dual(Complex) -- makes the dual of a complex

i1 : S = ZZ/101[a..d]

o1 = S

o1 : PolynomialRing

i2 : B = intersect(ideal(a,c),ideal(b,d))

o2 = ideal (c*d, a*d, b*c, a*b)

o2 : Ideal of S

i3 : C1 = freeResolution B

      1      4      4      1
o3 = S  <-- S  <-- S  <-- S
                           
     0      1      2      3

o3 : Complex

i4 : C2 = dual C1

      1      4      4      1
o4 = S  <-- S  <-- S  <-- S
                           
     -3     -2     -1     0

o4 : Complex

i5 : prune HH C2

o5 = cokernel {-4} | d c b a | <-- cokernel {-2} | c a 0 0 |
                                            {-2} | 0 0 d b |
     -3                             
                                   -2

o5 : Complex

i6 : Ext^2(S^1/B, S)

o6 = cokernel {-2} | c a 0 0 |
              {-2} | 0 0 d b |

                            2
o6 : S-module, quotient of S

i7 : Ext^3(S^1/B, S)

o7 = cokernel {-4} | d c b a |

                            1
o7 : S-module, quotient of S