reesCanonicalModule -- constructs the graded canonical module in a ring constructed via classicalReesAlgebra or extendedReesAlgebra

i1 : R = QQ[x,y];

i2 : J = ideal(x^2,x*y,y^2);

o2 : Ideal of R

i3 : S = classicalReesAlgebra(J);

i4 : T = extendedReesAlgebra(J);

i5 : reesCanonicalModule(S)

o5 = cokernel {1, 3} | -ly_1 ly_0  -y |
              {1, 3} | ly_2  -ly_1 x  |

                            2
o5 : S-module, quotient of S

i6 : reesCanonicalModule(T)

o6 = cokernel {1, 3} | bt_0 -bt_1 -y   x     0     0    -ti 0  |
              {1, 3} | bt_1 -bt_2 0    0     -y    x    0   ti |
              {0, 2} | 0    0     bt_1 -bt_2 -bt_0 bt_1 x   y  |

                            3
o6 : T-module, quotient of T