Normalization for modular_symbols is wrong

[williamstein]

The docstring for E.modular_symbol accidentally includes "normalize" twice. I think the first instance, which a user might read first, is wrong and should be deleted (it must have been accidentally left there).

sage: E = EllipticCurve('11a')
sage: E.modular_symbol?
...
        -  ``normalize`` - (default: True); if True, the
           modular symbol is correctly normalized (up to possibly a factor of
           -1 or 2). If False, the modular symbol is almost certainly not
           correctly normalized, i.e., all values will be a fixed scalar
           multiple of what they should be. But the initial computation of the
           modular symbol is much faster, though evaluation of it after
           computing it won't be any faster.
           
        -  ``use_eclib`` - (default: False); if True the computation is
           done with John Cremona's implementation of modular
           symbols in ``eclib``
                
        -  ``normalize`` - (default: 'L_ratio'); either 'L_ratio', 'period', or 'none';
           For 'L_ratio', the modular symbol is correctly normalized
           as explained above by comparing it to ``L_ratio`` for the
           curve and some small twists.
           The normalization 'period' is only available if
...

Apply the patch "trac_14900_modsymdoc.patch".

CC: @categorie

Component: elliptic curves

Author: Chris Wuthrich

Reviewer: William Stein

Merged: sage-5.12.beta3

Issue created by migration from https://trac.sagemath.org/ticket/14900

[JohnCremona]

comment:1

I think you are correct, including the reason why the old version is there. I hope that Chris Wuthrich will confirm.

[chriswuthrich]

exported againast 5.10

[chriswuthrich]

Author: Chris Wuthrich

[chriswuthrich]

comment:2

Attachment: trac_14900_modsymdoc.patch.gz

Yes, that is what happened an I am sorry. I submit a quick patch here that fixes this and a small other issue with this normalisation. If L_ratio fails it now falls back to period. The cases where this makes a real difference, like 1369b1 are too long to be included as a doctest.

In any case, I am writing on a new implementation of modular symbols which will change this normalisation business radically anyway.

[williamstein]

comment:3

Looks good to me. Thanks!

[jdemeyer]

Reviewer: William Stein

[jdemeyer]

Merged: sage-5.12.beta3