Tour of the SageMath Interface

We want to construct a module over the field of rational real numbers. Unlike in the C++ and pure Python case, we do not have to fix our generators, but just the base ring:

>>> from pyexactreal import ExactReals  # random output due to deprecation warnings  # byexample: +pass
>>> R = ExactReals(QQ)
>>> R
Real Numbers as (Rational Field)-Module

We pick two generators, one a random real in the interval (0, 1) and one a rational:

>>> x = R(1)
>>> y = R.random_element()

We can now perform some arithmetic in the module they generate:

>>> 2*x
2

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

Note that we can also multiply elements. The result then typically lives in a larger submodule of the reals:

>>> y * y
ℝ(<...>)^2

Divisions are supported when the result can be determined exactly:

>>> y * y / y == y
True

Otherwise, only floor division is possible:

>>> x // y >= 1
True

Consult the module reference for further details.