#9330: Documentation for sha_tate.py not quite looking right
-------------------------------+--------------------------------------------
Reporter: kcrisman | Owner: cremona
Type: defect | Status: new
Priority: minor | Milestone: sage-4.5
Component: elliptic curves | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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When you look at
[http://www.sagemath.org/doc/reference/sage/schemes/elliptic_curves/sha_tate.html
this], there are a number of things wrong or confusing in the
documentation.
Most importantly, several instances of Sha should have ticks, probably.
But are they referring to the mathematical object
{{{
`Sha`
}}}
or the computer structure of the class
{{{
``Sha``
}}}
? If I knew what was intended (given that the distinction is quite
small), I would do this patch myself. But it looks like sometimes the
group is intended, other times the class object.
In line 198,
{{{
You can increase the `descent_second_limit` (in the above example
}}}
should have double ticks.
We also get the following warning:
{{{
sage-4.4.4/local/lib/python2.6/site-
packages/sage/schemes/elliptic_curves/sha_tate.py:docstring of
sage.schemes.elliptic_curves.sha_tate.Sha.bound_kato:12: (WARNING/2)
Definition list ends without a blank line; unexpected unindent.
}}}
this probably refers to
{{{
THEOREM (Kato): Suppose `L(E,1) \neq 0` and `p \neq 2, 3` is a
prime such that
- `E` does not have additive reduction at `p`,
- the mod-`p` representation is surjective.
Then `{ord}_p(\#Sha(E))` divides
`{ord}_p(L(E,1)\cdot\#E(\QQ)_{tor}^2/(\Omega_E \cdot \prod c_q))`.
}}}
but I'm not sure.
In line 756 we have
{{{
We get no information the curve has rank 2.::
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9330>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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