NC2 computation of gcd-free basis and application to parallel algebraic numbers computation

Thierry Gautier, Jean-Louis Roch
1997 Proceedings of the second international symposium on Parallel symbolic computation - PASCO '97  
We establish that the problem of computing a gcd-free basis for a set of polynomials is in AfC~for any arbitrary field F. This leads to a proof that arithmetic for a simple algebraic extension is in N@. This result is applied to improve the complexity of the parallel deterministic algorithm to compute the Jordan normal form of a n dimensional matrix in time 0(log2 n). Fast Gcd-l%e Basis Computations Let F be an arbitrary commutative field. The computational model used in this section is the
more » ... hmetic PRAM model. We say that a problem lies in NC! [4, 11] if there exists a parallel algorithm which solves it in time is bounded by O(log~n) using nQ1) processors for all inputs of size n. 2.1
doi:10.1145/266670.266682 dblp:conf/cap/GautierR97 fatcat:7v6fdjfwafcfzbu7hr56v773ci