Re: numerator? denominator?

[Nils Barth <nbarth@fas.harvard.edu>]

Thus spake George:
> On Sun, Feb 06, 2000 at 04:07:00PM -0500, Nils Barth wrote:
> > Okay.
> > Actually, if you're working on that -anyhow-, you might want to
> > implement fast exponentiation. Basically, exponentiation mod n can be
> > done very quickly, so if
> > a^b mod n
> > were computed internally mod n, it would be MUCH faster than
> > a^b % n
> > i.e., first do a^b, then mod is slow.
> 
> That was one of the reasons for also doing the mod operator, so that such
> optimizations are possible.  However for a first stab at making it work it'll
> probably not be there :)
> 
> > To see the relevant algorithm, see:
> > dr-genius/lib/number_theory/misc.gel
> > function PowerMod
> > 
> > It's not a big deal if this isn't built-in (heck, m9a (=mathematica)
> > doesn't have it built-in), but it would be more elegant.
> 
> Oh it would be very nice to have this, and I don't think it should be so
> terribly complicated to build in either.
> 
> Another optimization which I'm thinking about is imagine you have a bunch of
> different sized matricies and you multiply them all together
> 
> A*B*C*D
> 
> genius could figure out the grouping of the matricies so that you do the
> least number of operations.

Cool!
And of course if you wanted to do A*B*C*D mod n, then it could do all
the multiplication mod n ;)

This would be nice -- a (semi-)smart math program!

-- 
  -nils