# CoCoA:Ord

(Redirected from ApCoCoA-1:Ord)

## Ord

matrix defining a term-ordering

### Description

The first two forms return matrices which describe the term-ordering

of the current ring or of the ring R, respectively. The last form is

used as a modifier when creating a new ring. In that case, it determines the term-ordering for the ring (see Orderings). Its argument is a matrix of small integers which defines a term-ordering; i.e. for a ring with N indeterminates it must be an NxN matrix of full rank where the first non-zero entry in each column is positive. The matrix entries must be in the range -32767 to +32767, otherwise an error results.

#### Example

```  Use S ::= Q[x,y,z], Ord(Mat([[1,0,0], [0,1,0], [0,0,1]]));

M := Mat([[1,1],[0,-1]]);
T ::= Q[a,b], Ord(M);
U ::= Z/(101)[x,y,z,t], DegRevLex;
-- The term-order for the current ring, S.
Ord();
Mat([
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]
])
-------------------------------
Ord(T);
Mat([
[1, 1],
[0, -1]
])
-------------------------------
Ord(U);
Mat([
[1, 1, 1, 1],
[0, 0, 0, -1],
[0, 0, -1, 0],
[0, -1, 0, 0]
])
-------------------------------
```

### Syntax

```Ord():MAT
Ord(R:RING):MAT
Ord(M:MAT):MAT
```

```   <type>ring</type>
```