couple of questions about complex expressions


________________________________
From: Raymond Toy [toy.raymond at gmail.com]
Sent: Tuesday, September 25, 2012 16:45
To: Barton Willis
Cc: Robert Dodier; maxima at math.utexas.edu
Subject: Re: [Maxima] couple of questions about complex expressions



On Tue, Sep 25, 2012 at 3:38 AM, Barton Willis <willisb at unk.edu<mailto:willisb at unk.edu>> wrote:
It's a mess. I think domain : complex and  m1pbranch : true is supposed to give the principle branch,
and domain : real and m1pbranch : false the real branch, I think. But sometimes numer matters (and maybe
radexpand too)

OK -- real branch:

  (%i8) block([domain : real, m1pbranch : false], (-8)^(1/3));
  (%o8) -2

Not OK -- principle branch (more-or-less)

  (%i9) block([domain : real, m1pbranch : false, numer : true], (-8)^(1/3));
  (%o9) 2.0*(-1)^0.33333333333333

  (%i10) rectform(%);
  (%o10) 2.0*%i*sin(0.33333333333333*%pi)+2.0*cos(0.33333333333333*%pi)

Isn't %o10 correct, given that domain, m1pbranch, and numer have their default values for rectform?  Even then, what would be the real branch (-1)^(0.333333...) since 0.3333..3 is not 1/3?

Agreed, I would say that %o10 is correct.

--Barton