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/