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Re: Handling branch cuts in trig functions
Posted:
Mar 25, 2013 8:52 AM


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 squareroot of the square of that is itself, not its absolute value. (Assuming principal branch.)
 G. A. Edgar http://www.math.ohiostate.edu/~edgar/



