Monomial order

A single murder drying or term order is a linear order on the set of monomials over a finite set of variables. Mono murder busbars are required to define the division with remainder of polynomials in several variables. A Gröbner basis with respect to defining the remainder of this division clearly.

Definition

A linear order on the set

The monomials in the variables is called mono murder drying, if the following holds

1 For all monomials

2 The monomial is the smallest monomial:

Condition ( 2), provided that ( 1 ) is satisfied, equivalently, that a well-ordering is, so there is no infinite descending chains

Are of monomials. This property is the basis of many scheduling algorithms for evidence in the context of Gröbner bases. If ( 2) is violated, for example, is then obtained by repeated application of ( 1) the descending chain

Examples of mono murder busbars

(Clean ) Lexical Rules

The lexical or lexicographic order is defined by

Total degree order

The total degree order or graduated lexical order is defined by

Block orders

Each monomial over a set of variables can be decomposed uniquely into a product so that only occur in variables and in only variables. With this notation is made ​​for a given mono murder busbars and on monomials over the variables and the block order on monomials in defined as