I am in school full time now so I can't get into this. It's like taking
the positive square root or the negative one, or so it seems to me, the
uninformed.
Rich
From: Richard Fateman
Sent: Friday, November 12, 2010 10:23 AM
To: Richard Hennessy ; Maxima - list
Subject: Re: [Maxima] caps complex tests
On 11/12/2010 6:19 AM, Richard Hennessy wrote: Is this a related bug?
radcan(sqrt((x^2-2*x+1)/x));
(x - 1)/sqrt(x)
radcan(sqrt(x-2+1/x));
(x - 1)/sqrt(x)
both answers are below the x axis from zero to 1. So integrate gives -4/3.
shouldn't there be a minus sign in front?
No.
Radcan uses what it calls a Positive Real Interpretation on the radicand.
As x-> positive (real) inf,
the 3 expressions are equivalent, and that is what radcan simplifies them
to.
The Macsyma documentation has this ...
%E_TO_NUMLOG default: FALSE
When set to TRUE, for "r" some rational number, and "x" some
expression, %E^(r*LOG(x)) will be simplified into x^r .
Caveat: RADCAN makes assumptions which can cause problems with
branches. So it needs to be used with care.
E.g. When LOGEXPAND is ALL, RADCAN((a^b)^c); gives a^(b*c)
which is not valid when a=-1,b=2,c=1/2 .
RADCAN((a*b)^c); gives a^c*b^c which is not valid when
a=-1,b=-1,c=1/2 .
RADCAN(log((c-b)^2)); gives 2*log(c-b) which is not
valid when b=2,c=1 .
RADCAN(sqrt(1/x)); gives 1/sqrt(x) which is not valid
when x=-1 .
.........
more info in in my thesis, online at
http://portal.acm.org/citation.cfm?id=888687
or
Simplification of radical expressions
Authors: B. F. Caviness
R. J. Fateman
Published in: ? Proceeding SYMSAC '76 Proceedings of the third ACM
symposium on Symbolic and algebraic computation