Class mwrank_MordellWeil

Create a \class{mwrank_MordellWeil} instance.

INPUT:
    curve -- \class{mwrank_EllipticCurve} instance
    verbose -- bool
    pp -- int
    maxr -- int

Overrides: object.__init__

helper for pickle

Overrides: object.__reduce__

(inherited documentation)

File: sage/structure/sage_object.pyx (starting at line 86)

Overrides: structure.sage_object.SageObject.__repr__

(inherited documentation)

This function allows one to add points to a mwrank_MordellWeil object.

Process points in the list v, with saturation at primes up to
sat.  If sat = 0 (the default), then saturate at all primes.

INPUT:

    v -- a point (3-tuple of ints), or a
         list of 3-tuples of integers, which define points on the curve.
         
    sat -- int, saturate at primes up to sat, or at all primes if sat=0.
    

Saturate this subgroup of the Mordell-Weil group.

INPUT:
    max_prime (int) -- (default: 97), saturation is performed
                       for all primes up to max_prime
                       
    odd_primes_only (bool) -- only do saturation at odd primes

OUTPUT:
    ok (bool) -- True if and only if the saturation
                 is provably correct at \emph{all} primes.
    index (int) -- The index of the group generated by
                   points in their saturation
    saturation (list) -- list of points that form
                         a basis for the saturation

\begin{notice}
We emphasize that if this function returns True as the first
return argument, then the points it found are saturated at
\emph{all} primes, i.e., saturating at the primes up to
\code{max_prime} are sufficient to saturate at all primes.
Note that the function might not have needed to saturate at
all primes up to \code{max_prime}.
It has worked out what prime you need to saturate up to,
and that prime is $\leq $ \code{max_prime}.

\end{notice}

\begin{notice}
Currently (July 2005), this does not remember the result of
calling search.  So calling search up to height 20 then
calling saturate results in another search up to height 18.
\end{notice}

   

Search for new points, and add them to this subgroup of the
Mordell-Weil group.

INPUT:
    height_limit -- float (default: 18) search up to
                    this logarithmetic height.
           On 32-bit machines, h_lim MUST be < 21.48 else
           $\exp(h_lim)>2^31$ and overflows.