interesting ROUND4 behavior

[Igor Schein <igor@txc.com>]

Hi,

I found 3 polynomials, namely polzagier(18,3), polzagier(34,3) and
polzagier(42,11), that behave funny when I run factorpadic(pol,2,r).
I run it at \g5 and grep for 'bound for resultant coeffs:'.  Here's
what I see for polzagier(18,3)

r=24
bound for resultant coeffs: 2^131
bound for resultant coeffs: 2^35702
bound for resultant coeffs: 2^140
bound for resultant coeffs: 2^40
r=120
bound for resultant coeffs: 2^131
bound for resultant coeffs: 2^100223
bound for resultant coeffs: 2^140
bound for resultant coeffs: 2^40
r=720
bound for resultant coeffs: 2^131
bound for resultant coeffs: 2^503151
bound for resultant coeffs: 2^140
bound for resultant coeffs: 2^40

As you can see, the number on the 2nd line gets big with the increase
of r, while the rest of the lines stay the same.

The numbers get really huge for the other 2 polynomials.

The only pattern I noticed is that all 3 polynomials (eventually)
split into 2 factors, but there're other Zagier polynomials, which
split into 2 factors but don't exhibit this unstable behavior - the
2nd line is missing for those polynomials. 

Xavier, any idea why ROUND4 behaves like that?

Thanks

Igor