Re: Curious behavior of Taylor series

Martin Rubey <[email protected]> writes:

> "Igor Khavkine" <[email protected]> writes:
>
>> Can someone explain the following behavior of Taylor series in Axiom?
>>
>> (113) -> y := taylor x
>>    (113)  x
>>                          Type: UnivariateTaylorSeries(Expression Integer,x,0)
>> (114) -> x*y
>>    (114)  x x
>>                          Type: UnivariateTaylorSeries(Expression Integer,x,0)
>> (115) -> coefficient(%,1)
>>    (115)  x
>>                                                      Type: Expression Integer
>
> The reason is that Axiom cannot really know whether you meant x in (114) to be
> an element of the coefficient Ring EXPR INT, or to be a univariate Taylor
> series. In case of doubt, it usually chooses the wrong possibility :-)

When multiplying two elements, shouldn't Axiom try to coerce them to
be in the same structure?  (I realize it doesn't, particularly here,
but wouldn't that be reasonable behavior?)

Jay