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.
CITATION STYLE
Andersson, M., & Wulcan, E. (2017). On the effective membership problem for polynomial ideals. In Trends in Mathematics (pp. 91–109). Springer International Publishing. https://doi.org/10.1007/978-3-319-52471-9_6
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