Euler calculus

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For numerical analysis of ordinary differential equations, see Euler's method.

Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions[1] by integrating with respect to the Euler characteristic as a finitely-additive measure. It was introduced independently by Pierre Schapira[2][3][4] and Oleg Viro[5] in 1988, and is useful for enumeration problems in computational geometry and sensor networks.[6]

See also[edit]

References[edit]

  1. ^ Baryshnikov, Y.; Ghrist, R. Euler integration for definable functions, Proc. National Acad. Sci., 107(21), 9525–9530, 25 May 2010.
  2. ^ Schapira, P. "Cycles Lagrangiens, fonctions constructibles et applications", Seminaire EDP, Publ. Ecole Polytechnique (1988/89)
  3. ^ Schapira, P. Operations on constructible functions, J. Pure Appl. Algebra 72, 1991, 83–93.
  4. ^ Schapira, Pierre. Tomography of constructible functions, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes Lecture Notes in Computer Science, 1995, Volume 948/1995, 427–435, doi:10.1007/3-540-60114-7_33
  5. ^ Viro, O. Some integral calculus based on Euler characteristic, Lecture Notes in Math., vol. 1346, Springer-Verlag, 1988, 127–138.
  6. ^ Baryshnikov, Y.; Ghrist, R. Target enumeration via Euler characteristic integrals, SIAM J. Appl. Math., 70(3), 825–844, 2009.

External links[edit]

  • Ghrist, Robert. Euler Calculus video presentation, June 2009. published 30 July 2009.