partialRegularities -- calculates Castelnuovo-Mumford regularity in each component of a multigrading

i1 : S = ZZ/101[x_0,x_1,y_0,y_1,z_0,z_1,Degrees=>{{1,0,0},{1,0,0},{0,1,0},{0,1,0},{0,0,1},{0,0,1}}]

o1 = S

o1 : PolynomialRing

i2 : I = ideal(x_0*x_1*y_0*z_0^2, x_1^2*y_0^2*y_1^2*z_0^2, x_0^3*y_0*z_1, x_0^2*x_1*y_1*z_0*z_1, x_0*x_1^2*y_1^2*z_0^3, x_1^3*y_0^2*y_1*z_1^2)

                   2   2 2 2 2   3       2             2 2 3   3 2   2
o2 = ideal (x x y z , x y y z , x y z , x x y z z , x x y z , x y y z )
             0 1 0 0   1 0 1 0   0 0 1   0 1 1 0 1   0 1 1 0   1 0 1 1

o2 : Ideal of S

i3 : M = S^1/I

o3 = cokernel | x_0x_1y_0z_0^2 x_1^2y_0^2y_1^2z_0^2 x_0^3y_0z_1 x_0^2x_1y_1z_0z_1 x_0x_1^2y_1^2z_0^3 x_1^3y_0^2y_1z_1^2 |

                            1
o3 : S-module, quotient of S

i4 : netList supportOfTor M

     +---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
o4 = |{0, 0, 0}|         |         |         |         |         |         |         |         |         |
     +---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
     |{2, 1, 2}|{3, 1, 1}|{3, 1, 2}|{2, 4, 2}|{3, 2, 3}|{3, 3, 2}|         |         |         |         |
     +---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
     |{4, 2, 2}|{4, 1, 3}|{3, 2, 3}|{3, 4, 2}|{3, 3, 3}|{4, 2, 4}|{6, 3, 2}|{5, 3, 3}|{4, 3, 4}|{3, 4, 4}|
     +---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+
     |{4, 2, 3}|{4, 3, 4}|{6, 3, 3}|{5, 3, 4}|{4, 4, 4}|         |         |         |         |         |
     +---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+

i5 : partialRegularities M

o5 = {4, 3, 2}

o5 : List