# 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 |  |

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