# ApCoCoA-1:DA.DiffTO

From ApCoCoAWiki

## DA.DiffTO

Matrix corresponding to predefined differential term orderings.

### Syntax

DA.DiffTO(D:STRING):MATRIX

### Description

This function returns the matrix corresponding to the indicated term ordering D.

@param

*D*Name of a predefined differential term ordering.@return The matrix corresponding to the predefined term ordering.

#### Example

-- Assume that the current ring is given by QQ[x[1..n,0..m]]. -- Then D can be one of the following values: -- <quotes>Lex</quotes>: Lexicographic ordering with 1<x[1,0]<x[1,1]<x[1,2]<...<x[2,0]<x[2,1]<... -- <quotes>DegLex</quotes>: S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Lex T -- <quotes>WLex</quotes>: S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Lex T -- <quotes>Ord</quotes>: Lexicographic ordering with 1<x[1,0]<x[2,0]<...<x[1,1]<x[2,1]<... -- <quotes>DegOrd</quotes>: S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Ord T -- <quotes>WOrd</quotes>: S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Ord T -- -- Use as follows: Use QQ[x[1..1,0..20]]; Use QQ[x[1..1,0..20]], Ord(DiffTO(<quotes>Lex</quotes>));