Computing the Homology of Real Projective Sets

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

4 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)929-970
Journal / PublicationFoundations of Computational Mathematics
Volume18
Issue number4
Online published4 Aug 2017
Publication statusPublished - Aug 2018

Abstract

We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of real projective varieties. Here numerical means that the algorithm is numerically stable (in a sense to be made precise). Its cost depends on the condition of the input as well as on its size and is singly exponential in the number of variables (the dimension of the ambient space) and polynomial in the condition and the degrees of the defining polynomials. In addition, we show that outside of an exceptional set of measure exponentially small in the size of the data, the algorithm takes exponential time.

Research Area(s)

  • Complexity, Condition, Exponential time, Homology groups, Real projective varieties

Citation Format(s)

Computing the Homology of Real Projective Sets. / Cucker, Felipe; Krick, Teresa; Shub, Michael.

In: Foundations of Computational Mathematics, Vol. 18, No. 4, 08.2018, p. 929-970.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal