Date: Mar 25, 2013 8:52 AM
Author: G. A. Edgar
Subject: Re: Handling branch cuts in trig functions

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)|
>
> simplify(abs(sec(x))- ans);
> 0
>
> -------------------------------------
>
> 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) .

>
> So Maxima was wrong then:
>
> sqrt(sec(x)^2);
> |sec(x)|
>
> No assumptions!



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.)

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/