Changes between Version 4 and Version 7 of Ticket #15483


Ignore:
Timestamp:
Feb 12, 2014, 10:46:34 AM (9 years ago)
Author:
Peter Bruin
Comment:

It seems that the bug is caused by a precision problem in subst, called by nfrealsign in ell.gp. The following GP input demonstrates this (using the latest version of ell.gp, see #11005):

\r src/ext/pari/simon/ell.gp
b = -1554544300737274875964190134520312870631312460283689944298138572669148295776039072867720281361776956435252620954745928376624817557704277432961924925312*y + 23524523971732905757341977352314040726186200302188191824300117738073539522011689544444863977622786771332621915440577829842674416407299864303146477224320
a = Mod(b, y^2 - 229);
\p 38                    \\ default precision
K = bnfinit(y^2 - 229);
nfrealsign(K, a, 1)      \\ result: 1
nfrealsign(K, a, 2)      \\ result: -1  (wrong)
subst(b, y, K.roots[2])  \\ result: -7.695704335233296721 E112, incorrect to this precision
\p 500                   \\ increase precision
K = bnfinit(y^2 - 229);
nfrealsign(K, a, 1)      \\ result: 1
nfrealsign(K, a, 2)      \\ result: 1
subst(b, y, K.roots[2])  \\ result: 55550556624985845118007242443189926820306719407.796355955086894963616120700422308457186069825115395206111444495243228840597412527828358943327267422898011087182852030228685210492253493260963313348652457717717703991690402543456279919008587884729307897541432624377818611055431792706380900043638904108307170236335925883131494247446074384269328376967381902948861789570537169455258630011202296209679102466188417

The value of K.roots does not seem to be the problem; the roots are calculated correctly to the requested precision.

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  • Ticket #15483

    • Property Milestone changed from sage-6.1 to sage-6.2
    • Property Dependencies changed from to #11005
  • Ticket #15483 – Description

    v4 v7  
    2525An error occurred while running Simon's 2-descent program
    2626}}}
    27 It appears that a certain number field element is expected to be a square, but in fact isn't.
    28 
    29 The bug is not fixed by first changing to an integral model.
    30 
    31 See #11041 for other bug reports related to Denis Simon's script, some of which may be caused by the fact that Sage currently uses an outdated version.
     27The problem is apparently that the square root of `norm(zc)` (which is indeed a square) is not computed due to a precision bug; see comment:7 below.