On Thursday 17 May 2007 03:02, Michel wrote: > > > sage: %timeit ((x+y+z)**3)(1/y,y,y**100) > > > 10 loops, best of 3: 752 ms per loop <=== look here! > > > sage: %timeit ((u+v+w)**3)(1/v,v,v**100) > > > 10 loops, best of 3: 48.2 ms per loop <=== look here! > > > > It's not at all clear to me without further discussion and benchmarking > > what the right optimization is so that rational functions over fields are > > sufficiently fast. > > My point was that the above command over a number field is 15 times > as fast as over the rationals. This is so counterintuitive that > I think it is unacceptable. > > > Basically, are you suggesting that one > > not call reduce until, e.g., printing? > > There are several options. > (1) declare reduce to be expensive so require the user to call it > explicitly (this is the approach followed by maxima). > As a refinement this behaviour could be triggered by a new flag for a > ring element: gcd_is_expensive (e.g. > for polynomials in several variables). > (2) call reduce lazily and cache the result (this is what you are > suggesting).
I think that the call to reduce can be made considerably faster. I ran into this particular bottleneck one day and found an ugly hack which made a huge difference. That was to check if the gcd(numerator,denominator) ==1 and immediately return. It didn't make sense to me that such a thing wasn't already implemented so I didn't submit any patches. The right code should somehow have that check built in a way that doesn't duplicate the logic of that gcd call when the gcd != 1. I don't know that that would make your code any faster. I'm just saying that the reduce call probably has a few very easy optimizations before heading for a design change. -- Joel --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
