Matches in SemOpenAlex for { <https://semopenalex.org/work/W2761385847> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W2761385847 abstract "Let [Formula: see text] be a set of elements in the polynomial ring [Formula: see text], let [Formula: see text] denote the ideal generated by the elements of [Formula: see text], and let [Formula: see text] denote the radical of [Formula: see text]. There is a unique decomposition [Formula: see text] with each [Formula: see text] a prime ideal corresponding to a minimal associated prime of [Formula: see text] over [Formula: see text]. Let [Formula: see text] denote the reduced algebraic set corresponding to the common zeroes of the elements of [Formula: see text]. Techniques from numerical algebraic geometry can be used to determine the numerical irreducible decomposition of [Formula: see text] over [Formula: see text]. This corresponds to producing a witness set for [Formula: see text] for each [Formula: see text] together with the degree and dimension of [Formula: see text] (a point in a witness set for [Formula: see text] can be considered as a numerical approximation for a general point on [Formula: see text]). The purpose of this paper is to show how to extend these results taking into account the field of definition for the polynomial system. In particular, let [Formula: see text] be a number field (i.e. a finite field extension of [Formula: see text]) and let [Formula: see text] be a set of elements in [Formula: see text]. We show how to extend techniques from numerical algebraic geometry to determine the numerical irreducible decomposition of [Formula: see text] over [Formula: see text]." @default.
- W2761385847 created "2017-10-20" @default.
- W2761385847 creator A5039450473 @default.
- W2761385847 creator A5078621088 @default.
- W2761385847 creator A5090012825 @default.
- W2761385847 date "2018-10-01" @default.
- W2761385847 modified "2023-09-24" @default.
- W2761385847 title "Numerical irreducible decomposition over a number field" @default.
- W2761385847 cites W1498760074 @default.
- W2761385847 cites W1570420806 @default.
- W2761385847 cites W1590879386 @default.
- W2761385847 cites W1645810705 @default.
- W2761385847 cites W1986180644 @default.
- W2761385847 cites W2035352599 @default.
- W2761385847 cites W2042877335 @default.
- W2761385847 cites W2052195169 @default.
- W2761385847 cites W2064804790 @default.
- W2761385847 cites W2105303994 @default.
- W2761385847 cites W2340785944 @default.
- W2761385847 cites W4234679232 @default.
- W2761385847 doi "https://doi.org/10.1142/s0219498818501955" @default.
- W2761385847 hasPublicationYear "2018" @default.
- W2761385847 type Work @default.
- W2761385847 sameAs 2761385847 @default.
- W2761385847 citedByCount "0" @default.
- W2761385847 crossrefType "journal-article" @default.
- W2761385847 hasAuthorship W2761385847A5039450473 @default.
- W2761385847 hasAuthorship W2761385847A5078621088 @default.
- W2761385847 hasAuthorship W2761385847A5090012825 @default.
- W2761385847 hasConcept C111472728 @default.
- W2761385847 hasConcept C114614502 @default.
- W2761385847 hasConcept C134306372 @default.
- W2761385847 hasConcept C138885662 @default.
- W2761385847 hasConcept C202444582 @default.
- W2761385847 hasConcept C2776639384 @default.
- W2761385847 hasConcept C33676613 @default.
- W2761385847 hasConcept C33923547 @default.
- W2761385847 hasConcept C90119067 @default.
- W2761385847 hasConcept C9376300 @default.
- W2761385847 hasConcept C9652623 @default.
- W2761385847 hasConceptScore W2761385847C111472728 @default.
- W2761385847 hasConceptScore W2761385847C114614502 @default.
- W2761385847 hasConceptScore W2761385847C134306372 @default.
- W2761385847 hasConceptScore W2761385847C138885662 @default.
- W2761385847 hasConceptScore W2761385847C202444582 @default.
- W2761385847 hasConceptScore W2761385847C2776639384 @default.
- W2761385847 hasConceptScore W2761385847C33676613 @default.
- W2761385847 hasConceptScore W2761385847C33923547 @default.
- W2761385847 hasConceptScore W2761385847C90119067 @default.
- W2761385847 hasConceptScore W2761385847C9376300 @default.
- W2761385847 hasConceptScore W2761385847C9652623 @default.
- W2761385847 hasLocation W27613858471 @default.
- W2761385847 hasOpenAccess W2761385847 @default.
- W2761385847 hasPrimaryLocation W27613858471 @default.
- W2761385847 hasRelatedWork W2013907906 @default.
- W2761385847 hasRelatedWork W2044530517 @default.
- W2761385847 hasRelatedWork W2163262938 @default.
- W2761385847 hasRelatedWork W2316396767 @default.
- W2761385847 hasRelatedWork W2363602426 @default.
- W2761385847 hasRelatedWork W2755521877 @default.
- W2761385847 hasRelatedWork W2922517763 @default.
- W2761385847 hasRelatedWork W2949213657 @default.
- W2761385847 hasRelatedWork W2959518726 @default.
- W2761385847 hasRelatedWork W3165069223 @default.
- W2761385847 isParatext "false" @default.
- W2761385847 isRetracted "false" @default.
- W2761385847 magId "2761385847" @default.
- W2761385847 workType "article" @default.