i1 : wtR = matrix{{5,6,6},{3,6,0}}; 2 3 o1 : Matrix ZZ <--- ZZ |
i2 : weightGrevlex(wtR) o2 = | 5 6 6 | | 3 6 0 | | 1 0 0 | 3 3 o2 : Matrix ZZ <--- ZZ |
It is standard in other algebra systems to have a weighted monomial ordering based on one row of weights such as matrix{{5,6,6}} being extended to matrix{{5,6,6},{1,1,0},{1,0,0}}, whereas M2 would extend it to matrix{{5,6,6},{1,1,1},{1,1,0}}. The method here allows for more than one independent row of weights matrix{{5,6,6},{3,6,0}} to be extended to matrix{{5,6,6},{3,6,0},{1,0,0}}. There is a grevlexWeight method in this package, but it is not exported since it is not needed explicitly. While it is the implicit monomial ordering on the integral closure outputs, the choice was to output only the weight matrix defining it or the weightGrevlex monomial ordering.