Quasi-Stability versus Genericity

Co-author(s): Amir Hashemi and Michael Schweinfurter

Reference: Computer Algebra in Scientific Computing - CASC 2012, V.P. Gerdt, W. Koepf, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2012, Lecture Notes in Computer Science 7442, pp. 172-184

Description: We compare the leading ideal in delta-regular coordinates (which is by definition quasi-stable) with the generic initial ideal of a polynomial ideal. It is shown that many properties associated with the generic initial ideal also hold for a quasi-stable leading ideal. As a special case we provide alternative proofs for some criteria for componentwise linear ideals. Finally, we study the relationship between Pommaret bases and linear quotients.

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