[Axiom-developer] Limits in Axiom

[Ralf Hemmecke]

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