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.
Let K be a field, let be the polynomial ring over K in n indeterminates and let be the set of all power products in P.
Let be a total order on T(P). For a pair , we write is called a term ordering on T(P) iff it is multiplicative, i.e. implies for each , and we have for all terms .
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 of f and
- is the leading coefficient of f.