%i arises when simplifying a square root in real domain

One possibility is to additionally assume that -1 < a. Then

  (%i1) assume(-1 < a,a< 1)$

  (%i2) ratsimp(1/sqrt(a**2/(1-a**2)+1));
  (%o2) sqrt(1-a^2)

Another possibility is 

  (%i1) (domain : complex, m1pbranch : true)$

  (%i2) ratsimp(1/sqrt(a**2/(1-a**2)+1));
  (%o2) 1/sqrt(-1/(a^2-1))

--Barton

________________________________________
From: maxima-bounces at math.utexas.edu [maxima-bounces at math.utexas.edu] on behalf of Jocelyn Etienne [jocelyn.etienne at ujf-grenoble.fr]
Sent: Thursday, October 04, 2012 07:17
To: maxima at math.utexas.edu
Subject: %i arises when simplifying a square root in real domain

Dear all,

I am having trouble with maxima when using square roots of the form
sqrt(1-a**2), as in some situations they get simplified into
%i*sqrt(a**2-1).

E.g., even with assume(a<1), if I try to get back to sqrt(1-a**2) from
this modified form:

(%i20) ratsimp(1/sqrt(a**2/(1-a**2)+1));
                                          2
(%o20)                         - %i sqrt(a  - 1)

It is then very awkward, as rootscontract e.g. would make the mistake of
writing %i=sqrt(-1), and get the wrong sign.

I could not find a boolean to tell maxima to avoid factoring out sqrt(-1),
does it exist?

Thanks.

--
Jocelyn ?TIENNE                           Research Scientist of the CNRS
Laboratoire Interdisciplinaire de Physique        Universit? de Grenoble
Jocelyn.Etienne at ujf-grenoble.fr   www-liphy.ujf-grenoble.fr/link/etienne
On leave at U. Cambridge until Dec 2012,  www.pdn.cam.ac.uk/staff/sanson
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