Abstract
Let U be a submodule of P 8, P a ring of multivariate polynomials, let G 1, …, G r generate U, and let F 1:= Σb 1j G j ,…, F m := Σb ij G j with b mj ∈ P. If a set of generators for the module of syzygies w. r. t. (G 1,…, G r ) is given, then one problem is to compute a set of generators for the module of syzygies w. r. t. (F 1,…, F m ) and to decide whether F 1, …, F m also generate U. For this purpose an algorithm is presented which is similar to the Gauß-Jordan algorithm in linear algebra. It uses Gröbner bases techniques for modules and allows to solve some constructive problems in connection with modules.
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© 1991 Springer Science+Business Media New York
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Möller, H.M. (1991). Computing Syzygies à la Gauß-Jordan. In: Mora, T., Traverso, C. (eds) Effective Methods in Algebraic Geometry. Progress in Mathematics, vol 94. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0441-1_22
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DOI: https://doi.org/10.1007/978-1-4612-0441-1_22
Publisher Name: Birkhäuser, Boston, MA
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