```Date: Mar 24, 2013 11:06 AM
Author: Axel Vogt
Subject: Re: Handling branch cuts in trig functions

Using Maple 17 for sqrt(sec(x)^2); simplify(%); gives csgn(1/cos(x))/cos(x).Better use t instead of sec(x) = 1/cos(x) to see what is meant, cf the help:1) sqrt(x) represents the "principal square root", defined by the formula    sqrt(x) = exp(1/2 * ln(x)) [they mean: using the pricipal branch of log]2) Without the symbolic option, Maple computes simplify((x^2)^(1/2)) as csgn(x)*x.3) The csgn function is used to determine in which half-plane ("left" or "right")    the complex-valued expression or number x lies. It is defined by    csgn(x) = piecewise(`or`(0 < Re(x), `and`(Re(x) = 0, 0 < Im(x))),   1,                        `or`(Re(x) < 0, `and`(Re(x) = 0, Im(x) < 0)),  -1)4) The value of csgn(0) is controlled by the environment variable _Envsignum0.Note that Maple extends *into* the (usual) branch cut counterclockwise,i.e. as limit from the upper left halfplane into the negative axis.
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