Resolving Decompositions of Polynomial Modules
Co-author(s): Mario Albert
Reference: Computer Algebra in Scientific Computing - CASC 2016, V.P. Gerdt, W. Koepf, W.M. Seiler, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2016, Lecture Notes in Computer Science 9890, pp. 15-29
Description: We provide a unifying framework for some results of [32, 89, 41] and for some generalisations of them. Starting with the axiomatic definition of a resolving decomposition as a basis inducing simultaneous combinatorial decompositions of the generated module and an associated monomial module and a normal form, we show first a Schreyer Theorem for the underlying basis and discuss then the construction of free resolutions based on it.
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