Hi All, I am now at the SAGE22 workshop and directly asked William Stein concerning this. He showed me a line
proof.number_field(False) Then we can turn off the certification process and the decomposition may work. Thanks, Chan-Ho On May 7, 10:20 am, Chan-Ho <chanho.m...@gmail.com> wrote: > Hi All, > > This is a continuation of the > questionhttp://www.mail-archive.com/sage-support@googlegroups.com/msg16973.html > > I am trying to decompose a fractional ideal into primes in a number > field (I use online SAGE.) > > I have a Number Field in a2 with defining polynomial > x^6 - 15*x^5 - 514*x^4 + 5312*x^3 + 83552*x^2 - 422208*x - 4272768 > and want to decompose Fractional ideal (3). > (SAGE can check this is not a prime ideal.) > However, "factor()" or "prime_above()" did not work because of the > Minkowski bound error. > > Thus, I tried to compute this using the following code: > > K_f2_bnf = gp(K_f2.pari_bnf()) ; K_f2_bnf ; > ideal = K_f2_bnf.idealprimedec(3) ; ideal ; > ideal1 = K_f2_bnf.idealprimedec(3)[1] ; ideal1 ; > ideal2 = K_f2_bnf.idealprimedec(3)[2] ; ideal2 ; > ideal3 = K_f2_bnf.idealprimedec(3)[3] ; ideal3 ; > ideal4 = K_f2_bnf.idealprimedec(3)[4] ; ideal4 > > I think that this code does not make errors, and the output was the > following. > > [3, [215, 8, 2, 2, 0, 2]~, 1, 2, [0, -1, -1, -1, 0, -1]~] > > To change this output (PARI ideals) to SAGE (SAGE ideals), I used > > from sage.rings.number_field.number_field_ideal import > convert_from_idealprimedec_form ; > convert_from_idealprimedec_form(K_f2, ideal1) > > But the Minkowski error occured again here. > This means that the Minkowski error comes from the translation between > PARI and SAGE? > Is there a better method to compute this in SAGE? > > Cheers, > > Chan-Ho > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group > athttp://groups.google.com/group/sage-support > URL:http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
