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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. ...##
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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. ...##
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Two Computational Techniques for Singularity Resolution

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. ...

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

2017
*
Theoretical Computer Science
*

This

doi:10.1016/j.tcs.2017.03.029
fatcat:e4pzuoxfanfnbktapa5zthp6li
*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. ...##
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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

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. ...

##
###
Rationalizing roots: an algorithmic approach
[article]

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 ...

##
###
Continuation techniques for reachability analysis of uncertain power systems

2014
*
2014 IEEE International Symposium on Circuits and Systems (ISCAS)
*

and evaluate

doi:10.1109/iscas.2014.6865510
dblp:conf/iscas/MarkovSHD14
fatcat:us4co7oaifb77eihmzvkftfh5i
*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 ...##
###
Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces

2012
*
Foundations of Computational Mathematics
*

In

doi:10.1007/s10208-011-9112-6
fatcat:x3ecohcci5en3mroqrlvfxwonm
*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) . ...##
###
A Local Resolution of the Problem of Time. III. The other classical facets piecemeal
[article]

2019
*
arXiv
*
pre-print

These are classically implemented piecemeal

arXiv:1905.06212v4
fatcat:3ok6wrmzfvbnfdvacjz65fgufq
*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). ...##
###
Computing characteristic classes of projective schemes

2003
*
Journal of symbolic computation
*

We discuss

doi:10.1016/s0747-7171(02)00089-5
fatcat:mbz4x5umbrh5lpatki3sbusbry
*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. ...##
###
Computing the global optimum of a multivariate polynomial over the reals

2008
*
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08
*

. , Xn]

doi:10.1145/1390768.1390781
dblp:conf/issac/Din08
fatcat:m3oif2xhsbgwfmz4vesjleldc4
*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*...##
###
Exact numerical computation in algebra and geometry

2009
*
Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09
*

(

doi:10.1145/1576702.1576757
dblp:conf/issac/Yap09
fatcat:he2bxcvzwjhxhied5zjjm22lz4
*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 ...##
###
Foreword

2010
*
Mathematics in Computer Science
*

Such

doi:10.1007/s11786-011-0088-z
fatcat:iwrfa7zfuvfahosel3ewbf5bgy
*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). ...##
###
An algorithm for computing the topological Euler characteristic of complex projective varieties
[article]

2013
*
arXiv
*
pre-print

We also give

arXiv:1301.4128v3
fatcat:usbs7wwbxnclrer7e762sh24py
*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. ...
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