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## [Axiom-developer] Re: [Axiom-mail] limits

 From: Ralf Hemmecke Subject: [Axiom-developer] Re: [Axiom-mail] limits Date: Mon, 26 Mar 2007 10:30:06 +0200 User-agent: Thunderbird 2.0b2 (X11/20070116)

```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

```