/*********************************************************************
(c) Copyright 2006-2010 Salman Baig and Chris Hall
This file is part of ELLFF
ELLFF is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
ELLFF is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*********************************************************************/
ELLFF (for elliptic curve L-function over function fields) computes
L-functions for non-constant elliptic curves over F_q(t) with
gcd(q,6)=1. It is a C++ library built on top of Victor Shoup's NTL
library and hooks into Sage and PSage via Cython.
Its files are as follows:
* ell_surface.cpp/h: Contain the C++ class for elliptic curves
over a function field, i.e. elliptic surfaces over a finite
constant field, along with basic associated functions and
context switching (a la NTL).
* ell.cpp/h: Contain the C++ class for elliptic curves over finite
fields and the requisite functionality needed to count
points. These curves are assumed to have an elliptic surface
context.
* ellff.cpp: Auto-generated C++ code from ellff.pyx.
* ellff.pyx: Cython interface for ELLFF. In particular, contains
functions to create an elliptic curve over a funtion field as a
Sage object, compute its L-function, form pullbacks and
quadratic twists, and interface with the table of Euler factors
(i.e. traces of Frobenius).
* euler.cpp/h: C++ code to compute tables of Euler factors for a
curve, along with a pullback or quadratic twist of the
curve. This file also computes the coefficients used to compute
the L-function.
* helper.cpp/h: Contains various helper routines for working over
a polynomial ring over a finite field: order elements of F_p[x],
F_q, F_q[x]; convert elements of F_p[x], F_q, F_q[x] to unsigned
longs; enumerate elements in F_p[x], F_q, F_q[x]; evaluate
elements of F_q[x] at element of F_q; and exponentiation in
F_q^*
* interface.h: <SHB: This should be deprecated I think>
* jacobi.cpp/h: Computes the (abstract) Jacobi sum for elements in
F_q^*
* lzz_pEExtra.cpp/h: Contains various helper routines for working
over F_q: table of multiplicative inverses and square roots;
evaluation of the Legendre character; the action of Frobenius;
and context-switching
* lzz_pEratX.cpp/h: Contains code for elements in F_q(t) as
quotients of elements in F_q[t], building on top of NTL's
lzz_pEX code.
