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Re: Another damn simplifying problem: ArcTan

• To: mathgroup at smc.vnet.net
• Subject: [mg59982] Re: [mg59910] Another damn simplifying problem: ArcTan
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 27 Aug 2005 04:11:11 -0400 (EDT)
• References: <200508251033.GAA10111@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 25 Aug 2005, at 11:33, Mathieu McPhie wrote:

> Can someone please explain this to me: (M v4.something)
>
> In:=  Simplify[ArcTan[-x]+ArcTan[x]]
> Out= 0
>
> In:=  Simplify[ArcTan[-x,1]+ArcTan[x,1]]
> Out= ArcTan[-x,1]+ArcTan[x,1]
>
> Note, I want something more complicated than this obviously. Actually
> want something like
>
> Simplify[ArcTan[-x,y]+ArcTan[x,y]]
>
> but above is the easiest example of this infuriating programs problem.
>
> Cheers, Mathieu
>
>


In Mathematica 5.1 the situation does not look much better.


First however, note that


Simplify[ArcTan[x,-y]+ArcTan[x,y],{x>0}]

0

Unfortunatley

Simplify[ArcTan[x,-y]+ArcTan[x,y],{x<0}] returns

ArcTan[x,-y]+ArcTan[x,y] instead of 0.

Adding assumptions on y does not help.

Your formula

ArcTan[x,-y]+ArcTan[x,y]

is not surprisingly harder for Mathematica to simplify since we have:


ArcTan[-x, y] + ArcTan[x, y] /. {x -> 1, y -> -1}


-Pi


ArcTan[-x, y] + ArcTan[x, y] /. {x -> 1, y -> 1}

Pi

  etc.





Still Mathematica ought to manage these cases with assumptions on x  
and y and it doesn't. In fact, for x>0 one can get the answer isn  
this way:


Simplify[ComplexExpand[ArcTan[x, -y] + ArcTan[x, y],TargetFunctions-> 
{Re,Im}], {x > 0}]

0




Andrzej Kozlowski

• Follow-Ups:
  • Re: Re: Another damn simplifying problem: ArcTan
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>

• References:
  • Another damn simplifying problem: ArcTan
    • From: Mathieu McPhie <m.mcphie@fz-juelich.de>