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In 1980 Schwartz gave a fast probabilistic method which tests if a matrix of polynomials over Z is singular or not. The method is based on the idea of signature functions which are mappings of mathematical expressions into finite rings. In Schwartz's paper, they were polynomials over Z into GF(p). Because computation in GF(p) is very fast compared with computing with polynomials, Schwartz's method yields an enormous speedup both in theory and in practice. Therefore it is desirable to extend the class of expressions for which we can find effective signature functions. In the mid 80's Gonnet extended the class of expressions, for which signature functions could be found, to include a restricted class of elementary functions and integer roots. In this paper we present and compare methods for constructing signature functions for expressions containing algebraic numbers. Some experimental results are given.