up previous next
 Ord

matrix defining a term-ordering
 Syntax
 ``` Ord():MAT Ord(R:RING):MAT Ord(M:MAT):MAT ```

 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 ::= QQ[x,y,z], Ord(Mat([[1,0,0], [0,1,0], [0,0,1]])); M := Mat([[1,1],[0,-1]]); T ::= QQ[a,b], Ord(M); U ::= ZZ/(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] ]) ------------------------------- ```