This directory has the Mathematica calculations
which accompany my paper

Pentagram Rigidity for Centrally Symmetric Octagons

You just load the file into Mathematica and the
relevant tests and quantities will print out.
Here is a run-down on the files.


main_formulas.m

This file has the formulas for the main
quantities defined in Chapter 2.
Nothing gets printed when you load
this file, but you can look up the
defined quantities and play with them.


verify_basics.m

This file checks that the invariants F1 and F2
really are invariants of the maps T3 and Delta.
The file also checks how the symmetries from
Chapter 2 interact with the invariants.

verify_commute.m

This file verifies that the Hamiltonian vector fields
X1 and X2 Poisson commute with respect to the symplectic form.


verify_symplectic.m

Ths file verifies that the map Delta preserves
the symplectic form.  The 3 files verify_symplectic.m
and verify_basics.m and verify_commute.m together
justify the proof of our Integrability Theorem.


verify_map formula.m

This file verifies that the formula we give for the
map T3 agrees with the geometrically constructed
version.


verify_gradient.m

This file verifies that the stored versions of
the Hamiltonian vector fields X1, X2, G are
the same as what we get by actually computing
these from the invariants F1,F2,G.


verify_XG.m

This file verifies that the 5 directional
derivatives from Lemma 2.4 are correct.


verify_dependence_set.m

This file checks that the crazy polynomial
Y defined in Section 3.1 really does vanish
on the pair F1,F2 when they are evaluated on
points of the dependency set.


verify_resultant.m

This file shows that the reultant function h
really does factor into the functions
phi1,...,phi9.


verify_reversal_lemma2.m

This file checks the properties of the map
iota5 which are mentioned in the
Reversal Lemma 2.

calc_sqrt_I.m

This file does the calculations giving the
formula for the map sqrt{I} in Chapter 2
of the paper.


calc_iota3.m

This file shows that the geometric definition of
iota3, in terms of duality, agrees with the
given formula.


calc_nonvanish.m

This file does the calculations for the 9 cases of
the proof of the Non Vanishing Lemma in Chapter 3.


calc_hessian.m

This file does the Hessian calculation related to the
local concavity of nice loop in Chapter 5.




