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FRAC: A Maple Package for Computing in the Rational Function Field K(X)

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Maple V: Mathematics and its Applications

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.

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References.

  • Abhyankar, S., Bajaj, C.: Computations with Algebraic Curves. ISSAC-89. L.N.C.S. No. 358, pp.274–284, Springer-Verlag, 1989.

    Google Scholar 

  • Abhyankar, S.:Algebraic Geometry for scientists and engineers. Math. Surveys and Monographs N.35. American Math. Society 1990.

    Google Scholar 

  • Alonso, C., Gutierrez, J., Recio, T.:An Implicitization Algorithm with fewer variables. To appear in Computer Aided Geometric Design, 1994.

    Google Scholar 

  • 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.

    Google Scholar 

  • Cade, J. J.: A new public-key cipher which allows signatures. Proc. 2nd SIAM Conf. on Appl. Linear Algebra, Raleigh NC, 1985.

    Google Scholar 

  • Dickerson, M.: Functional Decomposition of Polynomials. Tech. Rep. 89-1023, Dep. of Computer Science, Cornell University, Ithaca NY (1989).

    Google Scholar 

  • Farin, G.:Curves and Surf aces for Computer Aided Geometric Design. Academic Press, Boston 1988.

    Google Scholar 

  • Fried, M., MacRae, R.: On curves with separated variables. Math. Ann., 180, pp. 220–226, 1969.

    Google Scholar 

  • Gathen, J. von zur.: Functional decomposition of polynomials: the tame case. J. of Symbolic Computation 9, pp. 281–299 (1990).

    Google Scholar 

  • Gathen, J.& Weiss, J.:Homogeneus bivariate decompositions. Preprint, Dep. of Computer Science, University of Toronto, 1993.

    Google Scholar 

  • Gutierrez, J.: A polynomial decomposition algorithm over factorial domains. Compt. Rendues Math. Acad. ScienceCanada, Vol. xIII-2, pp. 437–452 (1991).

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Google Scholar 

  • Gutierrez, J. & Recio, T.: A Practical Implementation of two rational function decomposition Algorithms. Proc.of ISSAC’ 92. ACM (1992-11).

    Google Scholar 

  • Helmke, U. The variety of subfields of lK(x). Comm. in Algebra, 18(11) pp. 3775–3789, 1990.

    MathSciNet  MATH  Google Scholar 

  • Kovacs, P. & Hommel, G .:Simplification of Symbolic Inverse Kinematic Transformations through Functional Decomposition. Adv. in Robotics. Ferrara Sept. 1992.

    Google Scholar 

  • Kozen, D. & Landau, S.: Polynomial decomposition algorithms. J. of Symbolic Computation 7, pp. 445–456 (1989).

    Google Scholar 

  • Lenstra, A. K., Lenstra, H. W., Lovasz, L.:Facioring Polynomials with Rational Coefficients. Math. Ann. 261, pp.515–534, 1982.

    Google Scholar 

  • O11ivier, F. Inversibility of rational mappings and structural identifiability in Automatics. Proc. ISSAC’ 89, pp. 43–53, ACM; 1989.

    Google Scholar 

  • Ritt, F.: Prime and Composite polynomials. Trans. Amer. Math. Society 23, pp. 51–66 (1922).

    Google Scholar 

  • Schinzel, A.: Selected topics on polynomials. Ann Arbor, University of Michigan press, 1982.

    MATH  Google Scholar 

  • Sederberg, T. W.: Improperly parametrized rational cur-ves. Computer Aided Geometric Design, 3, pp. 67–75, 1986.

    Google Scholar 

  • 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.

    Google Scholar 

  • Zippel, R.: Rational Function Decomposition. Proc. of ISSAC-91. ACM press, 1991. Technical report, Cornell University, 1992.

    Google Scholar 

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© 1994 Springer Science+Business Media New York

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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

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  • 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

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