A broad and a narrow question... If Julia supports the definition of new integer types can I define a new type for a finite field and then use existing linear algebra libraries to do maths with them? Could I define an integer type for polynomials? Is this the kind of thing that would work in theory but not in practice? Has anyone done this?
Specifically, I need to solve a problem modulo 2 (GF(2) - addition and subtraction are XOR; multiplication is AND; division is trivial). I was about to write my own Gaussian Elimination and then remembered a comment from here saying Julia is the first language where you can define new integers... Am I talking rubbish? I'm not a mathematician, so I may be completely muddled anyway. Thanks, Andrew PS I guess for best speed I should use a Uint for my 0s and 1s? Assuming the problem is small enough that it will still fit in cache?
