Computing algebraic numbers of bounded height
Sage code for computing elements of bounded height in number fields may be downloaded here.
Below are a few examples of the code in action. This file has all the commands used below.
A computation of all the rational numbers of height at most 3:
An example over an imaginary quadratic field, with a height bound of 2,000:
An example over a cubic field, using a height bound of 1,000: