LLL convergence issue

[Igor Schein <igor@txc.com>]

Hi,

I found the following polynomial to be suprisingly hard:

{
x^72 - 36*x^69 - 108*x^68 + 576*x^66 + 648*x^65 + 7722*x^64 - 10848*x^63 + 2
7864*x^62 + 71928*x^61 - 151479*x^60 - 180144*x^59 - 1613412*x^58 - 3526704*
x^57 + 11084553*x^56 - 10584432*x^55 - 76345344*x^54 + 100241388*x^53 - 1640
55618*x^52 + 889724592*x^51 + 2270475360*x^50 - 9124649352*x^49 + 7434826587
*x^48 + 15371556624*x^47 - 49511492352*x^46 + 216470817164*x^45 - 1889237901
51*x^44 - 210503975472*x^43 + 2320108616700*x^42 - 3050229497544*x^41 - 2012
71100886*x^40 + 5634519503040*x^39 - 26474822631072*x^38 + 24686100778248*x^
37 + 30438936351627*x^36 - 67491229420656*x^35 + 244532799741924*x^34 + 8226
4721405688*x^33 - 202451647636197*x^32 - 211060378973376*x^31 + 742473885000
312*x^30 - 2976634371353796*x^29 - 335544830780670*x^28 + 426597868893216*x^
27 + 1313108347236696*x^26 + 2643541811261064*x^25 + 11095206442345728*x^24 
- 4890951353368080*x^23 + 6779895332135040*x^22 + 14854448984525136*x^21 + 8
424178075747215*x^20 - 39332972051432064*x^19 - 79087872055187636*x^18 - 122
125005890004744*x^17 - 59117462759089620*x^16 + 107469153057980880*x^15 + 23
3081198081681616*x^14 + 218091821306896800*x^13 + 74509657103569104*x^12 - 7
3281579504272640*x^11 - 127416021916178880*x^10 - 89692674549166080*x^9 - 27
117023934047040*x^8 + 8463490208308224*x^7 + 15966233326628352*x^6 + 1034447
4203152896*x^5 + 4583220663598848*x^4 + 2009377194163200*x^3 + 8224488265236
48*x^2 + 252655230523392*x + 43626479858688
}

When I run polred(,1) on it at \g{n>0}, I get these:

  ***   Warning: increasing prec in get_red_G; new prec = 90
  ***   Warning: increasing prec in get_red_G; new prec = 226
  ***   Warning: increasing prec in get_red_G; new prec = 498
  ***   Warning: increasing prec in get_red_G; new prec = 1042

I've run polred(,1) on polynomials with larger coefficient and of
large degrees, and never had this problem before.

Thanks

Igor