Description
This function takes as input a presentation matrix
m of a finitely generated graded
S-module
M an exterior algebra
E and two integers
l and
h. If
r is the regularity of
M, then this function computes the piece of the Tate resolution from cohomological degree
l to cohomological degree
max(r+2,h). For instance, for the homogeneous coordinate ring of a point in the projective plane:
i1 : S = ZZ/32003[x_0..x_2];
|
i2 : E = ZZ/32003[e_0..e_2, SkewCommutative=>true];
|
i3 : m = matrix{{x_0,x_1}};
1 2
o3 : Matrix S <-- S
|
i4 : regularity coker m
o4 = 0
|
i5 : T = tateResolution(m,E,-2,4)
1 1 1 1 1 1 1
o5 = E <-- E <-- E <-- E <-- E <-- E <-- E
0 1 2 3 4 5 6
o5 : ChainComplex
|
i6 : betti T
0 1 2 3 4 5 6
o6 = total: 1 1 1 1 1 1 1
-4: 1 1 1 1 1 1 1
o6 : BettiTally
|
i7 : T.dd_1
o7 = {-4} | e_2 |
1 1
o7 : Matrix E <-- E
|