Matches in SemOpenAlex for { <https://semopenalex.org/work/W331375819> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W331375819 abstract "This chapter is mainly devoted to algorithms for solving certain special zero-dimensional polynomial systems and certain applications. In the first section, we explain a few results on Grobner bases. This enables us to decide in Section 2 whether a polynomial system is zero-dimensional. We use these results to design various algorithms for zero-dimensional systems, for instance computing the multiplication table for the quotient ring and using the multiplication table to compute information about the solutions of zero-dimensional systems. A special case is treated in details in the third section. In the fourth section, we define the univariate representations and use trace computations to express the solutions of a zero-dimensional system as rational functions of the roots of a univariate polynomial. In the fifth section, we explain how to compute the limits of bounded algebraic Puiseux series which are zeros of polynomial systems. In the sixth section, we introduce the notion of pseudocritical points and design an algorithm for finding at least one point in every semi-algebraically connected component of a bounded algebraic set, using a variant of the critical point method. We end the chapter with an algorithm computing the Euler-Poincare characteristic of an algebraic set." @default.
- W331375819 created "2016-06-24" @default.
- W331375819 creator A5032403197 @default.
- W331375819 creator A5057052198 @default.
- W331375819 creator A5061872290 @default.
- W331375819 date "2003-01-01" @default.
- W331375819 modified "2023-10-01" @default.
- W331375819 title "Polynomial System Solving" @default.
- W331375819 cites W1991813962 @default.
- W331375819 cites W1996643891 @default.
- W331375819 cites W2001393258 @default.
- W331375819 cites W2011693299 @default.
- W331375819 cites W2067754486 @default.
- W331375819 cites W2089339786 @default.
- W331375819 cites W32754932 @default.
- W331375819 doi "https://doi.org/10.1007/978-3-662-05355-3_12" @default.
- W331375819 hasPublicationYear "2003" @default.
- W331375819 type Work @default.
- W331375819 sameAs 331375819 @default.
- W331375819 citedByCount "0" @default.
- W331375819 crossrefType "book-chapter" @default.
- W331375819 hasAuthorship W331375819A5032403197 @default.
- W331375819 hasAuthorship W331375819A5057052198 @default.
- W331375819 hasAuthorship W331375819A5061872290 @default.
- W331375819 hasConcept C111919701 @default.
- W331375819 hasConcept C118615104 @default.
- W331375819 hasConcept C134306372 @default.
- W331375819 hasConcept C136119220 @default.
- W331375819 hasConcept C138885662 @default.
- W331375819 hasConcept C17183583 @default.
- W331375819 hasConcept C198082693 @default.
- W331375819 hasConcept C199422724 @default.
- W331375819 hasConcept C202444582 @default.
- W331375819 hasConcept C2780129039 @default.
- W331375819 hasConcept C2780813799 @default.
- W331375819 hasConcept C33923547 @default.
- W331375819 hasConcept C34388435 @default.
- W331375819 hasConcept C41008148 @default.
- W331375819 hasConcept C41895202 @default.
- W331375819 hasConcept C90119067 @default.
- W331375819 hasConcept C9376300 @default.
- W331375819 hasConceptScore W331375819C111919701 @default.
- W331375819 hasConceptScore W331375819C118615104 @default.
- W331375819 hasConceptScore W331375819C134306372 @default.
- W331375819 hasConceptScore W331375819C136119220 @default.
- W331375819 hasConceptScore W331375819C138885662 @default.
- W331375819 hasConceptScore W331375819C17183583 @default.
- W331375819 hasConceptScore W331375819C198082693 @default.
- W331375819 hasConceptScore W331375819C199422724 @default.
- W331375819 hasConceptScore W331375819C202444582 @default.
- W331375819 hasConceptScore W331375819C2780129039 @default.
- W331375819 hasConceptScore W331375819C2780813799 @default.
- W331375819 hasConceptScore W331375819C33923547 @default.
- W331375819 hasConceptScore W331375819C34388435 @default.
- W331375819 hasConceptScore W331375819C41008148 @default.
- W331375819 hasConceptScore W331375819C41895202 @default.
- W331375819 hasConceptScore W331375819C90119067 @default.
- W331375819 hasConceptScore W331375819C9376300 @default.
- W331375819 hasLocation W3313758191 @default.
- W331375819 hasOpenAccess W331375819 @default.
- W331375819 hasPrimaryLocation W3313758191 @default.
- W331375819 hasRelatedWork W1510177106 @default.
- W331375819 hasRelatedWork W1852930718 @default.
- W331375819 hasRelatedWork W1863178044 @default.
- W331375819 hasRelatedWork W1963995257 @default.
- W331375819 hasRelatedWork W1968561983 @default.
- W331375819 hasRelatedWork W1999875564 @default.
- W331375819 hasRelatedWork W2034212384 @default.
- W331375819 hasRelatedWork W2050415272 @default.
- W331375819 hasRelatedWork W2076316357 @default.
- W331375819 hasRelatedWork W2088922099 @default.
- W331375819 hasRelatedWork W2135960888 @default.
- W331375819 hasRelatedWork W2140863255 @default.
- W331375819 hasRelatedWork W2183302872 @default.
- W331375819 hasRelatedWork W2610653156 @default.
- W331375819 hasRelatedWork W2738437438 @default.
- W331375819 hasRelatedWork W2952171880 @default.
- W331375819 hasRelatedWork W2953326132 @default.
- W331375819 hasRelatedWork W2963197642 @default.
- W331375819 hasRelatedWork W2994174225 @default.
- W331375819 hasRelatedWork W58346730 @default.
- W331375819 isParatext "false" @default.
- W331375819 isRetracted "false" @default.
- W331375819 magId "331375819" @default.
- W331375819 workType "book-chapter" @default.