Transforming an angle into [-Pi, Pi)

Questions
1

I have a strange problem with the Mod-function when used for transforming any angle \[Omega] into the half-open interval [-\[Pi], \[Pi]). This is done by Mod[\[Omega], 2 \[Pi], -\[Pi]]:

Plot[Mod[\[Omega], 2 \[Pi], -\[Pi]], {\[Omega], -3 \[Pi], 3 \[Pi]}]

6506b1.png
6506b1.png558×302 10.7 KB

This transformation does not work without error at the bounds [Omega] = …, -360°, -180°, 180°, 360°, …
Instead, we have to use:

If[ [Omega] == [Pi] Floor[N[ [Omega] / [Pi] ]], -[Pi], Mod[ [Omega] ,2 [Pi] , -[Pi] ] ]

For details, see this attached notebook “220109 Transforming an Angle.nb”.

Note: This was done with Wolfram desktop version 13.0.0, but happens as well with version 12.3.1 and version 12.0.0 on Windows 10 Pro (64 bit).

220109 Transforming an Angle.nb (110 KB)

2

BTW: How can I write or copy special characters like Pi into the community editor?

3

It is mentioned in READ FIRST . Example:

Evaluate TexForm with the expression as argument

TeXForm[\[Omega] == \[Pi] Floor[N[\[Omega]/\[Pi]]] // HoldForm]
(* \omega =\pi  \left\lfloor N\left[\frac{\omega }{\pi }\right]\right\rfloor *)

Copy the output and paste it in the editor, bracketed between $

\omega =\pi \left\lfloor N\left[\frac{\omega }{\pi }\right]\right\rfloor

4

Thanks Hans. I didn’t remember that.

5

Sorry, I had a minor error within my code. The correction must read:
\text{If}[\omega \neq 0\land \omega =\pi Floor[ N[\omega/\pi] ] ,-\pi ,\text{Mod}[\omega ,2 \pi ,-\pi]]

I had forgotten the case \omega =0.

For details, see the attached slightly changed notebook “220109b Transforming an Angle.nb”.

220109b Transforming an Angle.nb (114 KB)

6

Hi Werner,
You can also use this tool for special characters