I agree with everything Robert proposes (perhaps with some caveats) -- but perhaps sage-nt would be a more appropriate forum?
John 2010/1/27 Robert Miller <[email protected]>: > Hello, > > I recently discovered that the following command does not work: > > sage: EllipticCurve('390g1').quadratic_twist(-191).gens() > > The reason is that Sage tries to find generators using mwrank, and the > height bounds Sage uses by default are set too low: > > ------------------------------------------------------- > Summary of results: > ------------------------------------------------------- > 0 <= rank(E) <= 1 > #E(Q)/2E(Q) >= 2 > > Information on III(E/Q): > #III(E/Q)[phi'] <= 2 > #III(E/Q)[2] <= 2 > > Information on III(E'/Q): > #phi'(III(E/Q)[2]) = 1 > #III(E'/Q)[phi] = 1 > #III(E'/Q)[2] <= 2 > > The following false advice appears in the docstring: > {{{ > HINT: If you would like to control the height bounds used in the > 2-descent, first call the two_descent function with those height > bounds. However that function, while it displays a lot of output, > returns no values. > }}} > The problem with this is that E.two_descent does not cache any > information it computes, so this really doesn't help. > > Now that mwrank is available as a library, I'd like to clean up a few > places in ell_rational_field.py where Sage is using mwrank. I thought > it would be a good idea to open a thread on sage-devel first. I'd like > to do the following: > > 1. E.two_descent should call the mwrank library instead of the shell, > and should cache everything it computes. > 2. E.simon_two_descent should cache exactly the same data. > 3. E.rank should use the library instead of the shell. > 4. E.gens should use the library instead of the shell. > 5. E.gens should simply run indefinitely if sha[2]_an is trivial, or > at least have an option to this effect. Perhaps E.regulator should use > this option, so that E.heegner_index never blows up (right now, it can > fail if the height bounds are not high enough for the curve). > > Please comment on these ideas, I'm hoping to use this thread as a > place to organize my thoughts before I start doing the work. > > -- > Robert L. Miller > http://www.rlmiller.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 > -- 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
