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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];
/**/  M := mat([ [1,2,3], [3,4,5], [0,0,1]]);
/**/  P := NewPolyRing(CoeffRing(S), IndetSymbols(S), M, 2);
/**/  GradingDim(P);
2
/**/  ord(P);
matrix( /*QQ*/
 [[1, 2, 3],
  [3, 4, 5],
  [0, 0, 1]]
 )

/**/  GradingDim(S);
1
/**/  ord(S);
matrix( /*QQ*/
 [[1, 1, 1],
  [0, 0, -1],
  [0, -1, 0]]
 )

See Also