(INCOMPLETE) Replacing Field with Spire's equivalent

So I decided to take a look at #21, specifically porting breeze over to use Spire's Field implementation. I'm leaving Ring and Semiring alone for the moment, and converting Spire Fields to Breeze Semirings via an implicit. Obviously in the long run, everything would need to be ported over. 

I've got all the code, and most of the tests compiling. Most of the tests pass as well if I delete the one file that doesn't compile. The main source of failing tests seems to be "dot product distributes". 

I'd be curious to get some thoughts on this. Is this the right way to go? Is there a simpler way to do it? Anyone see a solution for the failing tests or the one that doesn't compile? (I've been beating my head against it all day.)