Indeed, but then I need to provide my own implementation. I was hoping
(navely in retrospect, since everyone else wants fast rather than generic
code) that I could call generic code for "matrix division" with a new
numerical type and it would "just work".
I think this is still the best approach - but I need to write that code
(Gaussian elimination) myself, in a generic way, then define my new numeric
type, then call it.
Which is much more work than I had hoped.
Cheers,
Andrew
On Thursday, 20 February 2014 21:14:38 UTC-3, Patrick O'Leary wrote:
>
> You can redefine the \ operator for your type to not do this.
>
> On Thursday, February 20, 2014 6:08:31 PM UTC-6, andrew cooke wrote:
>>
>>
>> While I still don't see a problem with the theory side of this, there is
>> a practical problem - Gaussian Elimination in Julia seems to be delegated
>> to LAPACK and arguments are promoted to Float:
>>
>> julia> [1 0; 0 1] \ [1, 2]
>> 2-element Array{Float64,1}:
>> 1.0
>> 2.0
>>
>> Andrew
>>
>>
>> On Thursday, 20 February 2014 19:45:28 UTC-3, andrew cooke wrote:
>>>
>>>
>>> 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?
>>>
>>
