On Oct 2, 2009, at 9:30 PM, rjf wrote:

> hey, factoring-testing guys..
> If you make up factoring problems this way, you are probably not doing
> much testing of the real factoring algorithms.

Actually, given this bug has been in Sage for so long, the real issue  
is that for several years no one had tested "easy" factorizations  
such as this--everyone was worried about timing and testing the  
"hard" ones.

> Repeated factors like
> this of different degree are detected by so-called square-free
> factorization.
> The time to factor F in Maxima is, to the resolution of the clock,
> 0.0000 seconds on
> a 3GHz Intel machine.
>
> F can also be entirely factored by the sqfr program, which uses a 5
> line program involving
> differentiation, GCD, and division.  So the problem is essentially no
> harder than factoring f and g separately.
>
> There are papers that show how to construct polynomials that are
> difficult to factor.
>
> I dunno about the Sage wrapper problem.  If that's the difficulty,
> maybe the subject line is wrong.

Yes, it was all about the wrapper (pari ignores the content, and  
there was a bug in reconstructing it). The subject perfectly  
describes the symptom, and was helpful in locating the cause.

- Robert



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