On Wednesday, October 15, 2014 12:29:52 PM UTC-7, Aaron Meurer wrote: > > Because it's nicer when the output looks like the input.
I agree > For > instance, sin and cos are easier to integrate if rewritten as tan > first, but it's annoying to write integrate(sin(x)) and get > -2/(tan(x/2)**2 + 1) instead of -cos(x). > So you can take the answer and convert it to sin/cos. > > For elementary functions, such as this one, the Risch algorithm should > handle them no matter what they look like. To be sure, internally it > might need to do all kinds of canoncalizing, but the difference is > that it can do very targeted simplifications and try to put things > back when it is done. The same kind of targeted simplification could be done on the the tan(x/2) expression. If you can do it.. > It's hard to tell the generic simplify() > something as simple as "ignore anything that doesn't have x" (i.e., > don't try simplifying complicated symbolic constants). > It doesn't seem like a hard task to have a different driver program that calls simplify only on subexpressions containing the integration variable. > > The other issue is that simplify() can sometimes be very slow, and it > would be a shame to run it if it weren't needed. > Again, I agree with you, but the alternative --- of making sure that your algorithms work on unsimplified inputs --- seems hard too. I think that most system have a rather modest simplify program but with extra-strength ones lurking in the background. For example, Maxima's solve program uses the radcan simplifier if some flag is set. Mathematica has a program FullSimplify which takes a very long time and so is generally NOT used... > > Also, note that the Risch algorithm for trig functions isn't actually > implemented in SymPy yet. I'm just pointing out that when it is > implemented, it will handle this better. > You were concerned with speed when you talked about the simplifier.. Since the trig functions can be trivially rewritten as complex exponentials, I guess you have not implemented the exponential case of Risch; this should be one of the more straightforward parts. Good luck RJF > > > On Wed, Oct 15, 2014 at 2:20 PM, Richard Fateman <fat...@gmail.com > <javascript:>> wrote: > > > > > > On Sunday, October 12, 2014 1:27:27 PM UTC-7, Aaron Meurer wrote: > >> > >> I don't think integrate() tries any simplification. Ideally it > >> shouldn't have to. > > > > > > Why not? It seems to me quite the opposite. That is, integration is > > much easier if the input is first converted to some canonical form > > (or one of a few canonical forms). > > > > RJF > >> > >> > >> Aaron Meurer > >> > >> On Sun, Oct 12, 2014 at 6:12 AM, Francesco Bonazzi > >> <franz....@gmail.com> wrote: > >> > > >> > > >> > On Sunday, October 12, 2014 1:50:10 AM UTC+2, Aaron Meurer wrote: > >> >> > >> >> That's correct. If integrate() returns an unevaluated Integral, it > >> >> means the algorithm couldn't compute an integral. The fu() function > is > >> >> able to simplify this expression (it equals 2*sin(x)), so > >> >> integrate(fu(fx), x) works. > >> >> > >> > > >> > Why is fu( ) not attempted in the integrate( ) algorithm? > >> > > >> > -- > >> > You received this message because you are subscribed to the Google > >> > Groups > >> > "sympy" group. > >> > To unsubscribe from this group and stop receiving emails from it, > send > >> > an > >> > email to sympy+un...@googlegroups.com. > >> > To post to this group, send email to sy...@googlegroups.com. > >> > Visit this group at http://groups.google.com/group/sympy. > >> > To view this discussion on the web visit > >> > > >> > > https://groups.google.com/d/msgid/sympy/6014ba22-a647-4e51-9905-730eadb5fd26%40googlegroups.com. > > > >> > > >> > For more options, visit https://groups.google.com/d/optout. > > > > -- > > You received this message because you are subscribed to the Google > Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send > an > > email to sympy+un...@googlegroups.com <javascript:>. > > To post to this group, send email to sy...@googlegroups.com > <javascript:>. > > Visit this group at http://groups.google.com/group/sympy. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/sympy/b04a7673-6ea0-4f3b-82ab-fef23babde38%40googlegroups.com. > > > > > > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/b0d0723d-14db-4bea-9c69-858bc44b0222%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
