grevlexWeight -- transform a weight matrix into a monomial ordering matrix

Synopsis

• Usage:

  wtgrev=grevlexWeight(wtR)

• Inputs:
  • wtR, a weight matrix
• Outputs:
  • wtgrev, a matrix, grevlex-over-weight matrix

Description

i1 : wtR = matrix{{5,6,6},{3,6,0}};

              2        3
o1 : Matrix ZZ  <--- ZZ

i2 : grevlexWeight(wtR) 

o2 = | 1 0 0 |
     | 5 6 6 |
     | 3 6 0 |

              3        3
o2 : Matrix ZZ  <--- ZZ

It is not standard in algebra systems to have a weighted monomial ordering based on one row of weights such as matrix{{5,6,6}} extended to matrix{{1,1,0},{1,0,0},{5,6,6}}, While M2 could extend it to matrix{{1,1,1},{1,1,0},{1,0,0},{5,6,6}} fairly easily, the method here allows for more than one independent row of a matrix matrix{{5,6,6},{3,6,0}} to be extended to matrix{{1,0,0},{5,6,6},{3,6,0}}.