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Rational function decomposition and Gröbner bases in the parameterization of plane curves

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LATIN '92 (LATIN 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 583))

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Partially supported by CICYT-PB 89/0379/C02/01. Part of this work was done during a stay at the Department of Computer and Information Science in the University of Massachussetts at Amherst, funded by a scholarship of the DGCYT.

Partially supported by CICYT-PB 89/0379/C02/01.

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References

  • Abyankar,S. Algebraic Geometry for scientists and engineers. Math. Surveys and Monographs No35. America Math. Society. (1990)

    Google Scholar 

  • Abyankar, S.&Bajaj,C.: Automatic parameterization of rational curves and surfaces I. Comp. Aided Design 19, pp 11–14 (II,III y IV to appear) (1987)

    Google Scholar 

  • Barton,R.&Zippel, R.: Polynomial decomposition algorithms. J. of Symbolic Computation, 1, pp. 159–168 (1985)

    Google Scholar 

  • Bochnak, J.& Coste, M.& Roy, M-F.: Geometrie Algebrique reelle. Springer-Verlag (1987)

    Google Scholar 

  • Buchberger, B.: Applications of Gröbner Bases in non-linear Computational Geometry. Trends in Computer Algebra. Ed. R. Janssen. Lect. Notes in Comp. Sci. 296, 52–91 (1987)

    Google Scholar 

  • Cox,D.&Little.J.&O'Shea, D.: Ideals, Varieties and algorithms. “An Introduction to Computation in Algebraic Geometry and Commutative Algebra”. Dep. Math. South Hadley, Mass 01075, Book in preparation, Sept 1990.

    Google Scholar 

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

    Google Scholar 

  • Fried, M. D. (1970). On a conjeture of Schur. Michigan Mth. J. 17, 41–50.

    Google Scholar 

  • Fried,M.&MacRae,R.: On the invariance of chains of fields. Illinois Journal Math. 13, pp. 165–171. (1969)

    Google Scholar 

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

    Google Scholar 

  • Gathen, J. von zur.: Functional decomposition of polynomials: the wild case. J. Symbolic Computation 10, pp. 437–452 (1990)

    Google Scholar 

  • Giesbrecht, M. W.: Complexity Results on the Functional Decomposition of Polynomials. Tech. Report 209/88. Dep. Computer Science. University of Toronto (1988)

    Google Scholar 

  • Gutierrez,J.: A polynomial Decomposition algorithm over Factorial Domains. Comptes Rendues Math. Acad. Sci. Canada. Vol. XIII, N-2 pp.81–86 (1991)

    Google Scholar 

  • Gutiérrez,J.& Recio, T. & Ruiz de Velasco, C.: Polynomial Decomposition algorithm of almost quadratic complexity. Proc. of AAECC-6 (1988) L.N.Comp.Science, 357. Springer-Verlag, 471–476(1989)

    Google Scholar 

  • Kalkbrener, M.: Three Contributions to Elimination Theory. Dissertation. Univ. of Linz, Austria, (Mai, 1991)

    Google Scholar 

  • Kozen, D. & Landau, S.: Polynomial Decomposition Algorithms. Tech.Rep. 86-773, Dep.Comp.Scienc, Cornell University, Ithaca NY(1986). J. Symbolic Computation 7, 445–456 (1989)

    Google Scholar 

  • Lüroth,P.: Beweis eines Satzes über rationale Curven. Math. Annalen, 9pp. 163–165. (1876)

    Google Scholar 

  • Netto,E.: Über einen Lüroth-Gordaschen Satz. Math. Annals, 46. pp. 310–318. (1895)

    Google Scholar 

  • Recio, T.: Curso de Algebra Computacional. Cursos de Laredo. Univ. de Cantabria, Spain (July 1990)

    Google Scholar 

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

    Google Scholar 

  • Shafarevich,I.R.: Basic algebraic Geometry. Springer-Verlag. Berlin-NY (1977)

    Google Scholar 

  • Sederberg, T. W.: Improperly parametrized rational curves. Computer Aided Geometric Design 367–75 (1986).

    Google Scholar 

  • Sederberg, T.W.: Algebraic Geometry for Durface and Solid Modeling. Geometric Modeling Algorithms and new trends. SIAM, Ed. Gerald E. Farm pp. 29–42 (1987).

    Google Scholar 

  • Sendra,R.&Winkler,F.: Symbolic Parameterization of Curves. To appear in J. of Symbolic Computation. (1990).

    Google Scholar 

  • Shannon, D. & Sweedler, M.: Using Gröbner bases to determine algebra membership, split surjective algebra hommorfhisms and determine birational equivalence. J. of Symbolic Computation 6, pp. 267–273 (1988)

    Google Scholar 

  • Schinzel, A.: Selected Topics on polynomials. Ann. Arbor, University of Michigan Press, (1982).

    Google Scholar 

  • Zippel, R.: Rational Functional Decompostion. Proc. of ISSAC-91. Bonn. ACM press (1991)

    Google Scholar 

  • Zippel, R.: Function Decomposition. Tech. Report 91-1209. Dep. Computer Science. Cornell UNiversity. Ithaca (1991)

    Google Scholar 

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Imre Simon

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© 1992 Springer-Verlag Berlin Heidelberg

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Gutierrez, J., Recio, T. (1992). Rational function decomposition and Gröbner bases in the parameterization of plane curves. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023832

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  • DOI: https://doi.org/10.1007/BFb0023832

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