[Maxima-bugs] [maxima:bugs] #4614 atan2 reflection rule

[Barton W. <wil...@us...>]

- **status**: open --> closed
- **Comment**:

Fixed by Commit [eb00d1] master.  Closing this ticket.



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**[bugs:#4614] atan2 reflection rule**

**Status:** closed
**Group:** None
**Created:** Sun Sep 21, 2025 11:11 AM UTC by Barton Willis
**Last Updated:** Tue Sep 23, 2025 05:49 PM UTC
**Owner:** nobody


Consider:
~~~
(%i1)	block([trigsign : true], atan2(-y,x) + atan2(y,x));
(%o1)	0

(%i2)	 block([trigsign : false], atan2(-y,x) + atan2(y,x));
(%o2)	atan2(y,x)+atan2(-y,x)
~~~
But `atan2(-y,x) + atan2(y,x)) = 0` is not an identity for `(x,y)` on the negative real axis; for example
~~~
(%i3)	atan2(0,-1) + atan2(0,-1);
(%o3)	2*%pi
~~~

The user documentation for `trigsign` says that

>  When trigsign is true, it permits simplification of negative arguments to trigonometric functions. 

I expect that in the context of trig-like functions that simplification would use only identities, for example `-sin(x) = sin(-x)`, not conditionally true identities.  

I think it's OK for `trigsign` to suppress using a reflection rule that is an unconditional identity.





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