Previous article Next article The Euclidean Algorithm and the Degree of the Gauss MapTakis SakkalisTakis Sakkalishttps://doi.org/10.1137/0219036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper examines the computation of the topological degree of the Gauss map, defined by polynomials in the plane, via the Euclidean algorithm.[1] G. E. Collins and , R. Loos, Real zeros of polynomials, Comput. Suppl., 4 (1982), 83–94 0533.68038 CrossrefGoogle Scholar[2] F. R. Gantmacher, The Theory of Matrices, Chelsea, New York, 1960 Google Scholar[3] Victor Guillemin and , Alan Pollack, Differential topology, Prentice-Hall Inc., Englewood Cliffs, N.J., 1974xvi+222 50:1276 0361.57001 Google Scholar[4] A. S. Householder, Bigradients and the problem of Routh and Hurwitz, SIAM Rev., 10 (1968), 56–66 10.1137/1010003 37:5371 0169.09003 LinkISIGoogle Scholar[5] Takis Sakkalis, Signs of algebraic numbersComputers and mathematics (Cambridge, MA, 1989), Springer, New York, 1989, 130–134, Proc. Conference, Massachusetts Institute of Technology, Berlin 90m:12004 0692.12003 CrossrefGoogle Scholar[6] T. Sakkalis, The topological configuration of a real algebraic curve, IBM Research Report, RC-13881, International Business Machines, Yorktown Heights, NY, 1988 Google Scholar[7] T. Sakkalis, Ph.D. Thesis, An algorithmic application of Morse theory to real algebraic geometry, University of Rochester, Rochester, NY, 1986 Google Scholar[8] Herbert S. Wilf, A global bisection algorithm for computing the zeros of polynomials in the complex plane, J. Assoc. Comput. Mach., 25 (1978), 415–420 10.1145/322077.322084 58:3390 0378.30003 CrossrefISIGoogle ScholarKeywordsinteger polynomialstopological degreeGauss map Previous article Next article FiguresRelatedReferencesCited byDetails Unorganized point classification for robust NURBS surface reconstruction using a point-based neural network18 December 2020 | Journal of Computational Design and Engineering, Vol. 8, No. 1 Cross Ref Improved subdivision scheme for the root computation of univariate polynomial equationsApplied Mathematics and Computation, Vol. 219, No. 14 Cross Ref A reliable algorithm for computing the topological degree of a mapping in R2Applied Mathematics and Computation, Vol. 196, No. 2 Cross Ref RESOLUTION OF MULTIPLE ROOTS OF NONLINEAR POLYNOMIAL SYSTEMSInternational Journal of Shape Modeling, Vol. 11, No. 01 Cross Ref Intersection Problems Cross Ref Computing the topological degree of polynomial maps17 April 2009 | Bulletin of the Australian Mathematical Society, Vol. 56, No. 1 Cross Ref The topological configuration of a real algebraic curve17 April 2009 | Bulletin of the Australian Mathematical Society, Vol. 43, No. 1 Cross Ref Nonlinear polynomial systems: multiple roots and their multiplicities Cross Ref Volume 19, Issue 3| 1990SIAM Journal on Computing History Submitted:05 October 1987Accepted:05 October 1989Published online:13 July 2006 InformationCopyright © 1990 Society for Industrial and Applied MathematicsKeywordsinteger polynomialstopological degreeGauss mapMSC codes68Q2555M20PDF Download Article & Publication DataArticle DOI:10.1137/0219036Article page range:pp. 538-543ISSN (print):0097-5397ISSN (online):1095-7111Publisher:Society for Industrial and Applied Mathematics