This directory contains the Mathematica files I
used for chapter 6, the chapter which gives the
local analysis of the Hessian.  There are 4 files in
this directory:

hessian1:  This computes the Hessian of the energy
functionals at the TBP.  You can use Mathematica to
compute the eigenvalues of the matrix, or you can get
it to manipulate the characteristic polynomial as I
did in the paper.  The bounds we get for the 5
functions are {10,24,36,43,1448}

hessian2:  This computes all the first partials of the
Hessian - i.e., the third partials of the energy.  The
goal of the chapter is to show that the third partials
are not too large, and this file contains the final
calculation.  For G3,G4,G5,G6 we get a global bound 
of 500 from the other terms in the Taylor series expansion.  
For G10 (which is all we need - we don't have to 
directly compute G10_hat) we get a global bound of 1600.
the bounds we get are {1,2,4,12,1091}.

bound1:  This computes the term M8 from Chapter 6.

bound2: This computes the terms mu4,mu5,mu6,mu7 from
Chapter 6, by taking the corresponding partial
derivatives and evaluating them at the TBP.  
