Igor Schein on Sun, 12 Oct 2003 15:07:00 -0400 |
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Re: polredabs failure |
On Fri, Oct 10, 2003 at 08:08:00PM +0200, Karim BELABAS wrote: > On Fri, 10 Oct 2003, Igor Schein wrote: > > On Fri, Oct 10, 2003 at 05:46:04PM +0200, Karim BELABAS wrote: > >> On Thu, 9 Oct 2003, Igor Schein wrote: > >>> Now, continuing the same topic: > >>> > >>> %1 = x^16 - 4*x^15 + 8*x^14 - 8*x^13 + 6*x^12 - 16*x^11 + 40*x^10 - 32*x^9 - 50*x^8 + 160*x^7 - 176*x^6 + 40*x^5 + 140*x^4 - 192*x^3 + 112*x^2 - 32*x + 4 > >>> ? polredabs(%) > >>> %2 = x^16 - 4*x^15 + 12*x^14 - 36*x^13 + 88*x^12 - 164*x^11 + 252*x^10 - 324*x^9 + 354*x^8 - 324*x^7 + 252*x^6 - 164*x^5 + 88*x^4 - 36*x^3 + 12*x^2 - 4*x + 1 > >>> ? polredabs(%) > >>> %3 = x^16 - 8*x^15 + 36*x^14 - 108*x^13 + 244*x^12 - 436*x^11 + 636*x^10 - 780*x^9 + 831*x^8 - 780*x^7 + 636*x^6 - 436*x^5 + 244*x^4 - 108*x^3 + 36*x^2 - 8*x + 1 > >>> \\ Takes 2 iterations to stabilize > >> > >> These polynomials have the same norm. All are valid results, and there's no > >> guarantee that iterating polredabs as above stabilizes at all. > > > > But now, after the change mentioned below, it indeed *stabilizes* > > after 1 interation. And I suspect it won't be easy to find another > > example of behavior above - I couldn't so far. > > Now it shouldn't be possible at all. After my change no minimal vector is > ever discarded, and their characteristic polynomials are sorted so as to > remove duplicates. Latest changes broke it again: ? p=x^16-4*x^15+8*x^14-8*x^13+6*x^12-16*x^11+40*x^10-32*x^9-50*x^8+160*x^7-176*x^6+40*x^5+140*x^4-192*x^3+112*x^2-32*x+4; ? v=polredabs(p,4); ? vector(#v,k,#polredabs(v[k],4)) [22, 21, 24, 24, 24, 20, 24, 12, 20, 12, 20, 24] The correct answer is vector(24,x,24). Thanks Igor