C. Mathematical background

This chapter introduces some of the mathematical notions and definitions used throughout the manual. It is mostly a collection of the most prominent definitions and properties. For details, please, refer to articles or text books (see References).

C.1 Standard bases
C.2 Hilbert function
C.3 Syzygies and resolutions
C.4 Characteristic sets
C.5 Gauss-Manin connection
C.6 Toric ideals and integer programming
C.7 Non-commutative algebra
C.8 Decoding codes with Groebner bases
C.9 References