[GiNaC-devel] series expansion

[Chris Dams]

Dear Jens,

On Wed, 26 Apr 2006, Jens Vollinga wrote:

> in order to avoid doubled effort I'd like to make an announcement:
> I am currently working on a better series expansion mechanism using 
> recurrence relations.

I think this is a great idea. I have since long thought that the current 
series expansion is bad.
 
> BTW, has anybody thought about ways to do Puiseux series? If one doesn't 
> care about the strange and obscure functions but concentrates on a 
> practical solution for "simple" functions like exp(sqrt(x)) for example, 
> it seems to me that the only thing needed would be an additional number 
> kept with every pseries that represents the denominator of non-integer 
> exponents (like 2 in the case of exp(sqrt(x))). Of course, this reduces 
> the performance for the small(?) benefit of rarely(?) used Puiseux 
> expansions.

Maybe the current representation of a series could be turned into
something that uses an exvector instead of an expairseq. You would store
the order at which the series starts and the stepsize by which the
exponent increases for every term. These could both be rational numbers.  
This may waste some space in case that, say, half the coefficients are
zero, but now space is often wasted by storing the exponents in cases
where they are subsequent natural numbers.

Best,
Chris