i1 : R = QQ[a..d];
|
i2 : C = res coker vars R
1 4 6 4 1
o2 = R <-- R <-- R <-- R <-- R <-- 0
0 1 2 3 4 5
o2 : ChainComplex
|
i3 : M = R^1/(a,b)
o3 = cokernel | a b |
1
o3 : R-module, quotient of R
|
i4 : C' = Hom(C,M)
o4 = 0 <-- cokernel {-4} | b a | <-- cokernel {-3} | b a 0 0 0 0 0 0 | <-- cokernel {-2} | b a 0 0 0 0 0 0 0 0 0 0 | <-- cokernel {-1} | b a 0 0 0 0 0 0 | <-- cokernel | b a |
{-3} | 0 0 b a 0 0 0 0 | {-2} | 0 0 b a 0 0 0 0 0 0 0 0 | {-1} | 0 0 b a 0 0 0 0 |
-5 -4 {-3} | 0 0 0 0 b a 0 0 | {-2} | 0 0 0 0 b a 0 0 0 0 0 0 | {-1} | 0 0 0 0 b a 0 0 | 0
{-3} | 0 0 0 0 0 0 b a | {-2} | 0 0 0 0 0 0 b a 0 0 0 0 | {-1} | 0 0 0 0 0 0 b a |
{-2} | 0 0 0 0 0 0 0 0 b a 0 0 |
-3 {-2} | 0 0 0 0 0 0 0 0 0 0 b a | -1
-2
o4 : ChainComplex
|
i5 : C'.dd_-1
o5 = {-2} | 0 0 0 0 |
{-2} | c 0 0 0 |
{-2} | 0 c 0 0 |
{-2} | d 0 0 0 |
{-2} | 0 d 0 0 |
{-2} | 0 0 d -c |
o5 : Matrix
|
i6 : C'.dd^2 == 0
o6 = true
|