Bounds for Elimination of Unknowns in Systems of Differential-Algebraic Equations

Abstract Elimination of unknowns in systems equations, starting with Gaussian elimination, is a problem general interest. The finding an priori upper bound for the number differentiations elimination system differential-algebraic equations (DAEs) important challenge, going back to Ritt (1932). first characterization this via asymptotic analysis due Grigoriev’s result (1989) on quantifier differential fields, but challenge still remained. In paper, we present new bound, which major improvement over previously known results. We also lower shows tightness our low dimensions, are frequently occurring applications. Finally, discuss applications results designing algorithms DAEs.