Computing minimal finite free resolutions
An algorithm to construct a minimal resolution for a graded submodule \(M\) of a free graded module over a polynomial ring is presented. Let \(m_1,\dots,m_d\) be a minimal basis of \(M\). The peculiarity of the proposed algorithm consists in the successive construction of the minimal basis for \(\text{Syz} (m_1, \dots, m_d)\) at every step in the process of running Buchberger's algorithm to obtain the Gröbner basis. Additional improvements, e.g., using the Poincaré series are indicated. Results of the computation for several examples are presented.
scientific article; zbMATH DE number 1025692