i1 = R = ZZ/101[x,y,z]
o1 = R
o1 : PolynomialRing
i2 = m = image vars R
o2 = image | x y z |
1
R - module, submodule of R
i3 = m2 = image symmetricPower(2,vars R)
o3 = image | x2 xy xz y2 yz z2 |
1
R - module, submodule of R
i4 = M = R^1/m2
o4 = cokernel | z2 yz xz y2 xy x2 |
1
R - module, quotient of R
i5 = N = R^1/m
o5 = cokernel | z y x |
1
R - module, quotient of R
i6 = C = cone extend(resolution N,resolution M,id_(R^1))
1 4 9 9
o6 = R <-- R <-- R <-- R
0 1 2 3
o6 : ChainComplex
Let's check that the homology is correct. HH_0 should be 0. i7 = prune HH_0 C
o7 = 0
R - module
HH_1 should be isomorphic to m/m2. i8 = prune HH_1 C
o8 = cokernel | 0 -y -z |
| -z x 0 |
| y 0 x |
3
R - module, quotient of R
i9 = prune (m/m2)
o9 = cokernel | 0 0 z 0 0 y 0 0 x |
| 0 z 0 0 y 0 0 x 0 |
| z 0 0 y 0 0 x 0 0 |
3
R - module, quotient of R
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