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## Re: [Axiom-mail] Unexpected results w.r.t. exponential operation of LODO

 From: Liu Xiaojun Subject: Re: [Axiom-mail] Unexpected results w.r.t. exponential operation of LODO (with july2008 release) Date: Thu, 28 Aug 2008 10:15:06 +0800

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
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 Monoid

Examples of ** from OrderedFreeMonoid

Examples of ** from Operator

Examples of ** from OutputForm

Examples of ** from Pattern

Examples of ** from SemiGroup

Examples of ** from SquareMatrixCategory

Examples of ** from StreamTranscendentalFunctionsNonCommutative

Examples of ** from StreamTranscendentalFunctions

Examples of ** from UnivariateTaylorSeriesCategory