COMPUTATIONAL COMMUTATIVE ALGEBRA 2

This book is the natural continuation of Computational Commutative Algebra 1 with some twists. The main part of this book is a breathtaking passeggiata through the computational domains of graded rings and modules and their Hilbert functions. Besides Gröbner bases, we encounter Hilbert bases, border bases, SAGBI bases, and even SuperG bases. The tutorials traverse areas ranging from algebraic geometry and combinatorics to photogrammetry, magic squares, coding theory, statistics, and automatic theorem proving. Whereas in the first volume gardening and chess playing were not treated, in this volume they are. This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand. The theories it describes can be applied to anything from children's toys to oil production. TOC:Foreword.- Introduction.- The Homogeneous Case.- Hilbert Functions.- Further Applications.- A. The ABC of CoCoA 5.- B. Suggestions for Further Reading.- C. Hints for Selected Exercises.- Bibliography.