Re: Unexpected results w.r.t. exponential operation of LODO (with july2008 release)

Oh, it looks quite different, thanks for your answer. But this didn't answer
my question: does L^2 (or L**2)
should produce the same result as L*L in LODO ?

Best Regards,
Xiaojun


2008/8/28 root <[email protected]>

> Although I believe ^ and ** are intended to be the same operation
> clearly they are not. This will require some thought:
>
> (1)-> )d op ^
>
> There are 6 exposed functions called ^ :
>   [1] Boolean -> Boolean from Boolean
>   [2] D -> D from D if D has BTAGG
>   [3] (D,Integer) -> D from D if D has DIVRING
>   [4] (D,Integer) -> D from D if D has GROUP
>   [5] (D,NonNegativeInteger) -> D from D if D has MONOID
>   [6] (D,PositiveInteger) -> D from D if D has SGROUP
>
> Examples of ^ from Boolean
>
>
> Examples of ^ from BitAggregate
>
>
> Examples of ^ from DivisionRing
>
>
> Examples of ^ from Group
>
>
> Examples of ^ from Monoid
>
>
> Examples of ^ from SemiGroup
>
> (1) -> )d op **
>
> There are 20 exposed functions called ** :
>   [1] (CardinalNumber,CardinalNumber) -> CardinalNumber from
>            CardinalNumber
>   [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat
>   [3] (D,Integer) -> D from D if D has DIVRING
>   [4] (D,D) -> D from D if D has ELEMFUN
>   [5] (Float,Float) -> Float from Float
>   [6] (D,NonNegativeInteger) -> D from D
>            if D has FS D2 and D2 has ORDSET and D2 has SGROUP
>   [7] (D,Integer) -> D from D if D has GROUP
>   [8] (PolynomialIdeals(D2,D3,D4,D5),NonNegativeInteger) ->
>            PolynomialIdeals(D2,D3,D4,D5)
>            from PolynomialIdeals(D2,D3,D4,D5)
>            if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5
>            has POLYCAT(D2,D3,D4)
>   [9] ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from
>            MappingPackage1 D3
>            if D3 has SETCAT
>   [10] (D,Integer) -> D from D
>            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG
>            D2 and D4 has FLAGG D2 and D2 has FIELD
>   [11] (D,NonNegativeInteger) -> D from D
>            if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG
>            D2 and D4 has FLAGG D2
>   [12] (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3)
>            from ModuleOperator(D2,D3)
>            if D2 has RING and D3 has LMODULE D2
>   [13] (BasicOperator,Integer) -> ModuleOperator(D3,D4)
>            from ModuleOperator(D3,D4)
>            if D3 has RING and D4 has LMODULE D3
>   [14] (D,PositiveInteger) -> D from D if D has MONAD
>   [15] (D,NonNegativeInteger) -> D from D if D has MONADWU
>   [16] (D,NonNegativeInteger) -> D from D if D has MONOID
>   [17] (D,Fraction Integer) -> D from D if D has RADCAT
>   [18] (D,PositiveInteger) -> D from D if D has SGROUP
>   [19] (D,Integer) -> D from D
>            if D has SMATCAT(D2,D3,D4,D5) and D3 has RING and D4 has
>            DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) and D3 has FIELD
>
>   [20] (D,D1) -> D from D
>            if D has UTSCAT D1 and D1 has RING and D1 has FIELD
>
> There are 18 unexposed functions called ** :
>   [1] (D1,Fraction Integer) -> D1 from AlgebraicFunction(D3,D1)
>            if D3 has RETRACT INT and D3 has Join(OrderedSet,
>            IntegralDomain) and D1 has FS D3
>   [2] (D1,D1) -> D1 from CombinatorialFunction(D2,D1)
>            if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS D2
>
>   [3] (D1,Fraction Integer) -> D1
