1,2,3,4]
--RcyclicCopy t1
--R
--E 127
)spool
)lisp (bye)

———-

References^{[1] nothing}

137