Projects aiming to speed up the gcd computations of TRIADE

Project 1 (van Hoeij & Monagan algorithm for TRIADE in MAPLE)   The algorithm by M. Monagan and M. van Hoeij [HM02] computes polynomial gcds over number fields by modular techniques. Its MAPLE implementation has been made available to us by M. Monagan.

A first goal of this project is to optimize the MAPLE version of TRIADE by calling Monagan's package where it applies. The second goal is to modify Monagan's package in order to compute the Bézout coefficients of the input polynomials. That is, to implement an Extended Euclidean version of the algorithm by M. Monagan and M. van Hoeij. This will also help improving the MAPLE version of TRIADE

Project 2 (van Hoeij & Monagan algorithm for TRIADE in AXIOM)   The main concern is the same as for Project 1. The differences are the language: AXIOM rather than MAPLE and the fact there is no implementation of [HM02] in AXIOM yet. So only the gcd (without Bézout coefficients) will be required here.

Project 3 (Moreno Maza & Oancea algorithm for TRIADE in MAPLE)   The algorithm by algorithm by M. Moreno Maza and C. Oancea [MO04] computes polynomial gcds over products of fields by modular techniques. It has been implemented in ALDOR by the authors.

A first goal of this project is to realize a MAPLE implementation of this algorithm. Then, the second goal is to optimize the MAPLE version of TRIADE by calling the algorithm [MO04] where it applies.

Project 4 (Moreno Maza & Oancea algorithm for TRIADE in AXIOM)   The goals are the same as for Project 3. The only differences is the language: AXIOM rather than MAPLE.