Replying to evanandel:

Sorry for the slow response.

It looks like everything is slight numerical problems, which is expected given (as mentioned above) the numerical sensitivity. I'll happily test, but I'm not sure how to upgrade Sage's numpy. If someone can tell me how to get that running, I'll be able to confirm this patch and #10821.

You can go through the following steps:

1) drop the numpy spkg in the spkg/standard folder

2) sage -f numpy-1.5.1

3) apply the patches (from here and #10821 ) the easiest way is to follow the procedure from the developer's manual http://www.sagemath.org/doc/developer/walk_through.html#reviewing-a-patch

4) sage -b

5) test

Side Note 1: I see that my code is apparently quite incomprehensible to people. The underlying mathematics is quite a bear, so it'll never be nice and accessible, but is there anything I can do to improve the documentation?

could you refer to a review of it in a journal or an online resource?

Side Note 2: What's the status of fast_callable these days? Patch #8867 is still out there, and if fast_callable is ready, I think we might be able to merge that as well (otherwise, I can try amending it to work with fast_callable as is)

No idea.