Re: FindRoots?

*To*: mathgroup at smc.vnet.net*Subject*: [mg112219] Re: FindRoots?*From*: Matthias Bode <lvsaba at hotmail.com>*Date*: Sun, 5 Sep 2010 05:27:39 -0400 (EDT)

Hola: In each re-posting of the original messages, cf. below, the Equal signs appear to increase in number according to two to the power n, n positive integer. Here == I wrote one equal sign. Just ONE. Best regards, MATTHIAS BODE COCHABAMBA/BOLIVIA > Date: Sat, 4 Sep 2010 03:58:24 -0400 > From: akozlowski at gmail.com > Subject: [mg112182] Re: FindRoots? > To: mathgroup at smc.vnet.net > > > On 3 Sep 2010, at 12:10, Gianluca Gorni wrote: > > > > > In my opinion Reduce can replace RootSearch in some > > cases but not in others. > > > > First of all, Reduce has bugs. Here is an analytic function > > that clearly has a real root: > > > > Plot[2 x + Log[-((-1 + 2 x)/(-1 + 2 x^2))], {x, -2, -1/Sqrt[2]}] > > > > Still, Reduce does not see it (as of version 7.0.1): > > > > Reduce[2 x + Log[-((-1 + 2 x)/(-1 + 2 x^2))] ================ 0 && -2 < > > x < -1/Sqrt[2], x, Reals] > > False > > > > (I reported this example to wolfram last year). > > You seem to be using ============ instead of ======== which is a very bas= ic error. In fact > > Reduce[2*x + Log[-((-1 + 2*x)/(-1 + 2*x^2))] ======== 0 && > -2 < x < -Sqrt[2]^(-1), x, Reals] > > x ======== Root[{Log[-((2*#1 - 1)/(2*#1^2 - 1))] + 2*#1 & , > -0.86193624643066461859672257230652325787900736031\ > > 58816695213`20.308604836334766}] > > In[4]:==== $Version > > Out[4]==== "7.0 for Mac OS X x86 (64-bit) (February 19, 2009)" > > > > > > > Next, Reduce has problems with inexact input, and with > > InterpolatingFunction, so that it won't work with > > the output of NDSolve: > > > > sol ======== x /. > > First@NDSolve[{x'[t] ================ x[t] + 2, x[0] ================ = -1}, x, {t, 0, 2}]; > > Reduce[sol[t] ================ 0 && 0 < t < 2, t] > > > > or, say, with functions obtained by interpolating between Locators. > > RootSearch works fine in these cases. > > What are these ================ doing in your code? I don't think they co= uld have been in it when you run it? > > Reduce used exact methods so you have to rationalize the output or use eq= uivalent approaches and it works fine in such cases. You are right that you= can't use it with Interpolating functions since of course they are not ana= lytic. > > > > > > > I have made some interactive panels where I can change the Locators > > with the mouse and I get in real time the roots of the interpolating > > function as big Points in the plot: I can do this with RootSearch, > > but not with Reduce. > > Unfortunately, I can't give these panels to other users, because > > I can't assume that they have RootSearch installed. > > > > I endorse the wish that the functionality of RootSearch were available > > in the kernel. > > > I concede that you make a reasonable case for this sort of capability. Ho= wever, computations of this kind with Interpolating functions are generally= quite unreliable, since the conditions required by FindRoot to work are of= ten not satisfied. I don't think this sort of hit or miss approach is appro= priate for a mathematical solver. Perhaps this sort of capabilities should = be available in a package designed specifically for dealing with interpolat= ing functions (which I don't consider as "mathematical objects"). > > Best regards > > Andrzej >

**Re: FindRoots?**

**Mathlink problem in C**

**Re: FindRoots?**

**Re: FindRoots?**