```Date: Mar 26, 2013 1:17 AM
Author: Richard Fateman
Subject: Re: Handling branch cuts in trig functions

this is still nonsense.-3 is a square root of 9, whether the 9 was produced by squaring 3 or squaring -3.-x is a square root of x^2 whether the x^2 was produced by squaring x or -x.It doesn't matter whether x is positive or negative.On 3/25/2013 5:52 AM, G. A. Edgar wrote:> In article <kimoma\$hru\$1@speranza.aioe.org>, Nasser M. Abbasi> <nma@12000.org> wrote:>>>>> But I am using Maple 17?>>>> ----------------------------------->> ans:=simplify(sqrt(sec(x)^2)) assuming x::positive;>>>>                                  1>>                               -------->>                               |cos(x)|this is wrong; see below>>>> simplify(abs(sec(x))- ans);>>                                  0>>well, this should be zero.>> ------------------------------------->>>> Unless x::positive implies x::real (since positive does>> not apply to complex numbers). Is this what you meant?>> Yes, positive implies real.  You will also get that result assuming x> is negative, or assuming x is an integer, and so on.  Not only on the> reals, but also on any subset of the reals we have sqrt(x^2) = abs(x) .If you visualize f(z)=sqrt(z^2) in the complex plane, you can specializeit for real z and see if it corresponds to abs(z).>>>>> So Maxima was wrong then:>>>>    sqrt(sec(x)^2);>>       |sec(x)|>>>> No assumptions!Yes, this is wrong.  The issue, at its core, is that computer algebrasystems are not programmed to deal with multiple-valued objectin a satisfactory way.>>> We cannot tell whether Maxima is wrong unless we know whether Maxima> assumes x is real (when you do not tell it).  Maple assumes x is> complex, as was said.  Perhaps the documentation for Maxima tells you> about this?>> sec(1+i) is about .4983370306+.5910838417*i,> and the square-root of the square of that is itself, not its absolute> value.  (Assuming principal branch.)>
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