tsimplify problem
11-21-2017, 04:10 PM
Post: #1
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
tsimplify problem
With the beta v2, I tried:

tsimplify(atan(cot(pi*x)))
which returned -pi*x-(1/2)*pi
...which isn't correct to the best of my knowledge (doesn't plot the same).
11-21-2017, 04:24 PM
Post: #2
 parisse Senior Member Posts: 1,321 Joined: Dec 2013
RE: tsimplify problem
tsimplify replaces trig expressions with exp and inverse trig with ln then it does simplifications without taking care of complex ln branches, the result is not necessarily valid on the whole complex plane.
11-21-2017, 05:45 PM (This post was last modified: 11-21-2017 05:46 PM by webmasterpdx.)
Post: #3
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: tsimplify problem
That doesn't look like what it did here...???

I mean the results are not equivalent to the input function.
11-22-2017, 10:26 AM
Post: #4
 AlexFekken Member Posts: 151 Joined: May 2016
RE: tsimplify problem
Perhaps Parisse should not have said "complex" because (unlike e.g. exp) tan is already periodic on the real line, and so atan has real branches there, separated by multiples of pi.

So the "simplified" answer is correct, up to a multiple pi, which in my opinion is probably as much as you should expect when you are using variable arguments (as opposed to an explicit numerical argument that would allow you to obtain a "principal value").
11-23-2017, 03:24 AM
Post: #5
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: tsimplify problem
True...
Thx
11-23-2017, 03:30 AM
Post: #6
 webmasterpdx Senior Member Posts: 541 Joined: Sep 2015
RE: tsimplify problem
It's actually valid for x in [-1,0], and y in [-1.5,1.5] approx.
-Donald
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