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Student Support Forum: 'Dedekind Eta Function and FindRoot' topicStudent Support Forum > General > "Dedekind Eta Function and FindRoot"

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Ben Dundee
09/02/09 1:49pm

Hello all (again)!

The forum mod suggested I post a new thread, with a copy of the notebook I've been working with. For the original description of the problem, see here:

In short, I have a function that is proportional to the Dedekind Eta function to some power:

f(t,s) = eta( i t )^p g(s),

for some function g. When I try to use FindRoot to find the minima of the potential, it gives me an error of about 10% (dt is a derivative wrt t):

In: FindRoot[dt f(t,s) == 0, {{t,12346/10000},{s,2}} ]

Out: t->1.3484(...),s->2.(...)

The answer which FindRoot gives me for s is correct, however, the answer that FindRoot gives me for t is wrong.

It's not that FindRoot is finding the WRONG root, it's that FindRoot isn't finding any root at all! I know that t=1.3484... is not a minima or maxima of f(t,s) because I can graph the function and see that there is no minimum at t=1.3484..., see the attached file. What's worse is that FindRoot is not throwing any error messages, either.

When I use NMinimize or FindMinimum, however, Mathematica finds the correct result. I would like to know if there's some issue with FindRoot (which, in my experience, works faster than NMinimize or FindMinimum) and Dedekind Eta functions.

Anyway, please see the attached notebook for an example of what's going on. It runs in about 10 seconds on my MacBook.

Attachment: bug_report.nb, URL: ,
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