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Page 682 of Mathematical Reviews Vol. , Issue 92b [page]

1992 Mathematical Reviews  
(English summary) [Localization of a real algebraic hypersurface by the exclusion algorithm] C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 13, 1013-1016.  ...  Summary: “We describe a new algorithm for the localization of an algebraic hypersurface V in R”. This algorithm computes a decreasing sequence of closed sets whose intersection is V.  ... 

Page 852 of Annals of Mathematics Vol. 41, Issue 4 [page]

1940 Annals of Mathematics  
ANNALS OF MATHEMATICS Vol. 41, No. 4, October, 1940 LOCAL UNIFORMIZATION ON ALGEBRAIC VARIETIES By Oscar ZARISKI* (Received March 22, 1940) CONTENTS A. INTRODUCTION I.  ...  The general uniformization theorem. ....................ccee ce eeeeeeeeees 857 IV. Reduction to an hypersurface. The main theorem........................ 858 B.  ... 

Two Computational Techniques for Singularity Resolution

Gábor Bodnár, Josef Schicho
2001 Journal of symbolic computation  
The first one allows the elimination of redundancies in the representation of quasi-projective varieties by atlases of affine charts.  ...  As the main application, we used these techniques to speed up Villamayor's algorithm for resolving hypersurface singularities in any dimension.  ...  This work was supported by the Austrian Science Fund (FWF) in the frame of the project SFB-P2 F1303.  ... 
doi:10.1006/jsco.2001.0452 fatcat:hlt4vclmszbolfgvgh2gmkka3y

A direct algorithm to compute the topological Euler characteristic and Chern–Schwartz–MacPherson class of projective complete intersection varieties

Martin Helmer
2017 Theoretical Computer Science  
This algorithm complements existing algorithms by providing performance improvements in the computation of the Chern-Schwartz-MacPherson class and Euler characteristic for certain types of complete intersection  ...  Let V be a possibly singular scheme-theoretic complete intersection subscheme of P^n over an algebraically closed field of characteristic zero.  ...  Acknowledgements This research was partially supported by the Natural Sciences and Engineering Research Council of Canada.  ... 
doi:10.1016/j.tcs.2017.03.029 fatcat:e4pzuoxfanfnbktapa5zthp6li

Page 82 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
See also «00005. 12D Real and complex fields 96a:12002 12D10 14Q10 Dedieu, Jean-Pierre (F-TOUL3-NA; Toulouse); Yakoubsohn, Jean-Claude (F-TOUL3-NA; Toulouse) Localization of an algebraic hypersurface by  ...  the exclusion algorithm.  ... 

Algorithms to compute the topological Euler characteristic, Chern–Schwartz–MacPherson class and Segre class of projective varieties

Martin Helmer
2016 Journal of symbolic computation  
The algorithm is based on a new method for calculating the projective degrees of a rational map defined by a homogeneous ideal.  ...  Let V be a closed subscheme of a projective space P^n. We give an algorithm to compute the Chern-Schwartz-MacPherson class, Euler characteristic and Segre class of V.  ...  Acknowledgments The author would like to thank Eric Schost for many helpful discussions on the content of this note.  ... 
doi:10.1016/j.jsc.2015.03.007 fatcat:c6aiaawuwfbvnaauc3igredfwu

Rationalizing roots: an algorithmic approach [article]

Marco Besier, Duco van Straten, Stefan Weinzierl
2018 arXiv   pre-print
The algorithm is applicable whenever the algebraic hypersurface associated with the root has a point of multiplicity (d-1), where d is the degree of the algebraic hypersurface.  ...  In this paper, we give an algorithm for rationalizing roots.  ...  We present an algorithm -well-known from algebraic geometrythat rationalizes the given root by first associating an algebraic hypersurface to the root and then parametrizing this hypersurface by an n-parameter  ... 
arXiv:1809.10983v2 fatcat:uzdfzkaoy5gntossh6k4xkocqm

Continuation techniques for reachability analysis of uncertain power systems

Maxim Markov, Mehdi Saghafi, Ian A. Hiskens, Harry Dankowicz
2014 2014 IEEE International Symposium on Circuits and Systems (ISCAS)  
and evaluate the impact of parameter uncertainty.  ...  This paper describes a novel suite of parameter continuation algorithms that may be applied to large-scale, stiff, hybrid power systems.  ...  It follows that the dynamic behavior can be described analytically by the flow φ, i.e., x(t) = φ(x 0 , t) where the time-dependence of the algebraic states is implicitly defined by the algebraic constraints  ... 
doi:10.1109/iscas.2014.6865510 dblp:conf/iscas/MarkovSHD14 fatcat:us4co7oaifb77eihmzvkftfh5i

Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces

Bernd Bank, Marc Giusti, Joos Heintz, Lutz Lehmann, Luis Miguel Pardo
2012 Foundations of Computational Mathematics  
In the case that the real variety defined by F is smooth, there exist already algorithms of intrinsic  ...  In worst case the complexity of our algorithms does not exceed the already known extrinsic complexity bound of (nd) O(n) for the elimination problem under consideration, where n is the number of indeterminates  ...  Observe that N i (h) is an algebraic variety which is isomorphic to the affine space A n × A i × A n−i and that H (h,γ) i is an R -definable locally closed subvariety of N i (h) .  ... 
doi:10.1007/s10208-011-9112-6 fatcat:x3ecohcci5en3mroqrlvfxwonm

A Local Resolution of the Problem of Time. III. The other classical facets piecemeal [article]

Edward Anderson
2019 arXiv   pre-print
These are classically implemented piecemeal by the Dirac Algorithm for 1) and the Lie Algorithm for 1').  ...  We introduce nine further local facets of the classical Problem of Time, and underlying Background Independence aspects, the previous two Articles having covered one further facet-and-aspect each for a  ...  This is achieved by the two end hypersurfaces coinciding up to a diffeomorphism of that hypersurface, as per the right hand side of (56).  ... 
arXiv:1905.06212v4 fatcat:3ok6wrmzfvbnfdvacjz65fgufq

Computing characteristic classes of projective schemes

Paolo Aluffi
2003 Journal of symbolic computation  
We discuss an algorithm computing the push-forward to projective space of several classes associated to a (possibly singular, reducible, nonreduced) projective scheme.  ...  For example, the algorithm yields the topological Euler characteristic of the support of a projective scheme S, given the homogeneous ideal of S. The algorithm has been implemented in Macaulay2.  ...  Acknowledgements I thank the Max-Planck-Institut für Mathematik in Bonn, Germany, for hospitality and support, and Florida State University for granting a sabbatical leave in 2001-2.  ... 
doi:10.1016/s0747-7171(02)00089-5 fatcat:mbz4x5umbrh5lpatki3sbusbry

Computing the global optimum of a multivariate polynomial over the reals

Mohab Safey El Din
2008 Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08  
. , Xn] of degree D. We provide an efficient algorithm in practice to compute the global supremum sup x∈R n f (x) of f (or its infimum inf x∈R n f (x)).  ...  We prove that the global optimum of f lies in its set of generalized critical values and provide an efficient way of deciding which value is the global optimum.  ...  In Section 3, we recall the basics of an efficient algorithm computing sampling points in the real counterpart of a smooth hypersurface which is used to test the emptiness of the considered real hypersurfaces  ... 
doi:10.1145/1390768.1390781 dblp:conf/issac/Din08 fatcat:m3oif2xhsbgwfmz4vesjleldc4

Exact numerical computation in algebra and geometry

Chee K. Yap
2009 Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09  
(Algebraic or Numeric) Algorithm = Sequence of Steps Steps = Construction x := y + 2; or Tests if x = 0 goto L Geometric relations determined by Tests (Zero or Sign) THUS: if Tests are error free , the  ...  (Algebraic or Numeric) 224 is exact, but 0.0223 is more useful! ◮ WHY? Want the locus of α in the continuum ◮ JOKE: a physicist and an engineer were in a hot-air balloon...  ...  If β 1 , . . . , β n are all the zeros of η(X ), then  ... 
doi:10.1145/1576702.1576757 dblp:conf/issac/Yap09 fatcat:he2bxcvzwjhxhied5zjjm22lz4


Gert Vegter, Chee K. Yap
2010 Mathematics in Computer Science  
Such an exploration is carried out by M. Mörig, I. Rössling and S. Schirra in the last paper of this issue.  ...  Batra's theorem bounds the number of steps in the algorithm by O(µ 2 ) (the algorithm can achieve this bound without explicitly knowing µ).  ... 
doi:10.1007/s11786-011-0088-z fatcat:iwrfa7zfuvfahosel3ewbf5bgy

An algorithm for computing the topological Euler characteristic of complex projective varieties [article]

Christine Jost
2013 arXiv   pre-print
We also give an example for using a theorem by Huh to compute an invariant from algebraic statistics, the maximum likelihood degree of an implicit model.  ...  We present an algorithm for the symbolic and numerical computation of the degrees of the Chern-Schwartz-MacPherson classes of a closed subvariety of projective space P^n.  ...  That the residuals may be a by-product of the regenerative cascade was pointed out by Jon Hauenstein.  ... 
arXiv:1301.4128v3 fatcat:usbs7wwbxnclrer7e762sh24py
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