PolyBoRi Tutorial
Release 0.8-3

Michael Brickenstein – Alexander Dreyer

January 30, 2013
1 Introduction
 1.1 Interfaces
 1.2 Ring Declarations
 1.3 Ordering
 1.4 Arithmetic
 1.5 Set operations
 1.6 Gröbner bases
2 How to program efficiently
 2.1 Low level friendly programming
 2.2 Replace algebra by set operations
 2.3 Direct constructions of diagrams
 2.4 Case study: Graded part of a polynomial
 2.5 Case study: Evaluation of a polynomial
3 Other techniques
 3.1 Storing polynomial data in a file
 3.2 Reinterpretation of Boolean sets as subsets of the vector space ℤ2n
 3.3 Lexicographical normal form of a polynomial against a variety
 3.4 Partial Boolean functions
 3.5 Building your own Gröbner basis algorithm
4 Alternative user interfaces
 4.1 PolyGUI
 4.2 Singular’s pyobject extension
References