Re: [Axiom-mail] Unexpected results w.r.t. exponential operation of LODO (with july2008 release)

[root]

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