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 mathematical functions

Documentation: http://fredrikj.net/python-flint/

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

Author: Fredrik Johansson [email protected]

Installation

First install both FLINT (version 2.5 or later) and Arb (version 2.15 or later). See:

• http://flintlib.org/
• http://arblib.org/

The latest release of Python-FLINT can then be installed using:

pip install python-flint

Python-FLINT can also be installed git checkout or a source archive as follows:

pip install .

See the documentation for further notes on building and installing Python-FLINT.

Examples

Import Python-FLINT:

>>> from flint import *

Number-theoretic functions:

>>> fmpz(1000).partitions_p()
24061467864032622473692149727991
>>> fmpq.bernoulli(64)
-106783830147866529886385444979142647942017/510

Polynomial arithmetic:

>>> a = fmpz_poly([1,2,3]); b = fmpz_poly([2,3,4]); a.gcd(a * b)
3*x^2 + 2*x + 1
>>> a = fmpz_poly(list(range(10001))); b = fmpz_poly(list(range(10000))); a.gcd(a * b).degree()
10000
>>> x = fmpz_poly([0,1]); ((1-x**2)*(1+x**3)**3*(1+x+2*x)).factor()
(-1, [(3*x + 1, 1), (x + (-1), 1), (x^2 + (-1)*x + 1, 3), (x + 1, 4)])

Matrix arithmetic:

>>> fmpz_mat([[1,1],[1,0]]) ** 10
[89, 55]
[55, 34]
>>> fmpq_mat.hilbert(10,10).det()
1/46206893947914691316295628839036278726983680000000000

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

Numerical integration:

>>> ctx.dps = 30
>>> acb.integral(lambda x, _: (-x**2).exp(), -100, 100) ** 2
[3.141592653589793238462643383 +/- 3.11e-28]

To do

• Write more tests and add missing docstrings
• Wrap missing flint types: finite fields, p-adic numbers, multiprecision integer mods, rational functions
• Vector or array types (maybe)
• Many convenience methods
• 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)
• Improved printing and string input/output
• IPython hooks (TeX pretty-printing etc.)
• Windows support

License

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