Re: Another damn simplifying problem: ArcTan
- To: mathgroup at smc.vnet.net
- Subject: [mg59979] Re: Another damn simplifying problem: ArcTan
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Sat, 27 Aug 2005 04:11:07 -0400 (EDT)
- References: <dek7hq$a2t$1@smc.vnet.net> <demlli$ra8$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Carl K. Woll" <carlw at u.washington.edu> wrote: > "Mathieu McPhie" <m.mcphie at fz-juelich.de> wrote in message > news:dek7hq$a2t$1 at smc.vnet.net... > > 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] > > Unfortunately the above isn't zero, even for real x: > > In[6]:= > ArcTan[-.1,1]+ArcTan[.1,1] > Out[6]= > 3.14159 But ArcTan[-x,1] + ArcTan[x,1] is always Pi. Wouldn't it be nice if Mathematica made that simplification? > > Note, I want something more complicated than this obviously. Actually > > want something like > > > > Simplify[ArcTan[-x,y]+ArcTan[x,y]] How about Sign[y]*Pi if y is a nonzero real? So, for a "generic" simplification, ignoring the case y = 0, we could just give Sign[y]*Pi. Or, if we don't want to ignore the case y = 0, we could give something which is slightly messier, such as (2*UnitStep[y] - 1)*Pi. In any event, it would be nice to have a simplification which gets rid of ArcTan, together with any apparent dependence on x. David Cantrell