Computer Algebra System

[Huaiyu Zhu]

On 20 Jun 2000 15:33:00 +0200, Konrad Hinsen <hinsen at cnrs-orleans.fr> wrote:
>Rodolphe Pollet <pollet at liliput.lct.jussieu.fr> writes:
>
>> Is anyone aware of a Computer Algebra System (CAS) ---
>> i.e a mathematical software that is able to derivate, integrate,
>> simplify, find limits, ... analytically --- in python ?
>> It should compete with Mathematica or Maple.
>
>Pythonica isn't there yet, but it's an interesting start. More at:
>
>       http://www.strout.net/python/pythonica.html

That looks like an emulator of Mathematica, but I think there could be a much
better symbolic package given python's oo capabilities. 

One should be able to define classes of mathematical objects with various
properties. Python allows a level of abstraction much closer to true
mathematics than Mathematica can.

For example, if one defines polynomial on a ring and someone defines a ring
of algebraic numbers then one immediately get polynomials of algebraic
numbers.

Python's simple interface mechanism that is not tied up to inheritance makes
it extremely easy to define mathamatical concepts with any given property.

I have some ideas on how this might be done, although my time is tied up for
numerical computations.  If anyone is interested I can take some time to
write a prototype to get it started.  An open source symbolic algebra
package base on python stands a chance of greatly outperforming Mathematica
or Maple, especially in its ease of user-defined extensions.  It would also
be a big boost to python itself.

Huaiyu

PS. And a lot of mathematicians just love to use indentation!

-- 
Huaiyu Zhu                       hzhu at users.sourceforge.net
Matrix for Python Project        http://MatPy.sourceforge.net