Algorithmic Number Theory

Volume 1122 of the series Lecture Notes in Computer Science pp 243-257


An algorithm of subexponential type computing the class group of quadratic orders over principal ideal domains

  • Sachar PaulusAffiliated withInstitute for Experimental Mathematics, University of Essen

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We present an algorithm which computes the class group of a quadratic order over a principal ideal domain that fulfills some properties which are implicated by computational requirements. It is a generalization of the subexponential method of Hafner and McCurley which computes the class group of an order in an imaginary quadratic number field. We discuss the concept of reduction theory of binary quadratic forms over a Euclidean domain which makes our algorithm practical. Several examples of principal ideal domains are given for which we have applied our generic algorithm implemented in C++ using template techniques.