README

How to use the code?

This repository contains Macaulay2 files and a Jupyter Notebook in Macaulay2.

• In order to use the Jupyter Notebook: install Jupyter Notebook and add the Macaulay2 kernel, following the guide reported in the following GitHub page. Then, download the Jupyter Notebook file in the same folder used by Jupyter Notebook;
• In order to use the Macaulay2 files: download the files in the same folder used by Macaulay2. If you want to use the functions and the results of the computation contained in the file sample.m2, you should use the command load "~/sample.m2".

What does this repository contain?

• M2_Hadamard.ipynb: a Jupyter Notebook in Macaulay2 with all the computations related to the paper;
• Hadamard_curves_P3.m2: a file containing a function that performs the Hadamard product of two curves L and R in 3-dimensional projective space defined by equations over the rationals. After loading this file, you can define the ideal I1 of L in the variables x0,...,x3, the ideal I2 of R in the variables y0,...,y3 and type X = preimage_Hadamard(I1+I2) to get the ideal of L \star R in the variables z0,...,z3;
• example_3_3.m2: a file containing the computation related to Example 3.3 of the paper;
• lemma_3_8.m2: a file containing the computation related to Lemma 3.8 of the paper;
• example_4_6.m2: a file containing the computation related to Example 4.6 of the paper.