Abstract

. F Algorithms on multivariate polynomials represented by straight-line programs are developed irst it is shown that most algebraic algorithms can be probabilistically applied to data that is given by y r a straight-line computation. Testing such rational numeric data for zero, for instance, is facilitated b andom evaluations modulo random prime numbers. Then auxiliary algorithms are constructed that a determine the coefficients of a multivariate polynomial in a single variable. The first main result is an lgorithm that produces the greatest common divisor of the input polynomials, all in straight-line r a representation. The second result shows how to find a straight-line program for the reduced numerato nd denominator from one for the corresponding rational function. Both the algorithm for that conl c struction and the greatest common divisor algorithm are in random polynomial-time for the usua oefficient fields and output a straight-line program, which with controllably high probab...

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