#4525: [with patch, needs review] LLL-reduction of elliptic curve bases (with
resulting speed enhancement to integral_points())
----------------------------+-----------------------------------------------
Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: elliptic curve |
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Comment (by cremona):
Replying to [comment:1 malb]:
> > I implemented the LLL-reduction via pari's lllgram function
>
> Is there any particular reason you are not using Sage's fpLLL based LLL
reduction? It is (supposed to be) much faster, but maybe the speed of the
LLL is negligible for your application? Just curious.
>
Unless I am mistaken, fpLLL only works on *integer* matrices, where the
input is a basis for the lattice. The same is true of NTL's LLL code.
What we need here is LLL on a lattice given only the real (floating point)
gram matrix; there is no underlying integer lattice.
It's the same reason why reduced_basis() for number fields uses pari, and
also why mwrank does not LLL-reduce its bases in the first place!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4525#comment:2>
Sage <http://sagemath.org/>
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