Force Field Algorithm for Matrices Consisting of Non-field Elements

[Michael Jung]

Dear community,

I've already opened a ticket on this topic.

In the manifold implementation, scalar fields behave a lot like symbolic ring elements: There is a division behind and "most" of the elements behave like field elements. Since the manifold package deals with quite sophisticated computations, it is desireable to speed up some computations, for example by using more efficient algorithms for matrix inversions on fields. It would be great to have an option somehow forcing Sage to use one of these algorithms (or at least try) even if the algebra is no field.

Is is already possible? If not, a corresponding implementation is highly appreciated.

Another thing: Is it possible to activate or implement multiprocessing for the division free algorithm? I run into computation time problems when using mixed forms and computing characteristic classes. This is not suprising anyway, though a multi-core support would be great!

Best wishes,
Michael