Before revision:  We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 presentation matrix %DIFAUXCMD which is ultimately decomposed . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.
After revision:  We also show how a recent algorithm of Lesnick and Wright can be adapted to convert the input filtration in O(n^{2d+1 presentation matrix %DIFAUXCMD . Various structural and computational results connecting the graded modules from commutative algebra to matrix reductions are established through the course.