On Sun, 30 Aug 2009 Dieter Kaiser wrote:
.....
This might be a problem of the simplifier, which does not handle the sqrt
function carefully.
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Dieter, I'm sure you are hyperaware of everything below,
but some mailing list readers might benefit from knowing that
the bug report you have referred to
BUG ID: 1010768 - sqrt(1/z) - 1/sqrt(z) => 0
has a link to the text file:
http://www.math.unm.edu/~wester/demos/ComplexDomain/Macsyma.problems
by Michael Wester of the Mathematics Department at the University of New
Mexico,
Albuquerque, reviewing the use of Macsyma with complex expressions, and
this
review might be useful for some readers.
This file is dated 1999 and uses Macsyma 422.0 for Sparc (Solaris 2.x)
computers.
Lines 128 - 175 appear to show careful and correct treatment of
expr : sqrt(1/z) - 1/sqrt(z);
which is not simplified unless various further information about z is
furnished. declare (z, complex) does not cause simplification, but
remove(z, complex)$ and assume(z > 0)$ causes
ratsimp(expr) --> 0.
forget(z > 0)$ and assume(z < 0)$ causes sqrt(1/z) + 1/sqrt(z);
to be automatically simplified to 0.
Using the principal branch definitions for both w1 = (z)^(1/2)
and w2 = (1/z)^(1/2) , sqrt(1/z) = 1 / sqrt(z) unless
z is real and negative (theta = pi radians), in which case
sqrt(1/z) = - 1 / sqrt(z).
I would welcome an improvement in simplification
of square roots of complex expressions, avoiding tedious
hand work.
Ted Woollett