Abstract
In this paper we present the programs package FRAC (= Funciones RACionales) which is designed for performing computations in the rational function field. The main objects in FRAC are rational functions over the field of rational numbers, but extensions to other computable fields can be done in a “natural” way. The key tool is using functional decomposition algorithms. We motivate the interest to work with rational function decomposition by presenting applications to computer science, engineering (CAD), pure mathematics or robotics. We also present some simple examples in order to illustrate the use of FRAC. Finally, we include the synopsis of the main procedures of FRAC.
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.
Abhyankar, S., Bajaj, C.: Computations with Algebraic Curves. ISSAC-89. L.N.C.S. No. 358, pp.274–284, Springer-Verlag, 1989.
Abhyankar, S.:Algebraic Geometry for scientists and engineers. Math. Surveys and Monographs N.35. American Math. Society 1990.
Alonso, C., Gutierrez, J., Recio, T.:An Implicitization Algorithm with fewer variables. To appear in Computer Aided Geometric Design, 1994.
Alonso, C.: Desarrollo Análisis e implementacion de algoritmos para la manipulación de variedades paramétricas. Ph. dissertation, Dep. Math. and Computing, Universidad de Cantabria, Mayo 1994.
Cade, J. J.: A new public-key cipher which allows signatures. Proc. 2nd SIAM Conf. on Appl. Linear Algebra, Raleigh NC, 1985.
Dickerson, M.: Functional Decomposition of Polynomials. Tech. Rep. 89-1023, Dep. of Computer Science, Cornell University, Ithaca NY (1989).
Farin, G.:Curves and Surf aces for Computer Aided Geometric Design. Academic Press, Boston 1988.
Fried, M., MacRae, R.: On curves with separated variables. Math. Ann., 180, pp. 220–226, 1969.
Gathen, J. von zur.: Functional decomposition of polynomials: the tame case. J. of Symbolic Computation 9, pp. 281–299 (1990).
Gathen, J.& Weiss, J.:Homogeneus bivariate decompositions. Preprint, Dep. of Computer Science, University of Toronto, 1993.
Gutierrez, J.: A polynomial decomposition algorithm over factorial domains. Compt. Rendues Math. Acad. ScienceCanada, Vol. xIII-2, pp. 437–452 (1991).
Gutierrez, J. & Recio, T. & Ruiz de Velasco.: A polynomial decomposition algorithm of almost quadratic complexity. Proc. AAECC-6/88. L. N. Computer Science 357, pp. 471–476 (1989).
Gutierrez, J. & Recio, T.: Rational function decomposition and Groebner Bases in the parameterization of plane curves. Proc. of LATIN’ 92. L. N. Computer Science 583, pp. 231–245 (1992-1).
Gutierrez, J. & Recio, T.: A Practical Implementation of two rational function decomposition Algorithms. Proc.of ISSAC’ 92. ACM (1992-11).
Helmke, U. The variety of subfields of lK(x). Comm. in Algebra, 18(11) pp. 3775–3789, 1990.
Kovacs, P. & Hommel, G .:Simplification of Symbolic Inverse Kinematic Transformations through Functional Decomposition. Adv. in Robotics. Ferrara Sept. 1992.
Kozen, D. & Landau, S.: Polynomial decomposition algorithms. J. of Symbolic Computation 7, pp. 445–456 (1989).
Lenstra, A. K., Lenstra, H. W., Lovasz, L.:Facioring Polynomials with Rational Coefficients. Math. Ann. 261, pp.515–534, 1982.
O11ivier, F. Inversibility of rational mappings and structural identifiability in Automatics. Proc. ISSAC’ 89, pp. 43–53, ACM; 1989.
Ritt, F.: Prime and Composite polynomials. Trans. Amer. Math. Society 23, pp. 51–66 (1922).
Schinzel, A.: Selected topics on polynomials. Ann Arbor, University of Michigan press, 1982.
Sederberg, T. W.: Improperly parametrized rational cur-ves. Computer Aided Geometric Design, 3, pp. 67–75, 1986.
Shannon, D., Sweedler, M.: Using Grobner bases to determine algebra membership, split surjective algebra homomorphisms, determine birational equivalence. J. Symbolic Computation, 6, pp. 267–273; 1988.
Zippel, R.: Rational Function Decomposition. Proc. of ISSAC-91. ACM press, 1991. Technical report, Cornell University, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this paper
Cite this paper
Alonso, C., Gutierrez, J., Recio, T. (1994). FRAC: A Maple Package for Computing in the Rational Function Field K(X). In: Lopez, R.J. (eds) Maple V: Mathematics and its Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0263-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0263-9_13
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3791-0
Online ISBN: 978-1-4612-0263-9
eBook Packages: Springer Book Archive