Pruning algorithm of the Taylor resolution - an implementation

• Philippe Gimenez ^[1] ; Elvira Pérez-Callejo ^[2]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
  2. [2] Universitat Jaume I

     Universitat Jaume I

     Castellón, España

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 91-94
• Idioma: inglés
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• Resumen

  • We propose MATLAB and Singular implementations of the pruning algorithm described in [11 that starting from the Taylor resolution of a monomial ideal, return the Betti diagram of another resolution which is much smaller and sometimes minimal. The algorithm strongly depends on the way we order the monomial generators. This opens the door to studying an optimal ordering of the generators in order to reach a minimal free resolution for some families of monomial ideals.