Books in the Algorithms and Computation in Mathematics series

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form.

The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

Among all computer-generated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. This accessible book summarizes the present knowledge about the computational properties of Julia sets in a self-contained way.

This comprehensive book covers both long-standing results in the theory of polynomials and recent developments. After initial chapters on the location and separation of roots and on irreducibility criteria, the book covers more specialized polynomials.

One of the most remarkable theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. This book develops a new theory which is powerful enough to include all the earlier generalizations. It is also in part an extensive encyclopedia listing the different types of self-dual codes and their properties.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity;

This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation.

This book is divided into two parts, one theoretical and one focusing on applications, and offers a complete description of the Canonical Groebner Cover, the most accurate algebraic method for discussing parametric polynomial systems.

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Groebner bases) and geometry (via quiver theory).

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Groebner bases) and geometry (via quiver theory).