HowTo:Term Orderings

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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 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.