Changes between Initial Version and Version 2 of Ticket #11023


Ignore:
Timestamp:
03/25/11 06:18:01 (11 years ago)
Author:
weigandt
Comment:

Ooops! I misread the documentation, which says that analytic_rank returns an integer that is *probably* the analytic rank of E, as opposed to *provably*.

Perhaps the documentation should be changed to make this clearer. The letters b and v are right next to each other on the keyboard.

Much like #1848 we should probably put a proof=False flag here with the current implementation and try to run something as provable as possible for a proof=True. It seems reasonable that this could be done at least in the case of analytic rank 0.

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  • Ticket #11023

    • Property Summary changed from analytic_rank() should set rank() and gens() when it returns 0 to Add proof=False and proof=True flags analytic_rank()
  • Ticket #11023 – Description

    initial v2  
    770
    88sage: E.rank()
    9 Unable to compute the rank with certainty (lower bound=0).
    10 This could be because Sha(E/Q)[2] is nontrivial.
    11 Try calling something like two_descent(second_limit=13) on the
    12 curve then trying this command again.  You could also try rank
    13 with only_use_mwrank=False.
    14 ---------------------------------------------------------------------------
    159BOOM!
    16 
    1710RuntimeError: Rank not provably correct.
    18 
    1911}}}
    2012
    21 We could also set the rank to 1 if the analytic rank is provably 1, but it seems customary only to set the rank when we can also set the generators, so that shouldn't be done until improved Heegner point functionality is available.
     13I suppose because analytic_rank() returns an integer that is *probably* the analytic rank, not *provably* the analytic rank. For example:
     14
     15{{{
     16sage: EllipticCurve([0,0,1,-7,36]).analytic_rank()
     174
     18}}}
     19
     20We should keep the current implementation under a flag of proof=False, and see how much can be said for proof=True. It seems like we should at least be able to prove that a curve of smallish conductor has analytic rank 0 without too much trouble.