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 : ChainComplexLet's check that the homology is correct. HH_0 should be 0.
i7 = prune HH_0 C o7 = 0 R - moduleHH_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
Go to main index.
Go to concepts index.