Supplementary Materials for Bates-Eklund-Peterson chern number paper


Click here to download an M2 script to run Example 4.3 with symbolic computation in M2, as in our paper.

Click here to download the Bertini and M2 files for the numerical computation of the various chern numbers of Example 4.1 of our paper.

In the directory, you will find a relatively self-explanatory README file that explains what each of the files does and how they are strung together to create the table in Example 4.1 of our paper.

To make a long story short, there is an M2 file -- chern_prog_linked_MASTER -- that produces Bertini input files to find the degrees of various zero-schemes whose generators are constructed from the starting ideal, as described briefly in the README and more thoroughly in the paper. These Bertini input files are named linked_good_final_approach_*. The exception is input_for_degree which simply provides the degree (15) of the starting ideal.

Each Bertini run comes in two phases. First, a randomization of the desired system is run, which will yield some Bertini Theorem junk points. Bertini (the software) can automatically sort junk points in certain settings, but not (currently) in this setting, so phase two eliminates junk points. In phase two, Bertini runs a homotopy that evaluates each solution from phase one in the set of original generators (not squared up). output_zero_counter*mw (a Maple file) will then parse the output file from that Bertini run to find which points are junk points and which are true solutions of the original problem.