Re: from range restriction to domain restriction

*To*: mathgroup at smc.vnet.net*Subject*: [mg72602] Re: from range restriction to domain restriction*From*: Peter Pein <petsie at dordos.net>*Date*: Thu, 11 Jan 2007 05:24:55 -0500 (EST)*References*: <eo4o86$mgn$1@smc.vnet.net>

Chris Chiasson schrieb: > If I wanted to ensure that Sqrt[x] was always a real number, perhaps > as a condition on Piecewise, I would say Im@Sqrt@x==0 (or > Element[Sqrt@x,Reals], but Mathematica doesn't like to simplify that). > In my real case, x isn't a symbol - and it comes from the output of > some other commands. However, I also know that Element[x,Reals], so I > was wondering if there is a way to make Mathematica do the following: > > (part of) input: > Im@Sqrt@x==0 > > output: > x>0 > > If someone knows how to do this (other than the obvious Cases + > pattern transformation), I would appreciate being told how. Thank you. > Hi Chris, is Reduce[ComplexExpand[Im[Sqrt[x]], x] == 0, x] --> x >= 0 acceptable? You would have to do sth. like expr/.{Assuming[a_,ex_]:>Reduce[...],Simplify[ex_,a_]:>... and so on} I guess I would use the Menu->Find->Find... to replace all "Im@Sqrt@==" with "0<=" ;-) Sorry, I've got no better idea :-( Peter