The specification of sqrfree()

[Richard B. Kreckel]

Hi,

On Wed, 9 Jan 2002, Roberto Bagnara wrote:
[...]
> During this work we have found that GiNaC's documentation
> is not very precise about what a "square-free factorization" is.

Yeah, the defintion given there is not very strict...  :-)

> Below you find what we believe is a sensible definition
> (which also seems to be compatible with the current implementation).
> Please, check if that is also consistent with the specification
> of GiNaC (we would like to avoid relying on non-features that
> may disappear on a subsequent release).
> 
>   A polynomial p(X) in Q[X] is said <EM>square-free</EM>
>   if, whenever two polynomials q(X) and r(X) in Q[X]
>   are such that p(X) = q(X)^2*r(X), q(X) is constant.

I had to read this three times.  Do we agree to read `X' ad a n-tuple of
symbols?  Then I thought this definition does not account of the
square-free factorization of p(a,b,c,d) = a*c - b*c - a*d + b*d into
(a-b)*(c-d), which is now handled -- this being the change that went into
version 1.0.1.  But now methinks your definition does indeed cover this.
Isn't there a canonical definition for the multivariate case in the
literature?

And at least over Z[X] and Q[X], you can rely on this extended behaviour.  
Maple and Mathematica do the same and I need it for my work.

If you think it over again with the above case in mind and find that it's
okay, a patch for the documentation would be welcome.

Regards
     -richy.
-- 
Richard B. Kreckel
<Richard.Kreckel at Uni-Mainz.DE>
<http://wwwthep.physik.uni-mainz.de/~kreckel/>