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
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- Re: Re: Another damn simplifying problem: ArcTan
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
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- Another damn simplifying problem: ArcTan
- From: Mathieu McPhie <m.mcphie@fz-juelich.de>
- Another damn simplifying problem: ArcTan