Abstract
This paper introduces a definition of polynomial first integrals in the differential algebra context and an algorithm for computing them. The method has been coded in the Maple computer algebra system and is illustrated on the pendulum and the Lotka-Volterra equations. Our algorithm amounts to finding linear dependences of rational fractions, which is solved by evaluation techniques.
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References
Boulier, F.: The BLAD libraries (2004). http://cristal.univ-lille.fr/~boulier/BLAD
Boulier, F., Lemaire, F.: A normal form algorithm for regular differential chains. Mathematics in Computer Science 4(2–3), 185–201 (2010)
Boulier, F.: Efficient computation of regular differential systems by change of rankings using Kähler differentials. Technical report, Université Lille I, 59655, Villeneuve d’Ascq, France (November 1999) Ref. LIFL 1999–14, presented at the MEGA 2000 conference. http://hal.archives-ouvertes.fr/hal-00139738
Boulier, F., Lazard, D., Ollivier, F., Petitot, M.: Computing representations for radicals of finitely generated differential ideals. Applicable Algebra in Engineering, Communication and Computing 20(1), 73–121 (2009); (1997 Techrep. IT306 of the LIFL)
Boulier, F., Lemaire, F.: A computer scientist point of view on Hilbert’s differential theorem of zeros. Submitted to Applicable Algebra in Engineering, Communication and Computing (2007)
Boulier, F., Lemaire, F., Sedoglavic, A.: On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2011. LNCS, vol. 6885, pp. 61–72. Springer, Heidelberg (2011)
Bunch, J.R., Hopcroft, J.E.: Triangular factorization and inversion by fast matrix multiplication. Mathematics of Computation 28(125), 231–236 (1974)
Faugère, J.C., Gianni, P., Lazard, D., Mora, T.: Efficient computation of Gröbner bases by change of orderings. Journal of Symbolic Computation 16, 329–344 (1993)
Gathen, J.V.Z., Gerhard, J.: Modern Computer Algebra, 3rd edn. Cambridge University Press, New York (2013)
Kolchin, E.R.: Differential Algebra and Algebraic Groups. Academic Press, New York (1973)
Ritt, J.F.: Differential Algebra. Dover Publications Inc., New York (1950)
Stoutemyer, D.R.: Multivariate partial fraction expansion. ACM Commun. Comput. Algebra 42(4), 206–210 (2009)
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Boulier, F., Lemaire, F. (2015). Finding First Integrals Using Normal Forms Modulo Differential Regular Chains. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_8
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DOI: https://doi.org/10.1007/978-3-319-24021-3_8
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