Abstract: | An algorithm is obtained for factoring polynomials in several variables over local fields with complexity which is polynomial in the length of notation of the input data and the characteristic of the residue field of the local field. Here by definition we assume that an infinite series can be calculated in polynomial time if its i-th partial sum can be calculated in time which is polynomial in the length of notation of the input data and i for any i.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 192, pp. 112–148, 1991. |