Okay, I'm sorry I didn't realized the spaces get messy after copy-paste. Here's a link to original discussion: http://comments.gmane.org/gmane.comp.mathematics.maxima.general/37853
On Thursday, April 19, 2012 10:40:45 PM UTC+2, Duc Trung Ha wrote: > > Alright, here is a message I posted to Maxima's mail-list: > > Hola, >> >> I am sorry if this would come as a completely stupid question but I was >> really >> amazed at this Maxima's behavior: >> >> When I searched for solution of goniometric equation `tan(x) = 1`:: >> >> >> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; >> (%i22) to_poly_solve(tan(x) = 1, x); >> %pi >> - 2 %pi %z30 - --- >> 2 >> (%o22) %union([x = - ------------------]) >> 2 >> >> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; >> >> answer was given to me. On the other hand, when I entered what I consider >> an >> equivalent form of the very same equation: >> >> >> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; >> (%i23) to_poly_solve((sin(x)/cos(x)) - 1 = 0, x); >> %pi >> - 4 %pi %z40 - --- >> %pi (8 %z40 + 1) 2 >> (%o23) %union(%if(cos(----------------) # 0, [x = - ------------------], >> 4 2 >> 3 >> %pi >> %union()), [x = 2 %pi %z38 - >> -----]) >> >> 4 >> >> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; >> >> output came out. After a brief inspection one can unravel that this >> solution is >> in fact identical, however, denoted in very much less elegant & >> transparent >> way. >> >> This may cause some serious troubles to external programs exploiting >> Maxima's >> functionality. For instance, I discovered this issue while using Sage's >> `solve` >> command -- original bug can be viewed at >> >> https://groups.google.com/forum/?hl=en&fromgroups#!topic/sage-support/ys3CASZ3vrs >> >> Similarly, `solve` also is not capable of recognizing `sin/cos` form of >> `tan`:: >> >> >> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; >> (%i24) solve(tan(x) = 1, x); >> >> solve: using arc-trig functions to get a solution. >> Some solutions will be lost. >> %pi >> (%o24) [x = ---] >> 4 >> (%i25) solve((sin(x)/cos(x)) - 1 = 0, x); >> (%o25) [sin(x) = cos(x)] >> >> ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; >> >> Is it somehow possible to alter the output for equivalent forms of such >> well-known goniometric functions and thus fix this pseudo-bug? >> >> --- >> Duc Trung Ha >> > > I've been given these replies: > > You can use trigreduce to convert sin(x)/cos(x) to tan(x). But I agree >> that it would be nice if solve(sin(x)/cos(x)=1,x) gave a reasonable >> answer. >> Besides to_poly_solve, another way to handle trigonometric equations more >> systematically is to put them in exponential form, e.g. >> rectform(solve(exponentialize(...), ...)). But the result can be ugly in >> some cases. >> >> As for to_poly_solve, it's unreasonable to expect in general that >> equivalent solution sets will be syntactically identical. That is a very >> hard problem (actually unsolvable in general), though over time, more and >> more cases will be handled nicely. >> >> -s >> > > Professor Barton Willis (who maintains to_poly_solve) gave me this answer: > > Appending 'simpfuncs = ['expand] helps somewhat; try >> to_poly_solve(sin(x)/cos(x) = 1, x, 'simpfuncs = ['expand]); >> >> I made no particular effort to make to_poly_solve (usually) find >> syntactically identical solution sets to semantically identical equations. >> That simply >> wasn't a design goal. Although it might seem easy to do write a >> pre-processor that would do things such as sin(x)/cos(x) --> tan(x), it's >> not so >> easy to do this in a way that doesn't make some answers much much more >> complicated, or to do it without introducing spurious solutions. >> >> Most days, I'm happy when nobody locates an abject bug in to_poly_solve >> :) >> >> Thanks for the interest in to_poly_solve. >> >> --bw >> > > To which it was responded thus: > > I think it should be this way. Maxima doesn't automatically convert >> sin(x)/cos(x) to tan(x). I don't think to_poly_solve should magically >> do that either. >> >> Although it would be nice for %union and %if were smarter so that %if >> would know that cos(%pi/4*(8*%z40+1)) is never zero. Then we'd just >> have %union of two values of x. And it would be nice to see that they >> differ by just an integral multiple of %pi so that they could be >> combined into one. >> >> Ray > > > It seems to me, that Maxima is doing its work properly, just some > solutions are given in rather inelegant way which consequently confuses > Sage in giving empty set of solutions... Am I correct with this hypothesis? > > On Tuesday, April 17, 2012 6:05:34 AM UTC+2, kcrisman wrote: >> >> >> >> On Sunday, April 15, 2012 5:09:59 PM UTC-4, Duc Trung Ha wrote: >>> >>> OK, I WILL try & strive to do my best... >>> >>> BTW By "Maxima list" is meant Maxima Google support group or something >>> else? >>> >> >> They have their own sourceforge list. >> >> http://www.math.utexas.edu/mailman/listinfo/maxima >> > -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
