Abstract
We discuss the possibility of representing elements in polynomial ideals in ℂN with optimal degree bounds. Classical theorems due to Macaulay and Max Noether say that such a representation is possible under certain conditions on the variety of the associated homogeneous ideal. We present some variants of these results, as well as generalizations to subvarieties of ℂN.
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Andersson, M., Wulcan, E. (2017). On the Effective Membership Problem for Polynomial Ideals. In: Andersson, M., Boman, J., Kiselman, C., Kurasov, P., Sigurdsson, R. (eds) Analysis Meets Geometry. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52471-9_6
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DOI: https://doi.org/10.1007/978-3-319-52471-9_6
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-52469-6
Online ISBN: 978-3-319-52471-9
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