Gatermann K. Computer Algebra Methods for...Systems 2000

Textbook in PDF format

This book starts with an overview of the research of Grbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Grabner bases
Algorithms for the computation of invariants and equivariants
Symmetric bifurcation theory
Orbit space reduction