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• W44736522 abstract "AbstractPolynomial algebra offers a standard, powerful, and robust approach to handle several important problems in geometric modelling and other areas. A key tool is the discriminant of a univariate polynomial, or of a well-constrained system of polynomial equations, which expresses the existence of multiple (or degenerate) roots. We describe discriminants in a general context, and relate them to an equally useful object, namely the resultant of an overconstrained polynomial system. We discuss several relevant applications in geometric modelling so as to motivate the use of such algebraic tools in further geometric problems. We focus on exploiting the sparseness of polynomials via the theory of Newton polytopes and sparse elimination.KeywordsDiscriminantGeometric applicationResultantSparse polynomialMathematics Subject Classification (2010)13P15" @default.
• W44736522 created "2016-06-24" @default.
• W44736522 creator A5055316106 @default.
• W44736522 creator A5087662998 @default.
• W44736522 date "2014-01-01" @default.
• W44736522 modified "2023-09-25" @default.
• W44736522 title "Sparse Discriminants and Applications" @default.
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• W44736522 doi "https://doi.org/10.1007/978-1-4471-6461-6_4" @default.
• W44736522 hasPublicationYear "2014" @default.
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