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
<http://portal.acm.org/author_page.cfm?id=81100450376&coll=DL&dl=ACM&trk=0&cfid=110554171&cftoken=23981166>;
R. J. Fateman
<http://portal.acm.org/author_page.cfm?id=81100507003&coll=DL&dl=ACM&trk=0&cfid=110554171&cftoken=23981166>;
Published in:
? Proceeding
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and
algebraic computation