Re: Curious behavior of Taylor series

On 08/21/2006 03:38 AM, Jay Belanger wrote:
> 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?)

But Axiom coerced the two x to the same domain!!! The first x is a 
coefficient, and the second x is the variable from the Taylor series. So 
you cannot complain.

The only problem is that it is terribly confusing. Unfortunately, I 
cannot even blame that the user did anything wrong since Axiom came up 
with this strange type UnivariateTaylorSeries(Expression Integer,x,0).

But I could blame the user for trying to do "x * y". Here you instruct 
the compiler to guess since there is no function

*: (Symbol, UTS(Expression Integer,x,0))->UTS(Expression Integer,x,0)

so the interpreter has to do something with the x. It coerces it to 
Expression(Integer). That is perfectly legal. But it is probably not 
what you want. Once again. The result "x x" for "x*y" shows two DIFFERENT x.

Ralf