On Sun, Feb 6, 2011 at 2:42 AM, koffie <[email protected]> wrote: > > > > On Feb 6, 6:49 am, Rob Beezer <[email protected]> wrote: >> William, Volker, >> >> Thanks for the replies. Kernels for the rationals go to IML and for >> number fields they go to PARI. Does either of those rely on linbox?
No, neither uses Linbox. IML and PARI are totally independent from IML. M.derickx, thanks for confirming that the output are isomorphic, so this is an acceptable change. >> >> Here's the requested output - three different number fields are >> evident. Thanks for the help. >> >> Rob >> > > The defining polynomials of the number fields might be different, but > the numberfields themselves are actually isomorphic. The squarefree > part of the discriminant of the polynomial is 3 in all cases so the > numberfield obtained is just adjoining the square root of 3. The code > below shows that the three awnsers generated by the code are at least > up to isomorphims the same: > > K.<x>=QQ[] > for a,f in [(-x-1,x^2 + 4*x + 1),(1/2*x+1/2,x^2 - 2*x - 11), > (-1/2*x-1/2,x^2 + 6*x - 3)]: > f.discriminant().squarefree_part() > K.<b>=QQ.extension(f) > K(a).minpoly() > > 3 > x^2 - 2*x - 2 > 3 > x^2 - 2*x - 2 > 3 > x^2 - 2*x - 2 > > -- > To post to this group, send an email to [email protected] > To unsubscribe from this group, send an email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
