Igor Schein on Fri, 30 Aug 2002 11:08:14 -0400 |
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interesting ROUND4 behavior |
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