Re: Series and Sqrt problem (a bug?)

*To*: mathgroup at smc.vnet.net*Subject*: [mg86961] Re: Series and Sqrt problem (a bug?)*From*: "David W.Cantrell" <DWCantrell at sigmaxi.net>*Date*: Thu, 27 Mar 2008 08:18:59 -0500 (EST)*References*: <fsd6o6$9h0$1@smc.vnet.net>

GS <vokaputs at gmail.com> wrote: > Numerically Mathematica defines square root of a positive number as a > positive number: > In[1]:= Sqrt[2.] > Out[1]= 1.41421 > > It is careful enough not to simplify a square root of a square: > In[2]:= Sqrt[x^2] > Out[2]= Sqrt[x^2] > because x can be either positive or negative. > > However, when I specify that x approaches minus infinity, and use > Series, it assumes that Sqrt[x^2] is equal to x: > In[4]:= Series[Sqrt[x^2], {x, -Infinity, 1}] // Normal > Out[4]= x > > It does the same thing when x approached plus infinity: > In[5]:= Series[Sqrt[x^2], {x, Infinity, 1}] // Normal > Out[5]= x > > This does not seem right to me, and caused grievances in my recent > research problem. In case it might help, note that In[11]:= Assuming[a < 0, Simplify[Normal[Series[Sqrt[x^2], {x, a, 1}]]]] Out[11]= -x David