Hello all, Although I'm certainly not competent in elliptic curves, I spent some time trying to identify this bug more precisely, and I believe the problem stems from Dp_valued_series; could someone help us identify which of these two outputs is correct? More details can be found on the trac page, and a basic summary is below:
http://trac.sagemath.org/sage_trac/ticket/9457#comment:9 Without the patch, we have: sage: E = EllipticCurve('53a1') sage: Et, D = E.minimal_quadratic_twist() sage: lp = Et.padic_lseries(5) sage: lps = lp.Dp_valued_series(4,quadratic_twist=D, prec=4) sage: lps (O(5^4) + (3 + O(5))*T + O(5)*T^2 + (4 + O(5))*T^3 + O(T^4), O(T^4)) With the patch, we have: sage: E = EllipticCurve('53a1') sage: Et, D = E.minimal_quadratic_twist() sage: lp = Et.padic_lseries(5) sage: lps = lp.Dp_valued_series(4,quadratic_twist=D, prec=4) sage: lps (O(5^4) + (3 + O(5))*T + O(5)*T^2 + (4 + O(5))*T^3 + O(T^4), O(5^5) + (4*5 + O(5^2))*T + O(5^2)*T^2 + (2*5 + O(5^2))*T^3 + O(T^4)) best, Niles On Jul 31, 9:17 am, "King, Simon" <simon.k...@nuigalway.ie> wrote: > Hi! > > Trying to review #9457, I found the following: > sage: R.<T> = QQ.completion(5,5)[[]] > sage: R > Power Series Ring in T over 5-adic Field with capped relative precision 5 > sage: O(T^2) == 0 > False > > Shouldn't the answer be True, because O(T^2) is indistinguishable from zero? > At #9457, niles provides a patch that fixes it. Unfortunately, > sage.schemes.elliptic_curves.sha_tate.Sha.an_padic relies on the wrong answer. > > More precisely, > sage: EllipticCurve('53a1').sha().an_padic(5) > results in an error if O(T^2)==0 returns True. > > Could please someone competent in elliptic curves explain how this can be > fixed? > > Cheers, > Simon -- 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
