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Abstract: In this paper we describe software for an efficient factorization of polynomials over global fields . The algorithm for function fields was recently incorporated into our system KANT. The method is based on a generic algorithm developed by the second author in an earlier paper in this journal. Besides algorithmic aspects not contained in that paper we give details about the current implementation and about some complexity issues as well as a few illustrative examples. Also, a generalization of the application of LLL reduction for factoring polynomials over arbitrary global fields is developed. [Copyright &y& Elsevier]

Abstract: A field k of characteristic unequal to 2 is called tractable if for every nonzero , , whenever the quaternion algebra is split for all and , then is split. In the present paper, we study tractability of algebraic function fields in one variable over global fields and give specific examples of tractable function fields and intractable function fields of genus one over , the rationals. [Copyright &y& Elsevier]

Abstract: In this paper we present a generic algorithm for factoring polynomials over global fields . As efficient implementations of that algorithm for number fields and function fields differ substantially, these cases will be treated separately. Complexity issues and implementations will be discussed in part II which also contains illustrative examples. [Copyright &y& Elsevier]