Am Dienstag, den 26.07.2011, 06:11 -0500 schrieb Barton Willis:
> Generally these stricter defaults involve calling sign or csign inside a
> simplifying function. This leads to undocumented behavior:
>
> (%i71) m : matrix([abs(x), log(exp(sqrt(x)))],[5,7]);
> (%o71) matrix([abs(x),sqrt(x)],[5,7])
>
> (%i74) m : matrix([log(exp(sqrt(x))),abs(x)],[7,5]);
> (%o74) matrix([sqrt(x),x],[7,5])
>
> The order matrix elements are simplified isn't documented. Another example
>
> (%i85) m : matrix([abs(x), if x > 0 then log(exp(sqrt(x))) else 42],[5,7]);
> (%o85) matrix([abs(x),if x>0 then sqrt(x) else 42],[5,7])
>
> (%i86) m : matrix([if x > 0 then log(exp(sqrt(x))) else 42, abs(x)],[7,5]);
> (%o86) matrix([if x>0 then sqrt(x) else 42,x],[7,5])
>
> Finally, sign & csign are somewhat slow functions (speed depends on fact database).
I will add more comments about the topic of this thread. But first, a
look at the reported bug of this posting. It is very interesting bug and
it is an old bug. The examples of this posting do not show the bug in
Maxima versions before 5.22, but the origin of the bug is very old.
First, an example with the current Maxima version. The problem is, that
the sign of the second call in a compound expression or in a list
depends on the first expression.
Maxima version: 5.24post
Maxima build date: 17:6 7/26/2011
Host type: i686-pc-linux-gnu
Lisp implementation type: SBCL
Lisp implementation version: 1.0.45
These are the expected results:
(%i1) sign(sqrt(x));
(%o1) pz
(%i2) sign(x);
(%o2) pnz
A compound statement with a wrong result for the sign of x:
(%i3) (sign(sqrt(x)), sign(x));
(%o3) pz
A list with a wrong result for the sign of x:
(%i6) [sign(sqrt(x)), sign(x)];
(%o6) [pz, pz]
Again the wrong results with Maxima 5.10:
Maxima version: 5.10.0
Maxima build date: 21:56 3/14/2011
host type: i686-pc-linux-gnu
lisp-implementation-type: SBCL
lisp-implementation-version: 1.0.45
(%i2) (sign(sqrt(x)), sign(x));
(%o2) pz
(%i3) [sign(sqrt(x)), sign(x)];
(%o3) [pz, pz]
In the examples from this posting the columns of the matrices are
evaluated and simplified like a list. In Maxima 5.22 a call to the
function csign was included for the log function, the second call to
csign is from the abs function. The function csign behaves similar to
the function sign and has the same bug. The second call gives a wrong
result. The problem is easy to see when tracing the function csign.
I suppose that the origin of the bug are some global variables in the
function sign which have old values from a first call.
The bug is not related to the functionality of the log function, but the
extension of the functionality shows an old bug.
Dieter Kaiser