# HowTo:Term Orderings

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Revision as of 17:57, 13 February 2021 by Andraschko (talk | contribs) (Small start (not finished yet))

This page is an introduction into term orderings in CoCoA-5 or ApCoCoA-2. In order to understand this topic, we assume that the reader is familiar with the concept of term orderings on polynomial rings.

## Mathematical definition

Let *K* be a field, let be the polynomial ring over * K* in

*indeterminates and let be the set of all power products in*

**n***.*

**P**Let be a total order on * T(P)*. For a pair , we write is called a

**term ordering**on

*iff it is multiplicative, i.e. implies for each , and we have for all terms .*

**T(P)**For a polynomial , we can write where and for each * i* such that . Then we use the following notation

- is the
**leading terms**of,**f** - is the
**leading monomial**ofand**f** - is the
**leading coefficient**of.**f**