Abelfunctions

An Enthought Python Distribution / Sage library for computing with Abelian functions and solving integrable partial differential equations.

License: Abelfunctions is licensed under the New BSD License which covers all files in the abelfunctions repository unless stated otherwise. See the LICENSE file for details.

Documentation and Usage

See the Abelfunctions Wiki for full details.

To begin using Abelfunctions from this directory start python and run:

>>> from abelfunctions import puiseux
>>> from sympy.abc import x,y
>>> from numpy import prod
>>> f = y**3 - x**5
>>> P = puiseux(f,x,y,0,5,parametric=False); P
[(-x**(1/3)/2 + 3**(1/2)*I*x**(1/3)/2)**5,
 (-x**(1/3)/2 - 3**(1/2)*I*x**(1/3)/2)**5,
  x**(5/3)]
>>> prod(y-pi for pi in P).simplify()
-x**5 + y**3

Prerequisites

Abelfunctions can be used either with the Enthought Python Distribution (EPD) or Sage. If using EPD, Abelfunctions needs the following libraries / software installed:

• PARI/GP: to install, obtain the most recent:

  $ curl -O http://pari.math.u-bordeaux.fr/pub/pari/unix/pari.tgz
  $ tar xzf pari.tgz
  $ cd pari
  $ ./Configure
  $ make all
  

  # make install

Installation

Download the Code. There are two ways to do this:

1. Download and extract a zipfile. First, go to the Abelfunctions homepage https://github.com/cswiercz/abelfunctions. Then, click on the button labeled "ZIP" near the top of the page.

2. If you have git (http://git-scm.com/) installed, run:

   $ git clone git://github.com/cswiercz/abelfunctions.git
   

EPD Installation. Enter the main directory, abelfunctions, and run:

# python setup.py install

Sage Installation. Enter the main directory, abelfunctions, and run:

$ sage -sh
$ python setup.py install

Authors

Chris Swierczewski <cswiercz@gmail.com>