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[Axiom-developer] Re: Limits in Axiom

From: Ralf Hemmecke
Subject: [Axiom-developer] Re: Limits in Axiom
Date: Mon, 26 Mar 2007 13:04:40 +0200
User-agent: Thunderbird 2.0b2 (X11/20070116)

On 03/26/2007 12:08 PM, Ondrej Certik wrote:
Ah, but that means formal power series with symbolic coefficients? Or
does one need Laurant or even Puiseux series?

Depending on the limit, sometimes you need to know how to make a
series of an expression like


around x=0+

You can try it in Maple, the trick is to treat any possible log(x)
that arise during the expansion as constants (as they are singular
around x=0+) and then do normal laurent series.

log(1+1/x) is trivial, but there are more complicated examples.

log(x) are later substituted for something normal.

Aha. Do you have lots of testcases like that one in SymPy?

And for computing the coefficients one probably need differentiation of
the (symbolic) expression and evaluation at some point (Taylor series
expansion). Is my understanding correct?

Right, but that's easy. But you need to know how to make a meaningful
series of almost everything. (it's enough what maple or sympy does)



Anyway, could you list a few more detailed requirements of the Gruntz
algorithm? What is simple, what do you think is complicated?

I think in Axiom you have pretty much everything prepared already.
Don't worry about the series expansion, you can use your current one,
it will work for most limits (but not the one I was trying to do in my
email for example).

For someone who knows Axiom well, it should take like a week of a
work. In SymPy I was doing it I think like 3 weeks, because I had to
implement many other things and I was spending most of the time in the
series facility.

I think one week is just too over-optimistic. Any new implementation in Axiom now requires to write in a literate programming style. So one actually has to understand the thesis first and then put that together with the program into a pamphlet (which is an article like form that contains the program). Maybe we should ask Gruntz whether we are allowed to include part of his thesis in an Axiom pamphlet then.

Isn't there someone interested in this limit stuff? I think this is not the main thing I want to follow now.

Best regards

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