
Re: Handling branch cuts in trig functions
Posted:
Mar 24, 2013 11:06 AM


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 halfplane ("left" or "right") the complexvalued 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.

