Software for Numerical Algebraic Geometry: A Paradigm and Progress Towards its Implementation.- PHClab: A MATLAB/Octave Interface to PHCpack.- Computing Gröbner Fans and Tropical Varieties in Gfan.- On a Conjecture for the Dimension of the Space of the Multiple Zeta Values.- DEMiCs: A Software Package for Computing the Mixed Volume Via Dynamic Enumeration of all Mixed Cells.- SYNAPS: A Library for Dedicated Applications in Symbolic Numeric Computing.- Tropical Implicitization and Mixed Fiber Polytopes.- Towards a Black-Box Solver for Finite Games: Computing All Equilibria With Gambit and PHCpack.- ApaTools: A Software Toolbox for Approximate Polynomial Algebra.

Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as, CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms.

This volume reflects the workshop "Software for Algebraic Geometry" held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.