This volume provides an overview of contemporary research in symbolic computation as it applies to the solution of polynomial systems. It focuses on systems of polynomials, systems of differential equations, noncommutative systems, and applications.

This volume presents the proceedings from the research conference, "Symbolic Computation: Solving Equations in Algebra, Analysis, and Engineering," held at Mount Holyoke College (MA). It provides an overview of current research in symbolic computation as it applies to the solution of polynomial systems. The conference brought together pure and applied mathematicians, computer scientists, and engineers, who use symbolic computation to solve systems of equations or who develop the theoretical background and tools needed for this purpose. Within this general framework, the conference focused on several themes: systems of polynomials, systems of differential equations, noncommutative systems, and applications.

Equations of parametric curves and surfaces via syzygies

An explicit description for the triangular decomposition of a zero-dimensional ideal through trace computations

Numerical irreducible decomposition using projections from points on the components

Counting stable solutions of sparse polynomial systems in chemistry

Central configurations in the Newtonian N-body problem of celestial mechanics

A power function approach to Kouchnirenko's conjecture

Finiteness for arithmetic fewnomial systems

Constructing double-exponential number of vectors of multiplicities of solutions of polynomial systems

Computing sparse projection operators

Grobner bases of abelian matrix groups

Lexicographic Grobner bases of 3-dimensional transportation problems

Simplicial complexes and syzygies of lattice ideals

Algorithmic determination of the rational cohomology of complex varieties via differential forms

Differential algebras on semigroup algebras

Noncommutative Grobner bases and Hochschild cohomology