Re: Another damn simplifying problem: ArcTan
- To: mathgroup at smc.vnet.net
- Subject: [mg59988] Re: Another damn simplifying problem: ArcTan
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Sat, 27 Aug 2005 04:11:25 -0400 (EDT)
- References: <dek7hq$a2t$1@smc.vnet.net> <demm3s$rd1$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Mathieu McPhie <m.mcphie at fz-juelich.de> wrote: > Sorry, I got my x's and y's mixed up, and so I was more curious about > why "M" can't simplify the following: > > Simplify[ArcTan[x,-y]+ArcTan[x,y]] > > This can be simplified by choosing x > 0, and not if x < 0. Which > according to the range of the ArcTan function should also evaluate to 0. As you noted, we have In[4]:= Simplify[ArcTan[x,-y] + ArcTan[x,y], x>0] Out[4]= 0 In[5]:= Simplify[ArcTan[x,-y] + ArcTan[x,y], x<0] Out[5]= ArcTan[x,-y] + ArcTan[x,y] I was a bit surprised that Mathematica simplified in the first case but not the second. But in fact, when x < 0, ArcTan[x,-y] + ArcTan[x,y] is not always 0: If y = 0 and x < 0, then ArcTan[x,-y] + ArcTan[x,y] equals 2*Pi. Of course, y = 0 is the special case, and so if we specify that y is nonzero, we might well hope for the sum to be simplified to 0. Alas, we are disappointed. For example, In[6]:= Simplify[ArcTan[x,-y] + ArcTan[x,y], x<0 && y>0] Out[6]= ArcTan[x,-y] + ArcTan[x,y] David Cantrell