Algorithms for polynomial GCD computation over algebraic function fields

Let L be an algebraic function field in k ≥ 0 parameters t1, . . . , tk. Let f1, f2 be non-zero polynomials in L[x]. We give two algorithms for computing their gcd. The first, a modular GCD algorithm, is an extension of the modular GCD algorithm of Brown for Z[x1, . . . , xn] and Encarnacion for Q(α)[x] to function fields. The second, a fraction-free algorithm, is a modification of the Moreno Maza and Rioboo algorithm for computing gcds over triangular sets. The modification reduces coefficient growth in L to be linear. We give an empirical comparison of the two algorithms using implementations in Maple.

• Type: Conference
• Year: 2004
• Where: ISSAC
• Authors: Mark van Hoeij, Michael B. Monagan
• Keywords: Algebraic Function, Algorithms, ISSAC 2004, Modular Gcd Algorithm