Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets

DOI10.1090/conm/697/14046zbMath1390.14175arXiv1608.06828OpenAlexW2508521651MaRDI QIDQ4635358

Saugata Basu, Cordian Riener

Publication date: 16 April 2018

Published in: Ordered Algebraic Structures and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.06828

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Effectivity, complexity and computational aspects of algebraic geometry (14Q20) Topology of real algebraic varieties (14P25)

Related Items (3)

Faster real root decision algorithm for symmetric polynomials ⋮ On the equivariant Betti numbers of symmetric definable sets: vanishing, bounds and algorithms ⋮ Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic sets

Cites Work

• Bounding the equivariant Betti numbers of symmetric semi-algebraic sets
• On the degree and half-degree principle for symmetric polynomials
• On the Piano Movers problem. II: General techniques for computing topological properties of real algebraic manifolds
• Operations on constructible functions
• Constructible motivic functions and motivic integration
• Computing the first Betti number of a semi-algebraic set
• Bounding the Betti numbers and computing the Euler-Poincaré characteristic of semi-algebraic sets defined by partly quadratic systems of polynomials
• Computing the Betti numbers of semi-algebraic sets defined by partly quadratic systems of polynomials
• Counting connected components of a semialgebraic set in subexponential time
• Construction of roadmaps in semi-algebraic sets
• A formula for the Euler characteristic of a real algebraic manifold
• On the positivity of symmetric polynomial functions. I: General results
• Computing the Euler-Poincaré characteristics of sign conditions
• Computing the first few Betti numbers of semi-algebraic sets in single exponential time
• Euler integration over definable functions
• On the Euler characteristic of semi-analytic and semi-algebraic sets
• Computing roadmaps of semi-algebraic sets on a variety
• On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines
• Algorithms in real algebraic geometry
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