cone

cone f -- produce the mapping cone of a map f of chain complexes

     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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