Editors' foreword

The January 2009 special issue of AAECC presents the first English translations of two posthumous papers of Jacobi, completed with some unpublished material discovered in Jacobi's Nachlaß. Jacques Calmet took in charge the editing process of the two translations and of the paper to which contributed F. Ollivier. Although known names of mathematics, such as Jordan, worked on the subject, nothing substantial was done before Ritt's paper, in which a first proof is given for arbitrary linear systems and for two variables. In 1960, Volevich rediscovered Jacobi's bound in the linear case. In 1983, Richard Cohn proved that Jacobi's bound implies the dimension conjecture and was the first to mention the existence of Jacobi's algorithm. In 2001, Pryce rediscovered Jacobi's shortest reduction method and the truncated determinant criterion. In 2004, Hrushovski gave a proof of Jacobi's bound for difference systems.