Karim BELABAS on Sat, 12 Dec 1998 16:39:38 +0100 (MET) |
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Re: roundoff(?) bug |
[Igor:] > ? A=x^12+16; > ? B=x^12+4*x^9+22*x^6+12*x^3+2; > ? C=x^12-4*x^9+22*x^6-12*x^3+2; > ? setsearch(Set(polred(B)),A) > 2 > ? setsearch(Set(polred(B)),C) > 3 > ? setsearch(Set(polredabs(A,4)),B) > 2 > ? setsearch(Set(polredabs(B,4)),C) > 4 > ? setsearch(Set(polredabs(A,4)),C) > 0 > > First two setsearch() commands verify that all three polynomials > define the same number field. > > The 3rd setsearch() command indicates that B has the same t2-norm as A. > The 4th setsearch() command indicates that C has the same t2-norm as B. > However, > The 5th setsearch() command indicates that C *does not* have the same > t2-norm as A. > > I'll allow myself to speculate that a round-off error occurred > somewhere, probably during the polroots() stage. Since C(-x) = B(x), they do have the same T2-norm. The "bug" is in the documentation: 4: Give all polynomials of minimal T_2 norm. should read: 4: Give all polynomials of minimal T_2 norm (only one of P(x) and P(-x) is given) And in version 2.0.13.alpha, it is actually true (in 2.0.12, you can have duplicates in the output of polredabs(., 4)). Karim. -- Karim Belabas email: Karim.Belabas@math.u-psud.fr Dep. de Mathematiques, Bat. 425 Universite Paris-Sud Tel: (00 33) 1 69 15 57 48 F-91405 Orsay (France) Fax: (00 33) 1 69 15 60 19 -- PARI/GP Home Page: http://pari.home.ml.org