Index of /~hgallegos/programs/hyperlogsOLD

	Name	Last modified	Size	Description
	Parent Directory		-
	example1.m	06-Mar-2017 12:24	5.9K
	heightdifference.m	06-Mar-2017 12:24	7.7K
	magmaperiods1.m	06-Mar-2017 12:24	21K
	output.txt	06-Mar-2017 12:24	1.5K
	upperbounds.m	06-Mar-2017 12:24	6.8K

This folder contains MAGMA programs related to my PhD thesis.

The file heightdifference.m contains a program for the computation of
a lower bound for the height difference
mu1  leq  h(P) - hcan(P).
This is given by Lemma 2.1.1 and Theorem 2.1.2 on the thesis.

The file upperbounds.m contains programs for the computation of an upper
bound for the size of the integral points on a given hyperelliptic
curve
a y2 = f(x).
This is given by Chapter 3 of the thesis.

The file magmaperiods1.m contains programs for the computations of the
periods of a genus 2 hyperelliptic curve 
y2 = f(x)
defined over the reals by a polynomial of degree 5 or 6 with real
roots only. The periods are computed by Bost and Mestre's algorithm
described in Chapter 4 of the thesis. It also contains programs for
the computation of hyperelliptic logarithms of real points on the
curve. This is an implementation of our algorithm presented in
Chapter 4 of the thesis. The periods and the hyperelliptic logarithms
are computed to as many decimal places required by the user.

The file example1.m computes the integral points on the curve
y2 = x5 - 5x3 - x2 + 3x +1.
This is the curve given in Example 5.4.4 of the thesis. It requires
the files upperbouns.m and magmaperiods1.m in order to run. In
particular, we require to compute periods and hyperelliptic logarithms
of certain real points to a thousand of decimal places.  The
computation of the real periods is done in a matter of seconds.  Each
computation of hyperelliptic logarithms takes less than two minutes.

The file output.txt contains the output of example1.m