Abstract
An algorithm is constructed for factoring polynomials in several variables over a finite field, which works in polynomial time in the size of the polynomial and q. Previously this result was known in the case of one variable. An algorithm is given for the solution (over the algebraic closure F of the field F) of systems of algebraic equations, where with working time of order where L is the size of a representative of the original system, ℓ is the degree of transcendence of the field F over the prime subfield, q=char(F). Previously the estimate was known for ℓ=0.
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