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## [Axiom-developer] Limits in Axiom

**From**: |
Ralf Hemmecke |

**Subject**: |
[Axiom-developer] Limits in Axiom |

**Date**: |
Mon, 26 Mar 2007 10:58:30 +0200 |

**User-agent**: |
Thunderbird 2.0b2 (X11/20070116) |

Let me copy that to axiom-dev since others might jump in...
On 03/25/2007 11:16 PM, Ondrej Certik wrote:

`The Gruntz thesis is nice, it's cleanly written and I had no problems
``with it.
`

I had a quick look at the Maple code of gruntz.pdf. Doesn't look overly
complicated, but it builds on some internals of Maple. I am quite

It only looks like that. The only thing that is needed is a (good)
series expansion facility. Nothing more than SymPy can do.

`Ah, but that means formal power series with symbolic coefficients? Or
``does one need Laurant or even Puiseux series?
``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?
`

`curious, how do *you* actually represent the input in python. Just
``strings?
`

Do you mean expressions? like x+2 ?

Yes.

as an instance of a respective class, for example x+2 is
Add(2,x). More info is here:

http://code.google.com/p/sympy/wiki/HowItWorks

Aha. It seems that Python makes it easy to deal with expressions.

`However, I must say that your expression approach is limited in the
``sense that it can only deal with commuting objects. Simplifying b*a+a*b
``to 2*a*b is not correct if b is the differentiation operator D on x and
``a=X is the "multiplication by x"-operator. Then you would have D*X=X*D+1.
`

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

**[Axiom-developer] Limits in Axiom**,
*Ralf Hemmecke* **<=**