Re: FindRoots?

*To*: mathgroup at smc.vnet.net*Subject*: [mg112280] Re: FindRoots?*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Tue, 7 Sep 2010 06:08:23 -0400 (EDT)

On 7 Sep 2010, at 06:03, Mark McClure wrote: > On Mon, Sep 6, 2010 at 4:13 AM, Andrzej Kozlowski <akozlowski at gmail.com> wrote: > >> The point of my original post was not that Mathematica should not have >> a functionality to produce complete solutions of numerical equations but >> that leasing packages from users is not the right approach for Wolfram. >> ... >> I know of only one exception that WRI has made to this rule: the >> Combinatorica package, co-authored by Steven Skiena > > Actually, Mathematica contains quite a lot of code authored by users. > The palettes introduced in V7 were created by Eric Schultz of Walla > Walla Community College. Much of the geodetic capabilities were > authored by Thomas Mayer of The University of Connecticut. Stan Wagon > of Macalester tells me that he's contributed functionality to the > kernel. Sometimes, Wolfram even hires such authors; the author of the > IMTEK Mathematica supplement is such and example. If you click on > "Credits" in the About Mathematica box, you'll find a huge amount of > third party software used by Mathematica. Well, as far as I can tell, none of these concern not "packages" that are already available for download from the Internet (free or not). I think such cases are very different and normally the authors should take full responsibility for them themselves. There may be of course exceptions (arguably Combinatorica was one of them) but they should be v. rare. > > As far as this specific discussion goes, I must say that I find Reduce > to be rather mysterious. The documentation actually states that > "Reduce[expr,vars] reduces the statement...". It's clearly very > powerful but it's primarily algebraic. Thus it doesn't seem > appropriate in many situations - if a function is defined via a > numerical technique, for example. > It really very much depends what you mean by "algebraic". If you think that all branches of mathematics where you actually prove things are "algebraic" than I agree. The methods Reduce uses to solve non-polynomial equations are baed on theorems in complex analysis, such as Rouche's theorem. Also, if you evaluate this Reduce[AiryAi[E^x] ==== E^-x + 1 && Abs[x] < 2, x] you will see a message referring to something that is not normally considered "algebraic". Andrzej