Hi all,


I want to compute in $\mathbb{F}\_q (x)((y))$ i.e. a Laurent series ring over the rational functions over $\mathbb{F}\_q$. The computations are fairly basic, but they involve raising to the qth power a lot. I thought that this would be easy (I thought that it will merely shirt powers around), so I tried it in SAGE. I have to say that I am highly impressed with the ease of programming in SAGE, but I think it is too big (and slow) for the calculation I need (I know that SAGE has lots of components (PARI, GAP, etc.) some of them may be what I need).


So I wanted to ask the people who have more experience then me for a recommendation. Which algebra system is good at Laurent series over rational function fields in char p if you need to do a lot of raising to the qth power. 


~AP



Choosing a fast computer algebra system that works in characteristic p?
My personal experience is a few years old, but I don't think things have changed much. Sage is (or actually, was) more about ease of use then about performance. The only three CAS's you want to consider are


* Singular (Macaulay 2 uses Singular's engine)
* Cocoa.
* Magma.


Back then the fastest of the bunch was Magma, but not by much. Regarding ease of use, it was a tie between Macaulay 2 and Magma. 


And now to some criticism: I never looked at Magma's code (proprietary), but I did look at both Singular and Cocoa. None of them uses SSE/GPGPU, which could probably give you an acceleration factor of 10-100.


