Python interfaces

There are two ways to use FLINT from Python.

python-flint is a separate project (https://github.com/flintlib/python-flint) maintained alongside FLINT, with Cython bindings to the main types: integers, rationals, integers modulo n, finite fields, polynomials, matrices, power series, and the ball arithmetic types arb and acb with many special functions. It is installed with pip install python-flint and is the recommended interface for production use.
flint_ctypes is a pure Python wrapper included with FLINT in the directory src/python. It accesses the library through ctypes and covers a large part of FLINT through the generic rings interface. It is not officially supported and should not be used in production, but it is convenient for experimenting with FLINT, including functionality that python-flint does not wrap yet. It is described in the rest of this section.

Other languages have their own interfaces: for example Nemo and Oscar.jl use FLINT from Julia, and SageMath uses it from Python.

Setting up flint_ctypes#

flint_ctypes.py loads the shared library libflint.so (libflint.dylib on macOS) with the default search path of the dynamic linker, so FLINT must be built as a shared library and be installed in a standard location or be on LD_LIBRARY_PATH. No compilation is needed:

cd src/python
LD_LIBRARY_PATH=/path/to/flint/lib python3
>>> from flint_ctypes import *

make check PYTHON=1 runs the doctests of flint_ctypes.py against the library that was just built. The directory also contains flint2.py and the modules RRmath.py and CCmath.py, which export the functions of the real and complex fields as module-level functions in the style of Python's math and cmath.

Examples#

Elements belong to parent rings such as ZZ (the integers, fmpz), QQ (fmpq), RR and CC (real and complex balls, arb and acb), QQbar (algebraic numbers, qqbar) and ZZx (polynomials). Methods on a ring compute functions with values in that ring:

>>> from flint_ctypes import *
>>> QQ.bernoulli(50)
495057205241079648212477525/66
>>> sign, primes, exponents = _.factor()
>>> sign
1
>>> primes
[5, 417202699, 47464429777438199, 2, 3, 11]
>>> exponents
[2, 1, 1, -1, -1, -1]
>>> sign * (primes ** exponents).product()
495057205241079648212477525/66

Operations are performed in the parent of the operands, with coercion between parents where it makes sense. An operation whose result is not in the parent raises FlintDomainError, and one that cannot be decided or computed raises FlintUnableError:

>>> ZZ(5).parent()
Integer ring (fmpz)
>>> ZZ(10) / ZZ(6)
Traceback (most recent call last):
  ...
FlintDomainError: x / y is not an element of {Integer ring (fmpz)} for {x = 10}, {y = 6}
>>> ZZ(10) / QQ(6)
5/3
>>> x = QQ(1) / 2; x ** x
Traceback (most recent call last):
  ...
FlintDomainError: x ** y is not an element of {Rational field (fmpq)} for {x = 1/2}, {y = 1/2}
>>> x = QQbar(1) / 2; x ** x
Root a = 0.707107 of 2*a^2-1

The precision of the real and complex fields is an attribute of the parent:

>>> RR.zeta(2)
[1.644934066848226 +/- 4.57e-16]
>>> RR.prec = 128
>>> RR.zeta(2)
[1.64493406684822643647241516664602518922 +/- 2.88e-39]
>>> RR.prec = 53       # restore the default

The docstrings of flint_ctypes.py contain many more examples, for polynomials, matrices, power series, finite fields, number fields, p-adic numbers, and other types.