Re: polredabs failure

[Igor Schein <igor@txc.com>]

On Thu, Oct 09, 2003 at 02:02:07PM -0400, Igor Schein wrote:
> Hi,
> 
> ? p1=x^16-4*x^15-20*x^14+80*x^13+138*x^12-712*x^11+736*x^10+1200*x^9-8138*x^8+9288*x^7+1904*x^6-25248*x^5+73988*x^4-19184*x^3+41192*x^2+69456*x+30724;
> ? p2=x^16 + 66*x^12 + 3627*x^8 + 48114*x^4 + 531441;
> ? p1==polredabs(p1)
> 1
> \\ p1 already *reduced*
> ? poldegree((v=polcompositum(p1,p2))[#v])
> 16
> \\ isomorphic
> ? norml2(polroots(p1))
> 91.81780460041328907655758261
> ? norml2(polroots(p2))
> 87.63560920082657815311516524
> \\ so we should have polredabs(p1)==p2
> 
> Thanks
> 
> Igor

Actually, here's a better IMO way to present this problem:

? v=polredabs(x^16-4*x^15-20*x^14+80*x^13+138*x^12-712*x^11+736*x^10+1200*x^9-8138*x^8+9288*x^7+1904*x^6-25248*x^5+73988*x^4-19184*x^3+41192*x^2+69456*x+30724,4);
? eval(Set(vector(#v,k,norml2(polroots(v[k])))))
[87.63560920082657815311516524, 91.81780460041328907655758261, 91.81780460041328907655758262]

Thanks

Igor