analytic_rank crashes

[zimmermann6]

Maybe the following is not feasible, but analytic_rank could crash smoothly.

sage: d=100032426715415089/251987961355200625
sage: E = EllipticCurve([0, -d^3+5*d^2, 0, -8*d^5+8*d^4, 4*d^8-8*d^7+4*d^6])
sage: F = E.minimal_model()
sage: F.analytic_rank(algorithm='cremona')
<type 'exceptions.RuntimeError'>: Error: '  *** elltors: precision too low in torsell.

sage: F.analytic_rank(algorithm='rubinstein')
<type 'exceptions.TypeError'>: unable to convert x (= 6.90579e+20 and is too large) to an integer

sage: F.analytic_rank(algorithm='sympow')
sympow 1.018 RELEASE  (c) Mark Watkins --- see README and COPYING for details
**ERROR** c4 invariant is too large

From John Cremona: the "cremona" version just wraps a gp script, which
needs to have sufficient precision even for ellinit() to work ok here.
Unfortunately this call will run in its own gp session, and it is not
possible for the user to set the precision. (I found the same while
running a lot of examples through Denis Simon's gp scripts). The
solution is to change the wrapper to have a precision parameter, with
some reasonable default for backwards compatibility, which gets passes
through to gp.

Component: algebraic geometry

Issue created by migration from https://trac.sagemath.org/ticket/1234

[JohnCremona]

comment:1

NB I think that all functions which wrap gp scripts should have the ability to set various gp defaults before the scripts are run. Notably the real precision (which is the culprit above), but also in other cases.

This should be easy but tedious -- is there anywhere a list of which functions operate by running a gp script?

jec

[sagetrac-mabshoff]

comment:3

Still an issue with Sage 2.10.2.alpha0.

Cheers,

Michael

[JohnCremona]

comment:4

I can only speak for the first of these, begin responsible for the gp script which computes analytic rank.

This curve has conductor N=690579402364042119390 which is vastly too big for the analytic rank algorithm anyway (it requires the computation of O(sqrt(N)) terms of the L-series).

Also relevant here is that my analytic rank gp code is old. When Magma adopted it, it was vastly improved (by Mark Watkins), which means that for several years I have not used my own gp program at all, let alone developed it. For this curve, I don't think even Magma would succeed in computing its analytic rank.

[sagetrac-mabshoff]

comment:5

What shall we do about this ticket?

Thoughts?

Cheers,

Michael

[JohnCremona]

comment:6

Replying to @sagetrac-mabshoff:

What shall we do about this ticket?

Thoughts?

Cheers,

Michael

Given the fundamental problem that computing the analytic rank increases rapidly with the conductor N (I think it is sqrt(N)), one solution would be to impose a (carefully-chosen but necessarily somewhat arbitrary) cutoff N_max, so that asking for the analytic rank of a curve of conductor>N_max would result in an error.

One way to implement this would be to have N_max a parameter to the analytic rank function, with a default value of (say) 10^6 or 10^7. (I would have to do some experiments to decide on a sensible value). The docstring could explain that the user is allowed to increase this but warn that it may take (effectively) for ever.

[JohnCremona]

comment:7

PS The vale of N_max would presumably be different for the different algorithms supported (sympow, lcalc, etc). I was only thing of the "cremona" algorithm. I also note that the docstring claims that lcalc is the most efficient, but cremona is the default -- that was not my decision!

[williamstein]

Attachment: trac_1234.patch.gz

[williamstein]

comment:8

The attached patch cleans up the exceptions raised, as requested. Also, in the (default) case where Cremona's gp script is used, the precision is automatically doubled until it doesn't fail. I also start the precision at 16 rather than the default, since it will get automatically double if necessary, and it's about 3 times faster usually by using this smaller precision to start:

BEFORE:
sage: E = EllipticCurve('5077a')
sage: time E.analytic_rank()
CPU times: user 0.01 s, sys: 0.01 s, total: 0.02 s
Wall time: 0.21 s


AFTER:
sage: E = EllipticCurve('5077a')
sage: time E.analytic_rank()
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 0.06 s


and another

BEFORE:
sage: time elliptic_curves.rank(4)[0].analytic_rank()
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.50 s
4

AFTER:
sage: time elliptic_curves.rank(4)[0].analytic_rank()
CPU times: user 0.01 s, sys: 0.00 s, total: 0.01 s
Wall time: 0.33 s
4