Re: positive square root

*To*: mathgroup at smc.vnet.net*Subject*: [mg58700] Re: positive square root*From*: Peter Pein <petsie at dordos.net>*Date*: Fri, 15 Jul 2005 03:02:15 -0400 (EDT)*References*: <db57ne$4no$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

paulvonhippel at yahoo schrieb: > I work in a world where the square root is always a positive number. > But Mathematica allows for the possibility of negative square roots. > Two questions arise: > > (1) Is there a way to tell Mathematica that I'm only interested in > positive square roots? > > (2) My current solution is to use, e.g., Abs[Sqrt[z]]. But when > Mathematica echoes this, it puts the Abs function *under* the radical, > so it looks like Sqrt[Abs[z]]. Is this a bug in the display? > Hi Paul, I don't think so. It is just in general easier, to evaluate Sqrt[Abs[z]] than Abs[Sqrt[z]]: In[1]:= Assuming[(x | y) \[Element] Reals, FullSimplify[ {Abs[ComplexExpand[Sqrt[x + I*y]]],(*sqrt first*) ComplexExpand[Sqrt[Abs[x + I*y]]]}]](*abs first*) Out[1]= {(x^2 + y^2)^(1/4)* Abs[Cos[(1/2)*ArcTan[x, y]] + I*Sin[(1/2)*ArcTan[x, y]]], x^2 + y^2)^(1/4)} These are of course equivalent: In[2]:= SameQ @@ Simplify[ComplexExpand[%]] Out[2]= True -- Peter Pein Berlin http://people.freenet.de/Peter_Berlin/