This repository contains the code that was used by the authors to obtain part of the results in the article
Ülo Reimaa, Tim Van der Linden and Corentin Vienne, Associativity and the cosmash product in operadic varieties of algebras, preprint arXiv:2206.12096, 2022.
All mathematical explanations are in the article; use of the code is explained in the file how_to.txt and in the code files themselves. Briefly:
The files generate_equations.singular and solve_equations_*.singular contain code which can be run in the software package Singular. The file version.txt shows which is the precise version we used. First run
Singular -q generate_equations.singular
to generate the file equations.txt which contains the equations. Then run
Singular -q solve_equations_m.singular
to check that the number m in the article is indeed a linear combination of the f[i]. The number m' and proof that the system is inconsistent in characteristic 2 are obtained by applying the same process to solve_equations_mprime.singular and solve_equations_m2.singular. In each case a new file is created which can be opened inside Mathematica to check the outcome: the coefficients obtained by Singular are multiplied with the corresponding equations, the results are added, and what we get is the same number m or m' = mprime or 1. Once inside Mathematica, run the file in question by entering
ToExpression[Import["output-m.mathematica", "Text"]]
% == m
and the likes. Further information can be found in the article. Please contact us by email with any questions you may have.
Ülo Reimaa, Tim Van der Linden and Corentin Vienne
Research of the first author was supported by the Estonian Research Council grant PUTJD948. The second author is a Senior Research Associate of the Fonds de la Recherche Scientifique-FNRS. Research of the third author was supported by the Fonds Thelam of the Fondation Roi Baudouin. Computational resources have been provided by the Consortium des Équipements de Calcul Intensif (CÉCI), funded by the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS) under Grant No. 2.5020.11 and by the Walloon Region.