Explicit representation of membership in polynomial ideals |
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Authors: | Mats Andersson Elin Götmark |
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Affiliation: | 1.Department of Mathematical Sciences,Chalmers University of Technology and the University of Gothenburg,G?teborg,Sweden;2.Department of Mathematics and Mathematical Statistics,Ume? University,Ume?,Sweden |
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Abstract: | We introduce a new division formula on projective space which provides explicit solutions to various polynomial division problems with sharp degree estimates. We consider simple examples as the classical Macaulay theorem as well as a quite recent result by Hickel, related to the effective Nullstellensatz. We also obtain a related result that generalizes Max Noether’s classical AF + BG theorem. |
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