/*[
 * Copyright 2008  Bharti Pridhnani   bharti@maia.ub.es
 *
 * Permission to use, copy, and distribute this software and its
 * documentation for any purpose with or without fee is hereby granted,
 * provided that the above copyright notice appear in all copies and
 * that both that copyright notice and this permission notice appear
 * in supporting documentation.
 *
 * This 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.
 *
 * This software is provided "as is" without express or implied warranty
 * to the extent permitted by applicable law.
]*/


This program gives you the best bounds found for the Bloch Landau constant,
the first Dirichlet eigenvalue for the laplacian and the expectation of a
Brownian motion for the domain D_{w1w2,R}.

Execute the file

./execution_program.bsh

and it will create some files. The images are the domains which gives the
best bound for each constant. All the files which have the number 001
corresponds to the Bloch Landau constant, 002 to constant 'a' (lambda_D)
and 003 to constant 'b' (expectation). For each case you have two images:

domain001.jpeg
domain001zoom.jpeg

In the first one you can see the domain which is giving the best bound and
in the second one you can see that the domain has inradius 1.

Also it creates you the file iterates.dat. It contains all the iterations
of the method used in doing the minimization to find the best bounds and
the solution.

Then you will have the files

valuesBL.dat
valuesLambdaD.dat
valuesExpectation.dat

These files contains all the values of the bounds calculated in each case
during the process of minimization.

The file boundsconstants.dat contains the value of the three bounds for each
x calculated.

We just want to show the calculations done for this problem, 
it shows the way we have applied one particular instance of the
tchebotarev problem.
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Bharti Pridhnani