A new library for large computations involving MacLaurin (Taylor) series

Thomas Baruchel baruchel at bluebottle.com
Sun Nov 6 09:48:21 CET 2005


for my own purposes, I wrote a tiny library for performing
arithmetic operations between functions, represented internally
either as a vector of successive derivates evaluated at 0 :
  [ f(0), f'(0), f''(0), f'''(0), ... ]
or (high-level functions) as a MacLaurin series expansion :
  a0 + a1 x + a2 x^2 + a3 x^3 + ... + O(x^k)
  (where the a0, a1, ... are the MacLaurin coefficients, ie. :
    a7 = f'''''''(0)/7! )

The classical part was implementing multiplication between these
objects. A more interesting challenge was implementing the
inversion and division, but now, everything is done.

Since it is implemented at a low level (C code using GMP library),
it wants to be very efficient.

This is a pre-pre-pre-pre alpha version ; I have very little time
for the moment, but I want later to include more sophisticated
functions for the exact things I want to do. Here are the basics.

If you are interested, please use it. If you have comments, I would be
glad to hear them. If you find bugs, please tell me.

The code is here:
Note that the Makefile is a quick and dirty one ; it merely
lanches the compilation, but for the moment it is probably the
best to leave the shared compiled object in the current
directory (where you can perfectly use it) ; don't install
it in your local directories.


Thomas Baruchel
  Home Page: http://baruchel.free.fr/~thomas/

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