Critical Points of Discrete
Periodic Operators

This page accompanies the article Critical Points of Discrete Periodic Operators, providing the code used to check the examples mentioned in section 5. We also present some additional graphics. For each example you will need the following m2 file in your directory so helper functions can be called.

In these examples we take the periodic Schrödinger operator over the corresponding graphs displayed below. We also display the Newton polytope of the characteristic equation of the matrix representation of the operator.

Note that in each example, the output is recorded in the Macaulay2 code as comments. For additional details and context see the paper.

Dense graph from Example 5.3 Macaulay2 code

Dense graph from Example 5.4 Macaulay2 code

Dense graph from Example 5.5 Macaulay2 code

Research supported in part by Simons Collaboration Grant for Mathematicians 636314.