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              <p>Le résultant est un polynôme permettant de déterminer si plusieurs polynômes donnés ont une racine commune. Canny a pu donner un algorithme PSPACE calculant le résultant à l'aide de calculs de déterminants, mais pose la question de sa complexité exacte. On s'intéresse ici à donner une estimation plus fine de cette complexité. D'une part, on montre que le résultant est dans AM, et qu'il est NP-difficile sous réduction probabiliste. D'autre part, les matrices en jeu étant descriptibles par des circuits de taille raisonnable, on montre que le calcul du déterminant pour de telles matrices est PSPACE-complet.</p>
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