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A polynomial-time algorithm for computing the permanent in any field ofcharacteristic 3 is presented in this article. The principal objects utilizedfor that purpose are the Cauchy and Vandermonde matrices, the discriminantfunction and their generalizations of various types. Classical theorems on thepermanent such as the Binet-Minc identity and Borchadt's formula are widelyapplied, while a special new technique involving the notion of limit re-definedfor fields of finite characteristics and corresponding computational methodswas developed in order to deal with a number of polynomial-time reductions. Allthe constructions preserve a strictly algebraic nature ignoring the structureof the basic field, while applying its infinite extensions for calculatinglimits.  A natural corollary of the polynomial-time computability of the permanent ina field of a characteristic different from 2 is the non-uniform equalitybetween the complexity classes P and NP what is equivalent to RP=NP (Ref. [1]).

A Polynomial-time Algorithm for Computing the Permanent in GF(3^q)