How to add term order to free module?
I am working with a free module over a ring of polynomials, and need more than what's available in FreeModule. To be specific, I want to define an order on the terms in the module (think term orders for Grobner bases), and then to be able to obtain leading monomials of module elements.
I tried to augment sage.modules.free_module_element.FreeModuleElement.__bases__ with my own mix-in as described in the tutorial, but apparently FreeModuleElement cannot be augmented in this way.
Presumably I could also put together derived classes for FreeModule and FreeModuleElement, but I'm somewhat up in the air as how to do this.
I considered augmenting my ring of polynomials with extra variables as a back-door way to produce my free module, but the term orders available in polynomial rings are not general enough for my application.
Any suggestions? So far I have worked around the problem, but it's ugly.