Martin RUBEY <rubey@labri.fr> writes:
> On Mon, 3 Mar 2003, Richard Fateman wrote:
>
> > Sometimes changing the GCD algorithm to one without
> > a bug in it helps. gcd:subres for example.
>
> this should probably read
>
> gcd:spmod; gcd:ez; work,
>
> gcd:subres; gcd:red; don't
> Quotient by a polynomial of higher degree
> -- an error. Quitting. To debug this try DEBUGMODE(TRUE);)
[...]
> (C15) taylor(asin(sin(x)+e),x,0,2);
This is not really a problem with the algorithm itself. As I tried to
explain in my message
http://www.math.utexas.edu/pipermail/maxima/2003/003694.html
the main problem is that we don't really control the consequences of
setting ALGEBRAIC:TRUE (which is implicitly done by TAYLOR). Using
the notation of the cited message, Maxima sometimes thinks that some
element is only in the quotient field of R/I but not in R/I itself.
Hence error messages like `Quotient by a polynomial of higher degree'.
Note that I assumed here that I is a prime ideal (in order to have an
integral domain R/I). In fact, another problem is that this is not
necessarily the case, but algorithms like SUBRESGCD are applied,
anyway. So there are some fundamental mathematical problems and not
mere bugs here.
By the way, the example above works with my SUBRESGCD patch (but the
other example given by Stavros doesn't, presumably because of the
reasons just explained).
Wolfgang