Matches in SemOpenAlex for { <https://semopenalex.org/work/W4306253790> ?p ?o ?g. }
Showing items 1 to 65 of
65
with 100 items per page.
- W4306253790 abstract "Let $R$ be a real closed field. We consider basic semi-algebraic sets defined by $n$-variate equations/inequalities of $s$ symmetric polynomials and an equivariant family of polynomials, all of them of degree bounded by $2d < n$. Such a semi-algebraic set is invariant by the action of the symmetric group. We show that such a set is either empty or it contains a point with at most $2d-1$ distinct coordinates. Combining this geometric result with efficient algorithms for real root finding (based on the critical point method), one can decide the emptiness of basic semi-algebraic sets defined by $s$ polynomials of degree $d$ in time $(sn)^{O(d)}$. This improves the state-of-the-art which is exponential in $n$. When the variables $x_1, ldots, x_n$ are quantified and the coefficients of the input system depend on parameters $y_1, ldots, y_t$, one also demonstrates that the corresponding one-block quantifier elimination problem can be solved in time $(sn)^{O(dt)}$." @default.
- W4306253790 created "2022-10-15" @default.
- W4306253790 creator A5043861722 @default.
- W4306253790 creator A5048254079 @default.
- W4306253790 date "2018-06-21" @default.
- W4306253790 modified "2023-09-26" @default.
- W4306253790 title "Real root finding for equivariant semi-algebraic systems" @default.
- W4306253790 doi "https://doi.org/10.48550/arxiv.1806.08121" @default.
- W4306253790 hasPublicationYear "2018" @default.
- W4306253790 type Work @default.
- W4306253790 citedByCount "0" @default.
- W4306253790 crossrefType "posted-content" @default.
- W4306253790 hasAuthorship W4306253790A5043861722 @default.
- W4306253790 hasAuthorship W4306253790A5048254079 @default.
- W4306253790 hasBestOaLocation W43062537901 @default.
- W4306253790 hasConcept C114614502 @default.
- W4306253790 hasConcept C118615104 @default.
- W4306253790 hasConcept C121332964 @default.
- W4306253790 hasConcept C134306372 @default.
- W4306253790 hasConcept C171036898 @default.
- W4306253790 hasConcept C186219872 @default.
- W4306253790 hasConcept C201482947 @default.
- W4306253790 hasConcept C202444582 @default.
- W4306253790 hasConcept C24890656 @default.
- W4306253790 hasConcept C2731732 @default.
- W4306253790 hasConcept C2775997480 @default.
- W4306253790 hasConcept C33923547 @default.
- W4306253790 hasConcept C34388435 @default.
- W4306253790 hasConcept C51544822 @default.
- W4306253790 hasConcept C78045399 @default.
- W4306253790 hasConcept C9376300 @default.
- W4306253790 hasConceptScore W4306253790C114614502 @default.
- W4306253790 hasConceptScore W4306253790C118615104 @default.
- W4306253790 hasConceptScore W4306253790C121332964 @default.
- W4306253790 hasConceptScore W4306253790C134306372 @default.
- W4306253790 hasConceptScore W4306253790C171036898 @default.
- W4306253790 hasConceptScore W4306253790C186219872 @default.
- W4306253790 hasConceptScore W4306253790C201482947 @default.
- W4306253790 hasConceptScore W4306253790C202444582 @default.
- W4306253790 hasConceptScore W4306253790C24890656 @default.
- W4306253790 hasConceptScore W4306253790C2731732 @default.
- W4306253790 hasConceptScore W4306253790C2775997480 @default.
- W4306253790 hasConceptScore W4306253790C33923547 @default.
- W4306253790 hasConceptScore W4306253790C34388435 @default.
- W4306253790 hasConceptScore W4306253790C51544822 @default.
- W4306253790 hasConceptScore W4306253790C78045399 @default.
- W4306253790 hasConceptScore W4306253790C9376300 @default.
- W4306253790 hasLocation W43062537901 @default.
- W4306253790 hasLocation W43062537902 @default.
- W4306253790 hasLocation W43062537903 @default.
- W4306253790 hasOpenAccess W4306253790 @default.
- W4306253790 hasPrimaryLocation W43062537901 @default.
- W4306253790 hasRelatedWork W1871156538 @default.
- W4306253790 hasRelatedWork W1995849923 @default.
- W4306253790 hasRelatedWork W2021197935 @default.
- W4306253790 hasRelatedWork W2035991160 @default.
- W4306253790 hasRelatedWork W2049968816 @default.
- W4306253790 hasRelatedWork W2063132333 @default.
- W4306253790 hasRelatedWork W2332529075 @default.
- W4306253790 hasRelatedWork W2766222296 @default.
- W4306253790 hasRelatedWork W2963854314 @default.
- W4306253790 hasRelatedWork W2964207094 @default.
- W4306253790 isParatext "false" @default.
- W4306253790 isRetracted "false" @default.
- W4306253790 workType "article" @default.