Solving trig functions



Dear Aleksas,

Your email is replying to one sent in April [1], and since you didn't
use the reply feature in your email client, even that was hard to work
out. Since the contents of your email is almost entirely code (unlike
Barton's email), it's quite hard to tell what you're trying to do here.

Are you trying to demonstrate some code you've written to use
to_poly_solve in order to solve trigonometric equations? If so, it needs
a little bit of work: In your definition, I notice the code

  makelist(ev(s[i],%z0=k),k,-10,10)

Obviously this is a bit of a hack: what happens if the first solution in
the interval of interest is at z0 = 11?

I'm not sure whether it's possible to write a function that takes the
output from to_poly_solve and an interval and then computes the relevant
solutions. After all, you've basically got a function f(n) : Z ? R
together with an interval [a,b] and you're trying to compute the
pre-image f??([a,b]). Maybe there's something more clever that you can
do if you have extra information about f, or maybe even something
numerical using find_root - after all absolute precision isn't required
since we're mapping from the integers. If you had some code that
attempted to solve that sort of problem, it'd be really cool!

Anyway, another way to interpret your email is that you were trying to
help Daniel (the original poster) with his problem. If so, you probably
need to explain more thoroughly what your code does and why: a black box
that may or may not solve ones problems isn't particularly enlightening.

I'd be very interested if you had some ideas on how to approach the
problem of finding roots trig roots in a given interval though - I feel
like I'm missing something obvious in what I wrote above.

Yours,

Rupert

[1] http://thread.gmane.org/gmane.comp.mathematics.maxima.general/37797
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