# ApCoCoA-1:DA.DiffTO

## DA.DiffTO

Matrix corresponding to predefined differential term orderings.

### Syntax

```DA.DiffTO(D:STRING):MAT
```

### 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&lt;x[1,0]&lt;x[1,1]&lt;x[1,2]&lt;...&lt;x[2,0]&lt;x[2,1]&lt;...
-- <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&lt;x[1,0]&lt;x[2,0]&lt;...&lt;x[1,1]&lt;x[2,1]&lt;...
-- <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(DA.DiffTO(<quotes>Lex</quotes>));
```