Python-FLINT

Python extension module wrapping FLINT (Fast Library for Number Theory) and Arb (arbitrary-precision ball arithmetic). Features:

• Integers, rationals, integers mod n
• Real and complex numbers with rigorous error tracking
• Polynomials, power series and matrices over all the above types
• Lots of special functions

Author: Fredrik Johansson fredrik.johansson@gmail.com

Repository: https://github.com/fredrik-johansson/python-flint/

Installation

First install both FLINT and Arb (currently, the git versions are required). See:

• https://github.com/fredrik-johansson/flint2/
• https://github.com/fredrik-johansson/arb/

Install build dependencies:

sudo apt-get install cython python-dev

Build and install python-flint from source:

python setup.py build_ext
sudo python setup.py install

Run the test suite:

python test/test.py

Import using:

>>> from flint import *

Additional paths

The FLINT and Arb header files and library files (libflint.so and libarb.so) must be available at compile time. If they are in a nonstandard location (for example, if they have been built but not installed), use a command such as the following to build:

python ./setup.py build_ext \
    --include-dirs=/home/fredrik/src/flint2:/home/fredrik/src/arb \
    --library-dirs=/home/fredrik/src/flint2:/home/fredrik/src/arb

Likewise, before starting the Python interpreter, tell the linker where to find the library files using something like:

export LD_LIBRARY_PATH=/home/fredrik/src/flint2:/home/fredrik/src/arb:$LD_LIBRARY_PATH

You may also have to install the CPimport file:

sudo cp /home/fredrik/src/flint2/qadic/CPimport.txt /usr/local/share/flint/CPimport.txt

Examples

Number-theoretic functions:

>>> fmpz(1000).number_of_partitions()
fmpz(24061467864032622473692149727991)
>>> fmpq.bernoulli_ui(64)
fmpq(-106783830147866529886385444979142647942017,510)

Polynomial arithmetic:

>>> a = fmpz_poly([1,2,3]); b = fmpz_poly([2,3,4]); a.gcd(a * b)
fmpz_poly([1, 2, 3])
>>> a = fmpz_poly(range(10001)); b = fmpz_poly(range(10000)); a.gcd(a * b).degree()
10000

Matrix arithmetic:

>>> (fmpz_mat(2,2,[1,1,1,0]) ** 10)
fmpz_mat(2, 2, [89, 55, 55, 34])

Numerical evaluation:

>>> showgood(lambda: (arb.pi() * arb(163).sqrt()).exp() - 640320**3 - 744, dps=25)
-7.499274028018143111206461e-13
>>> showgood(lambda: (arb.pi() * 10**100 + arb(1)/1000).sin(), dps=25)
0.0009999998333333416666664683

Documentation

API documentation is available here: http://fredrikj.net/python-flint/

To do

• Work on packaging and the build system
• Continuous integration
• Write more tests and add missing docstrings
• Wrap missing flint types: finite fields, p-adic numbers, multiprecision integer mods, rational functions
• Rational functions
• Vector or array types (maybe)
• Many convenience methods
• Lots of FLINT and Arb functions/methods that haven't been wrapped yet
• Write generic implementations of functions missing for specific FLINT types
• Proper handling of special values in various places (throwing Python exceptions instead of aborting, etc.)
• Various automatic conversions
• Conversions to and from external types (numpy, sage, sympy, mpmath, gmpy)
• Support for Python-level multithreading (there is some global state)
• Support for subclassing (maybe, not a priority)
• Improved printing and string input/output
• IPython hooks (TeX pretty-printing etc.)
• Python 3.x support (should mostly work, needs minor touches)
• Windows support

License

Python-FLINT is licensed MIT. FLINT and Arb are LGPL v2.1+.