computations in the original basis (like the "characteristic
polynomial of"), which can be much faster when the original basis
contains only rational entries.
+
+Debugging
+---------
+There are several places in the code where we set check_field=False
+and check_axioms=False because the theory guarantees that they will be
+satisfied. Well, you know what they say about theory and practice. The
+first thing you should do when a problem is discovered it replace all
+of those with check_field=True and check_axioms=True, and then re-run
+the test suite.