Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Nearly Optimal Algorithms For Canonical Matrix Forms
SIAM Journal on Computing
A new algorithm for the computation of canonical forms of matrices over fields
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
An O(n3) algorithm for the Frobenius normal form
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Modern computer algebra
Challenges of symbolic computation: my favorite open problems
Journal of Symbolic Computation
Computational aspects of discrete logarithms
Computational aspects of discrete logarithms
Computer algebra handbook
Reliable Krylov-based algorithms for matrix null space and rank
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
On finding multiplicities of characteristic polynomial factors of black-box matrices
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
transalpyne: a language for automatic transposition
ACM Communications in Computer Algebra
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A new randomized algorithm is presented for computation of the Frobenius form and transition matrix for an n × n matrix over a field. Using standard matrix and polynomial arithmetic, the algorithm has an asymptotic expected complexity that matches the worst case complexity of the best known deterministic algorithmic for this problem, recently given by Storjohann and Villard [16]. The new algorithm is based on the evaluation of Krylov spaces, rather than an climination technique, and may therefore be superior when applied to sparse or structured matrices with a small number of invariant factors.