Real algebraic geometry
By Vladimir I. Arnold, I. Itenberg, Viatcheslav Kharlamov, Eugenii Shustin. 2013
1,051 citations recorded by the source corpus.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b7da7fd102560d2b64692d26d0893a3c8a759d0f
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In Geometry and Topology
Citations in the corpus
- Identification of Social Interactions (2011, neutral): “For more on semi-algebraic geometry see Bochnak, Coste, and Roy (1998).”
- The Convex Geometry of Linear Inverse Problems (2010, background): “r the reader to the vast literature on this subject for more details (see [38, 57] and the references therein). For subsequent reference in this section, we recall the definition of a polynomial ideal [9, 40]: Definition 4.2. A polynomial ideal I⊂ R[x] is a subset of the ring of polynomials that conta”
- Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, background): “Let u be a local minimizer of (1.1), and ℓ be the local dimension of V R ( h ) at u (cf. [2, § 2.8]). was We first state a condition about parameterizing K around u locally, which proposed by Marshall.”
- Benefits of Depth in Neural Networks (2016, background): “Note that the name semi-algebraic set is standard (Bochnak et al., 1998, Definition 2.1.4), and refers to a set defined by unions and intersections of polynomial inequalities (and thus the name is somewhat abused here).”
- Linear growth of quantum circuit complexity (2021, methodology): “Therefore, F ′ has a property prescribed by the Tarski-Seidenberg principle [4] (Theorem 2): The image F ′ (SU(4)×R ′ ) is a semialgebraic set of dimension ≤ dim(SU(4)×R) = R′ dim(SU(4)) = 15R′.”
- A semi-algebraic version of Zarankiewicz's problem (2014, background): “We say that a real variety V is irreducible if it is irreducible over R (see e.g. [7, Section 2.8]).”