#4741: [with patch, needs review again] Implement S-integral point finding for
elliptic curves over Q
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.2
Component: number theory | Resolution:
Keywords: |
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Comment (by cremona):
OK, so I found 2 more trivial bugs in kodaira which only mattered in the
tamagawa_exponent() function used (only) in S_integral_points and
padic_elliptic_log functions. Fixed, and tested that tamagawa_exponent()
works on all curves in the database to 6000, with all bad primes for each.
(Sorry, I have not checked that this covers all Kodaira types, but I think
so. The code even failed on 1 curve of conductor 15.)
That revealed a but in pari_curve(), for example 903b3, where the default
pari precision was not enough. I now test for this (with try: ... except
PariError) and double the precision on failure, continuing until success.
The crazy thing is that I remember fixing that bug before, but it must
have been while working on something which never got submitted (or is
bitrotting on trac perhaps;)).
Next I tested again the database curves of rank at least 2 with S=[2,3,5].
No problems until 2175c3, and that just takes a long time. So I think it
is safe to proceed (famous last words, but it's my bedtime). The
*-fix3.patch contains the above-mentioned fixes and also adapts the
doctests to agree with the output from the enhanced p-adic precision which
I forgot earlier.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4741#comment:16>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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