README

This page contains supplementary material to the paper "Hadamard ranks of algebraic varieties".

How to use the code?

This repository contains two Jupyter Notebooks in SageMath, a SageMath object and a text file.

• In order to use the notebooks: we recommend installing SageMath using conda-forge, then in the sage environment you can install Jupyter Notebook;
• In order to use the SageMath objects: download the files in the same folder used by SageMath or by Jupyter Notebook. You can load the object sample.sobj with name F by typing F = load('sample.sobj').

What does this repository contain?

• notebook_expected_defectivecases_SV.ipynb: a Jupyter Notebook in SageMath regarding, among other things, the computational cases left to prove Corollary 4.10 and 4.12;
• notebook_expected_defectivecases_SV.pdf: a printed version of the notebook above;
• notebook_experiments_conjecture_SV.ipynb: a Jupyter Notebook in SageMath with some experiments that confirm Conjecture 1 from the paper in many small cases;
• notebook_experiments_conjecture_SV.pdf: a printed version of the notebook above;
• sigma_2_rnc_6_Hadamard_square_eqn.sobj: a SageMath object containing the degree 18 polynomial with 2088 monomials in the variables x0,...,x6 defining the second Hadamard power of the second secant variety to the rational normal curve of degree 6;
• sigma_2_rnc_6_Hadamard_square_eqn.txt: a text file containing the text version of the above polynomial. The polynomial is written in Python format, so exponentiation is denoted by **. You can easily search and replace it by ^ if you wish.

Acknowledgements

We thank Yulia Alexandr and Bernd Sturmfels for sharing with us the polynomial contained in the file sigma_2_rnc_6_Hadamard_square_eqn.sobj.