On Tue, Jun 12, 2012 at 10:41 AM, Henry Rich <henryhr...@nc.rr.com> wrote: > That may be. But no way do you do a determinant with just one multiply > - it takes 0 for a 1x1, 2 for a 2x2.
You are thinking about scalars. -/ .(*&([smoutput)) i. 2 2 3 1 0 2 _2 Here, we are computing 0 2 * 3 1 This is what I mean by "one multiply". You are correct that if I investigated at rank 0 that there would be two multiplies. > The definition of DET is so quirky that it makes sense only when you > have subtraction/ . multiplication All I had to do to make it behave like the implementation was terminate recursion when derived lists contain 1 element instead of 0 elements. > for suitably defined operations on > the space of interest. Even +/ . * runs in factorial time. For the > case of finding the characteristic polynomial, why not just use the verb > definitions I gave earlier, rather than requiring a new DET? Which verb? Anyways, one issue here is whether the dictionary and the implementation agree. Currently, they do not. But I currently see no value in using the dictionary definition over the actual implementation -- they are equivalent for -/ .* and I have not found a useful case where the dictionary DET does something meaningful that the implementation does not. Another issue here is generality, and motivation. There is something nice about being able to use the same "determinant primitive" to compute both regular determinants and eigenvalues. And even if that never gets into the interpreter, I find some joy in modeling things that way. The "resource cost" issue you are raising can be significant, in some contexts, but it's not going to be significant in all contexts. In the case I am working up to dealing with (several hundred collections 4x4 matrices where each collection typically contains of several thousand of these 4x4 matrices), it's hard for me to see why I should care about it. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
