Re: [Axiom-mail] limits

[Ralf Hemmecke]

Hello,

On 03/26/2007 06:31 AM, Bill Page wrote:
> On March 25, 2007 11:54 AM Ondrej Certik wrote:
>> I am sorry for this stupid question - but how can I
>> calculate the limit of:
>>
>> (3**x+5**x)**(1/x)
>>
>> for x->+infinity?

[snip]

> In Axiom you should write:
>
>  limit((3**x+5**x)**(1/x), x=%plusInfinity)
>
> But if you got "failed" as a result you probably wrote
> %plusInfinity and it's just a typo in your email.

>> Also, this works correctly:
>>
>> simplify(2**x * 2**(2*x))
>>
>> simplifies to 2**(3x)
>>
>> but this doesn't simplify at all:
>>
>> simplify(2**(5*x)/2**(4*x))

But I don't think that expression simplification in general is Ondrej's 
point (see subject). In fact, he has implemented the algorithm of Gruntz 
 dissertation (http://www.cs.fh-aargau.ch/~gruntz/publications2.html) 
which is in Maple and there also seems to be an implementation in MuPad 
and Mathematica. Axiom is just lacking that new algorithm. Maybe we 
should also implement it and Ondrej could help to do so. (In fact, that 
would be a good small project for Google Summer.) Any volonteers out there?

Unfortunately, I haven't found a .pdf file of Gruntz thesis, but 
shouldn't we copy it to a section on 
http://portal.axiom-developer.org/refs ?

Ralf