On some basic applications of Gröbner Bases
Abstrakt
In this paper, we introduced notions and basic facts on Gröbner Basis Theory. An application of the theory for solving algebraic equations is a fundamental result presented in the paper. Methods of elimination of parameter from parametric equation for determining a polynomial implicit form of an equation is the second one result presented in the paper, the methods are illustrated with curves: Folium of Descartes, Bézier’s curve and many surfaces, especially Enneper surface.
Bibliografia
D. Cox, J. Little, D. O’Shea, "Ideals, Varietes and algorithms: : An Introduction to Computational Algebraic Geometry and Commutative Algebra", Springer, New York, 2007.
M. Dumnicki, T. Winiarski, "Bazy Gröbnera", Wydawnictwo Naukowe Uniwersytetu Padagogicznego, Kraków, 2009.
I. M. Gelfand, M. M. Kapranov, A. V. Zelevinsky, "Discirminants, resultants and multidimensional determinants", Birkhäuser, Boston-Basel-Berlin, 1994.
C. G. Gibson, "Elementary Geometry of Algebraic Curves: an Undergraduate Introduction", Cambridge University Press, Cambridge, 1998.
http://z2.math.us.edu.pl/perry/papers/okruchy.pdf, dnia 15 XI 2012, godz. 16.00.
http://mathworld.wolfram.com/FoliumofDescartes.html, dnia 15 XI 2012, godz. 16.00.
Refbacks
- There are currently no refbacks.
Ta praca dostępna jest na licencji Creative Commons Attribution 3.0 License.