I On 21 Sep., 16:23, rjf <[email protected]> wrote: > On Sep 20, 7:14 am, maldun <[email protected]> wrote: > > > > > That's true, but it is important that automated routines do good error > > estimation > > especially for smooth functions. > > That is pretty easy if you have a smooth function. So perhaps we need > a program > to test if a function is smooth :) > > > But it is the wrong way to say: Hey I can't do it > > for every case, so why bother? > > The example I gave is smooth simple function but causes already > > troubles. > > The example you gave is what is called "oscillatory" and is a well > known kind > of problem that can be done -- if you recognize it as oscillatory -- > by methods > devised by Filon, or more recently Levin, Iserles, Olver, ... But is > difficult > by regular quadrature programs. > I'm aware of that and it was the reason I gave that example. And from the comments above from Fredrik Johansson it seems to me that it was not a such bad test...
Perhaps I should sort out my point before we cause misunderstandings: It's true that a user familiar with numerics knows about such behavior. But since Sage is a program for a wide range of users, I think it's important to offer user friendly integration routines also for people who are beginners, or not so familiar with that topic. Perhaps I'm wrong, but isn't it a good thing to open sage to a broader audience? And of course all packages are included in Sage, so it's no big deal to use them if I want for example specific integration points. And I don't claim here it's some job for overnight. I'm well aware of this, but I think it should be considered as long time goal, and I don't see anything wrong about that, and I believe it deserves some discussion. And since I offer my own manpower and knowledge to work on this improvements, I personally think it's nothing wrong about making suggestions, and point out problems. But it's quite disturbing for me that something simple like integrate(sin(x^2),x,0,pi).n() already crashes. But I think there are already some little improvements, which are not such big deal, e.g. offer the possibility for the user to set a specific algorithm in the .n(), or distinguish between integral.n() and n(integral) > There is a great deal written about integration. Perhaps instead of > offering > to do some basic programming you could offer to read some books or > papers on > numerical integration. Probably the documentation for NIntegrate > would be a start. I think to read documentation and papers is a natural thing. But I'm not a pro in Python, and will hopefully change that. I'm just claiming that I can't help out with too advanced programming skills. -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
