This function computes a minimal free resolution of the (pruned) module $M$, reduces it by the maximal ideal, and returns a list of the unique degrees that occur at each step.
i1 : S = multigradedPolynomialRing {1,2}
o1 = S
o1 : PolynomialRing
|
i2 : B = irrelevantIdeal S
o2 = ideal (x x , x x , x x , x x , x x , x x )
0,1 1,2 0,0 1,2 0,1 1,1 0,0 1,1 0,1 1,0 0,0 1,0
o2 : Ideal of S
|
i3 : M = S^1/B
o3 = cokernel | x_(0,1)x_(1,2) x_(0,0)x_(1,2) x_(0,1)x_(1,1) x_(0,0)x_(1,1) x_(0,1)x_(1,0) x_(0,0)x_(1,0) |
1
o3 : S-module, quotient of S
|
i4 : F = res prune M
1 6 9 5 1
o4 = S <-- S <-- S <-- S <-- S <-- 0
0 1 2 3 4 5
o4 : ChainComplex
|
i5 : multigraded betti F
0 1 2 3 4
o5 = 0: 1 . . . .
2: . 6ab . . .
3: . . 3a2b+6ab2 . .
4: . . . 3a2b2+2ab3 .
5: . . . . a2b3
o5 : MultigradedBettiTally
|
i6 : supportOfTor M
o6 = {{{0, 0}}, {{1, 1}}, {{2, 1}, {1, 2}}, {{2, 2}, {1, 3}}, {{2, 3}}}
o6 : List
|
i7 : netList supportOfTor M
+------+------+
o7 = |{0, 0}| |
+------+------+
|{1, 1}| |
+------+------+
|{2, 1}|{1, 2}|
+------+------+
|{2, 2}|{1, 3}|
+------+------+
|{2, 3}| |
+------+------+
|
Alternately, the minimal free resolution can be given directly.
i8 : netList supportOfTor F
+------+------+
o8 = |{0, 0}| |
+------+------+
|{1, 1}| |
+------+------+
|{2, 1}|{1, 2}|
+------+------+
|{2, 2}|{1, 3}|
+------+------+
|{2, 3}| |
+------+------+
|
The object supportOfTor is a method function.