>            from ElementaryFunctionsUnivariateLaurentSeries(D3,D4,D1)
>            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has
>            UTSCAT D3 and D1 has ULSCCAT(D3,D4)
>   [4] (D1,Fraction Integer) -> D1
>            from ElementaryFunctionsUnivariatePuiseuxSeries(D3,D4,D1,D5
>            )
>            if D3 has FIELD and D3 has ALGEBRA FRAC INT and D4 has
>            ULSCAT D3 and D1 has UPXSCCA(D3,D4) and D5 has PTRANFN D4
>
>   [5] (D1,Integer) -> FreeGroup D1 from FreeGroup D1 if D1 has SETCAT
>
>   [6] (D1,NonNegativeInteger) -> FreeMonoid D1 from FreeMonoid D1
>            if D1 has SETCAT
>   [7] (Vector D3,Integer) -> Vector D3 from
>            InnerNormalBasisFieldFunctions D3
>            if D3 has FFIELDC
>   [8] (InputForm,Integer) -> InputForm from InputForm
>   [9] (InputForm,NonNegativeInteger) -> InputForm from InputForm
>   [10] (Matrix D3,NonNegativeInteger) -> Matrix D3
>            from StorageEfficientMatrixOperations D3 if D3 has RING
>   [11] (D1,NonNegativeInteger) -> OrderedFreeMonoid D1
>            from OrderedFreeMonoid D1 if D1 has ORDSET
>   [12] (Operator D2,Integer) -> Operator D2 from Operator D2 if D2 has
>            RING
>   [13] (BasicOperator,Integer) -> Operator D3 from Operator D3 if D3
>            has RING
>   [14] (OutputForm,OutputForm) -> OutputForm from OutputForm
>   [15] (Pattern D1,Pattern D1) -> Pattern D1 from Pattern D1 if D1 has
>            SETCAT
>   [16] (Pattern D2,NonNegativeInteger) -> Pattern D2 from Pattern D2
>            if D2 has SETCAT
>   [17] (Stream D2,Stream D2) -> Stream D2
>            from StreamTranscendentalFunctionsNonCommutative D2
>            if D2 has ALGEBRA FRAC INT
>   [18] (Stream D2,Stream D2) -> Stream D2
>            from StreamTranscendentalFunctions D2 if D2 has ALGEBRA
>            FRAC INT
>
> Examples of ** from AlgebraicFunction
>
>
> Examples of ** from CardinalNumber
>
>  c2:=2::CardinalNumber
>  c2**c2
>  A1:=Aleph 1
>  A1**c2
>  generalizedContinuumHypothesisAssumed true
>  A1**A1
>
>
> Examples of ** from CombinatorialFunction
>
>
> Examples of ** from DoubleFloat
>
>
> Examples of ** from DivisionRing
>
>
> Examples of ** from ElementaryFunctionsUnivariateLaurentSeries
>
>
> Examples of ** from ElementaryFunctionsUnivariatePuiseuxSeries
>
>
> Examples of ** from ElementaryFunctionCategory
>
>
> Examples of ** from FreeGroup
>
>
> Examples of ** from Float
>
>
> Examples of ** from FreeMonoid
>
>
> Examples of ** from FunctionSpace
>
>
> Examples of ** from Group
>
>
> Examples of ** from PolynomialIdeals
>
>
> Examples of ** from InnerNormalBasisFieldFunctions
>
>
> Examples of ** from InputForm
>
>
> Examples of ** from MappingPackage1
>
>
> Examples of ** from MatrixCategory
>
>
> Examples of ** from StorageEfficientMatrixOperations
>
>
> Examples of ** from ModuleOperator
>
>
> Examples of ** from Monad
>
>
> Examples of ** from MonadWithUnit
>
>
> Examples of ** from Monoid
>
>
> Examples of ** from OrderedFreeMonoid
>
>
> Examples of ** from Operator
>
>
> Examples of ** from OutputForm
>
>
> Examples of ** from Pattern
>
>
> Examples of ** from RadicalCategory
>
>
> Examples of ** from SemiGroup
>
>
> Examples of ** from SquareMatrixCategory
>
>
> Examples of ** from StreamTranscendentalFunctionsNonCommutative
>
>
> Examples of ** from StreamTranscendentalFunctions
>
>
> Examples of ** from UnivariateTaylorSeriesCategory
>
>

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