Index of /~maseap/progs/chabnf

      Name                    Last modified       Size  Description

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