The MatrixOrder command returns a matrix representation for a monomial order tord as a list of lists. If a list of variables is given as an optional second argument, the columns of the matrix are permuted to match the order of the variables.  If vars is a name, then the default permutation of the columns is assigned to vars.

$\mathrm{with}\left(\mathrm{Groebner}\right)\:$

$\mathrm{MatrixOrder}\left(\mathrm{plex}\left(x\,y\,z\right)\right)$

$\left[\left[1\,0\,0\right]\,\left[0\,1\,0\right]\,\left[0\,0\,1\right]\right]$

$\mathrm{MatrixOrder}\left(\mathrm{plex}\left(x\,y\,z\right)\,\left[z\,x\,y\right]\right)$

$\left[\left[0\,1\,0\right]\,\left[0\,0\,1\right]\,\left[1\,0\,0\right]\right]$

$\mathrm{MatrixOrder}\left(\mathrm{tdeg}\left(x\,y\,z\right)\,'\mathrm{vars}'\right)$

$\left[\left[1\,1\,1\right]\,\left[0\,0\,\mathrm{-1}\right]\,\left[0\,\mathrm{-1}\,0\right]\right]$

$\mathrm{vars}$

$\left[x\,y\,z\right]$

$\mathrm{MatrixOrder}\left(\mathrm{grlex}\left(x\,y\,z\right)\right)$

$\left[\left[1\,1\,1\right]\,\left[1\,0\,0\right]\,\left[0\,1\,0\right]\right]$