Abstract
We describe the integration of a well known algorithm for computing and displaying plane loci based on ideal elimination using Gröbner bases in the dynamic geometry software JSXGraph. With our approach it is not only possible to determine loci depending on other loci but it is also possible to extend JSXGraph to deal with loci depending on arbitrary plane algebraic curves. For Gröbner bases calculations we use CoCoa, a computer algebra system with its focus on computations in commutative algebra.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Becker, T., Weispfenning, V.: Gröbner bases: a computational approach to commutative algebra. Springer, Heidelberg (1993)
Botana, F., Valcarce, J.L.: A software tool for the investigation of plane loci. Mathematics and Computers in Simulation 61(2), 139–152 (2003)
Botana, F.: A Web-Based Intelligent System for Geometric Discovery. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003, Part I. LNCS, vol. 2657, pp. 801–810. Springer, Heidelberg (2003)
Botana, F., Abánades, M.A., Escribano, J.: Computing Locus Equations for Standard Dynamic Geometry Environments. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007, Part II. LNCS, vol. 4488, pp. 227–234. Springer, Heidelberg (2007)
Buchberger, B.: Introduction to Gröbner Bases. In: Buchberger, B., Winkler, F. (eds.) Gröbner bases and applications. London Mathematical Society Lecture Note Series. Cambridge University Press (1998)
CoCoA: a system for doing Computations in Commutative Algebra, urlhttp://cocoa.dima.unige.it
Cox, D.A., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, New York (2008)
Fröberg, R.: An Introduction to Gröbner Bases. John Wiley & Sons (1997)
von zur Gathen, J., Gerhard, J.: Modern Computer Algebra. Cambridge University Press (1999)
Gerhäuser, M., Miller, C., Valentin, B., Wassermann, A., Wilfahrt, P.: JSXGraph: Dynamic Mathematics Running on (nearly) Every Device. To be published in The Electronic Journal of Mathematics and Technology
Hunter, J.D.: Matplotlib: A 2D Graphics Environment. In: Computing in Science & Engineering, vol. 9, pp. 90–95. IEEE Computer Society, Los Alamitos (2007)
Kortenkamp, U.: Foundations of Dynamic Geometry. Dissertation (1999)
Lebmeir, P., Richter-Gebert, J.: Recognition of Computationally Constructed Loci. In: Botana, F., Recio, T. (eds.) ADG 2006. LNCS (LNAI), vol. 4869, pp. 52–67. Springer, Heidelberg (2007)
Pilgrim, M.: Dive Into Python. APress (2004)
Recio, T., Vélez, M.P.: Automatic Discovery of Theorems in Elementary Geometry. Journal of Automated Reasoning, 63–82 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gerhäuser, M., Wassermann, A. (2011). Automatic Calculation of Plane Loci Using Gröbner Bases and Integration into a Dynamic Geometry System. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds) Automated Deduction in Geometry. ADG 2010. Lecture Notes in Computer Science(), vol 6877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25070-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-25070-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25069-9
Online ISBN: 978-3-642-25070-5
eBook Packages: Computer ScienceComputer Science (R0)