> Are you aware of the results of Daniel Richardson on the recursive > undecidability of > (rather simple) identities? He proved that in general there is no > algorithm possible.
Yeah, and the halting problem is undecidable too, but you would still call the following program "stupid": while 1: continue There are a huge number of intractable problems. Determining whether sin^2 x + cos^2 x = 1 is not one of them. > Especially given that as background, > > How much work do you think Maxima should do to try to determine for > arbitrary f, if f(x)>0 or not? Enough that it doesn't ask the user obviously stupid questions. > Now Maxima does know, in many different contexts, that sin^2+cos^2 can > be simplified to 1 > But looking for all such relationships that it is aware of (and there > are many such relationships), > at every decision point, is time consuming. Yes, but I'd bet that Maxima could answer 99% of such questions faster than I could find a piece of paper. It's great that Maxima is "aware" of many relationships. It'd be awesome if it would effectively wield them. > Mathematica has a function which tries searching for smaller > equivalent expressions. > Simplify, or maybe FullSimplify. > > The difficulty is that the program tends to take too much time for any > but rather small expressions > to start with. Ah! So the problem is that Maxima is slow. I complain about that a lot, actually. > Such a program could presumably be written in Sage, > where each subexpression > is repeatedly submitted to 15 or 20 or 30 different "simplifier-like" > programs to see which > equivalent expression is smaller. This is not a great idea. No, sending 20-30 requests to Maxima is not a great idea. Fewer is better, usually. > But if you really really want to make sure that Maxima always knows > that sin^2+cos^2=1, you can consider > wrapping trigsimp() around every expression that you send to it. > > > > By the way, Macsyma is not 30 years old. The first paper describing > it dates back to 1967. > So it is 42 years old or more. Neat! In a few years, it'll be an antique! I used to own a 1969 Ford 150. Nothing like old iron -- but the damned thing burned a gallon of gasoline in under 6 miles on a straight, flat road in a tailwind! Out with the old, in with the new -- my '05 pickup gets 25 miles to the gallon in hilly city conditions. > Richardson's results date to about 1968. Pythagoras's result dates back to about 500BC. Have you heard of it? > > RJF > > > > > > On Feb 11, 11:11 am, mabshoff <mabsh...@googlemail.com> wrote: >> On Feb 11, 9:45 am, kcrisman <kcris...@gmail.com> wrote: >> >> Hi, >> >>> There are of course several trac tickets related to this, so this is >>> not a bug report (for Sage or for Maxima), but I had to laugh when >>> this came up today in preparing for class - enjoy! >> >> Well, it would be truly funny if we didn't use Maxima for symbolics, >> but this is a sad, sad bug for a 30 year old system. >> >>> TypeError: Computation failed since Maxima requested additional >>> constraints (try the command 'assume(sin(t)^2+cos(t)^2>0)' before >>> integral or limit evaluation, for example): >>> Is sin(t)^2+cos(t)^2 positive or zero? >> >>> - kcrisman >> >> Cheers, >> >> Michael > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
