Re: [Maxima-discuss] Avoiding trig in calculus solutions

[Barton W. <wi...@un...>]

If you get an expression that involves atan2(sin(x), cos(x)), you can try to clean it up with a tellsimpafter rule. Maybe something like

(%i2)  matchdeclare(xxx, lambda([q], true))$

(%i3)  tellsimpafter(atan2(sin(xxx), cos(xxx)), xxx - 2*%pi  * ceiling((xxx-%pi)/(2*%pi)))$

(%i4)  atan2(sin(x), cos(x));
(%o4) x-2*%pi*ceiling((x-%pi)/(2*%pi))

Assuming -%ip < x <= %pi cleans up this mess:
(%i5)  assume(-%pi < x, x <= %pi)$

(%i6)  atan2(sin(x), cos(x));
(%o6) x

Or was there something else that was overly complex?  Would a simple assume clean it up?

You should check that the function  xxx --> xxx - 2*%pi  * ceiling((xxx-%pi)/(2*%pi)  is OK—it’s a bit tricky for me to remember.

--Barton

From: Michael Gough<mailto:inn...@gm...>
Sent: Saturday, September 30, 2023 12:59 PM
To: <max...@li...><mailto:max...@li...>
Subject: [Maxima-discuss] Avoiding trig in calculus solutions

Non-NU Email

Hi gang,

I have a calculus problem and Maxima's solution is riddled with atan2 and sin and cos. I want to invoke some e ratpolywhatever declaration to get rid of those.

Mike