Triangular Decomposition for Algebraic and Geometric Computing

In this talk, we present several algorithms for decomposing systems of multivariate polynomials into triangular systems of various kinds. The algorithms have been efficiently implemented and successfully applied to numerous problems of scientific computing, ranging over computational polynomial algebra, automated geometric reasoning, solving systems of nonlinear equations, qualitative analysis of biological systems, and computer aided geometric design. We discuss some of the applications with a number of illustrative examples.