Tour of the Python Interface

The pyexactreal package provides three interfaces to exact-real from Python.

There is a very low-level interface that is provided by cppyy. This interface is very low-level and just exposes the C++ namespace exactreal at pyexactreal.exactreal. While in principle this interface is fully functional, it can be very tedious to work with. The translation from C++ to Python is not without problems and you’ll likely run into segfaults at some point.

There is a higher-level interface which works around most of the oddities coming from the C++ interface. We showcase some of its features below. More examples can be found in the module documentation. In principle most objects exposed in this interface are just somewhat tweaked wrappers of the C++ objects so most functions that you may find in the C++ documentation should be available.

Finally, there is a SageMath interface that wraps the exact-real machinery in the language of SageMath parents and elements.

Example

We want to construct a module over the field of rational real numbers. We fix our generators, one is a random real number in the interval (0, 1).

>>> from pyexactreal import RealNumber, QQModule  # byexample: +timeout=30

>>> a = RealNumber.rational(1)
>>> b = RealNumber.random()

We construct the module generated by these reals:

>>> M = QQModule(a, b)
>>> M
ℚ-Module(1, ℝ(0.303644…))

We construct some elements in this module, namely its generators:

>>> x = M.gen(0)
>>> y = M.gen(1)

We perform some arithmetic in this module:

>>> 2*x
2

>>> y + x - y == x
True

Note that we can also multiply elements, however the result then typically lives in a larger module:

>>> (y * y).module() == M
False

Divisions are supported when the result can be determined exactly:

>>> (y * y) / y == y
True

Otherwise, only :cpp:func;`floor division <exactreal::Element::floordiv>` is possible:

>>> x.floordiv(y) >= 1
True