Absolute polynomial factorization in two variables and the knapsack problem

A recent algorithmic procedure for computing the absolute factorization of a polynomial P(X, Y ), after a linear change of coordinates, is via a factorization modulo X3 . This was proposed by A. Galligo and D. Rupprecht in [16], [8]. Then absolute factorization is reduced to finding the minimal zero sum relations between a set of approximated numbers bi, i = 1 to n such that Pn i=1 bi = 0, (see also [17]). Here this problem with an a priori exponential complexity, is efficiently solved for large degrees (n > 100). We rely on L.L.L. algorithm, used with a strategy of computation inspired by van Hoeij’s treatment in [23]. For that purpose we prove a theorem on bounded integer relations between the numbers bi, also called linear traces in [19]

• Type: Conference
• Year: 2004
• Where: ISSAC
• Authors: Guillaume Chèze
• Keywords: Absolute Factorization, Factorization Modulo, ISSAC 2004, Numbers Bi