Algorithms Differential algebra Polynomials Straight-line programs Computation theory Computational complexity Differential equations Elimination theory Functions Probabilistic algorithms ALGEBRA Algebra Complexity Computation of the radical of a regular ideal Differential Hilbert function Differentiation index Efficient generation of polynomial ideals Geometric resolution Implicit systems of Differential Algebraic Equations Index Kronecker algorithm Number and degree of generators of polynomial ideals Probabilistic logics Regular signs Resolvent representation Complete intersection polynomial ideals DAE systems Effective Nullstellensatz Geometry Hilbert