A new Las Vegas algorithm is presented for the composition of two polynomialsmodulo a third one, over an arbitrary field . When the degrees of thesepolynomials are bounded by $n, the algorithm uses $O(n^{1.43)$ field operations . The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require $ O(n.63) field operations in general, and ${n.3/2+o(1)$ in particular case of power series over a field of large enoughcharacteristic . The new algorithm relies on the computation of a matrix of algebraic relationsthat is typically of small size .

Author(s) : Vincent Neiger, Bruno Salvy, √Čric Schost, Gilles Villard

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Keywords : field - algorithm - operations - composition - algebraic -

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