Re: Unexpected warning with ArcTan
- To: mathgroup at smc.vnet.net
- Subject: [mg71777] Re: Unexpected warning with ArcTan
- From: "dimitris" <dimmechan at yahoo.com>
- Date: Wed, 29 Nov 2006 02:56:07 -0500 (EST)
- References: <ekh7ab$sar$1@smc.vnet.net>
ArcTan[Simplify[1/(1/2 + (1/2)*(-1 + 1/E^63))]] ArcTan[2*E^10] Strangely, In[42]:= ArcTan[1/(1/2 + 1/2*(-1 + 1/E^10))] ArcTan[1/(1/2 + 1/2*(-1 + 1/E^20))] ArcTan[1/(1/2 + 1/2*(-1 + 1/E^30))] ArcTan[1/(1/2 + 1/2*(-1 + 1/E^40))] Out[42]= ArcTan[1/(1/2 + 1/2*(-1 + 1/E^10))] Out[43]= ArcTan[1/(1/2 + 1/2*(-1 + 1/E^20))] Out[44]= ArcTan[1/(1/2 + 1/2*(-1 + 1/E^30))] Out[45]= Power::"infy" : "Infinite expression \!\(1\/0.`\) encountered." ArcTan[1/(1/2 + 1/2*(-1 + 1/E^40))] Regards Dimitris Ï/Ç Andrew Moylan Ýãñáøå: > Hi all. > > 1/(1/2 + (1/2)*(-1 + 1/E^63)) is an exact expression that's equal to > 2*E^63: > > 1/(1/2 + (1/2)*(-1 + 1/E^63)) // Simplify > gives > 2*E^63 > > Now, evaluating > ArcTan[2*E^63] > gives > ArcTan[2*E^63] > > Evaluating > ArcTan[1/(1/2 + (1/2)*(-1 + 1/E^63))] > similarly gives > ArcTan[1/(1/2 + (1/2)*(-1 + 1/E^63))] > but first it issues the following warnings: > > Power::"infy" : "Infinite expression \!\(1\/0.`\) encountered." > Power::"infy" : "Infinite expression \!\(1\/0.`\^1.`\) encountered." > > The warnings suggest finite- or machine-precision arithmetic is being > used somewhere (1/0.); but this is an exact expression. > > If ArcTan is replaced by e.g. ArcSin the same warnings are generated. > If it is replaced by e.g. Sin, no warnings are generated. Either way, > Mathematica returns the exact expression unchanged. > > Can anyone explain the origin of these warnings? > > Cheers, > Andrew