Submitted Contributions

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Volume 948 of the series Lecture Notes in Computer Science pp 347-364


Integration of multivariate rational functions given by straight-line programs

  • Guillermo MateraAffiliated withDepartamento de Matemáticas, Fac. de Ciencias Exactas, Univ. de Buenos Aires

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We present a well-parallelizable algorithm which, taking a straight-line program for the evaluation of a vectorial field of rational functions of Q(X 1,...,X n ) as input, decides whether they allow a rational potential function and, in case of affirmative answer, computes it as output. We introduce a mixed model of representation of polynomials to allow the application of integration techniques and show how to perform some basic operations with it. The algorithm is presented as a family of arithmetic networks of polynomial size and poly logarithmic depth in the degree of the occurring polynomials.