# Index of /~maseap/progs/chabnf

Name Last modified Size Description

Parent Directory 14-Jan-2019 06:44 - Parent
FermatI.m 11-May-2009 16:34 3k
FermatII.m 11-May-2009 16:34 1k
JSearch.m 11-May-2009 16:34 10k
JSearch.sig 11-May-2009 16:34 1k
add.m 11-May-2009 16:34 7k
add.sig 11-May-2009 16:34 2k
addChecks.m 11-May-2009 16:34 3k
chabChecks.m 11-May-2009 16:34 3k
g2-jac.m 11-May-2009 16:34 37k
g2-jac.sig 11-May-2009 16:34 8k
integrationChecks.m 11-May-2009 16:34 1k
FermatII.txt 11-May-2009 16:34 39k Text file

This directory contains programs needed for the computational part
of the paper
"Explicit Chabauty over Number Fields" by Samir Siksek
g2-jac.m contains many routines for genus 2 Jacobians over number fields
including an implementation of Chabauty and the Mordell-Weil sieve
as described in the paper
add.m routines for rigourous arithmetic on genus 2 Jacobians over p-Adic fields
JSearch.m routines for:
(1) searching for points on genus 2 Jacobians over number fields
(rather primitive at the moment)
(2) computing all rational points on genus 2 curves over Jacobians
by first computing the Mordell-Weil group (this might very well fail)
and then applying Chabauty and the Mordell-Weil sieve (this will
fail if the Chabauty criterion is not satisfied)
FermatI.m verifies the computations in the paper for $x^2+y^3=z^{10}$
with $y$ odd
FermatII.m verifies the computations in the paper for $x^2+y^3=z^{10}$
with $y$ even
FermatII.txt gives the output for FermatII.m
integrationChecks.m checks that the v-adic integration techniques are giving
the same answers as some other papers and that the results are plausible
chabChecks.m checks that our Chabauty program is working correctly
by giving several instances where it fails whenever
there is more than one rational point in the p-unit ball
addChecks.m several examples that check that our rigourous arithmetic
over local fields is giving the same results as exact operations
over number fields to within the chosen precision