chainComplex(Matrix) -- make a small chain complex

i1 : R = QQ[x,y];

i2 : f = vars R

o2 = | x y |

             1       2
o2 : Matrix R  <--- R

i3 : chainComplex f

      1      2
o3 = R  <-- R
             
     0      1

o3 : ChainComplex

i4 : HH oo
-- ker (70) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (70) returned CacheFunction: -*a cache function*-
-- ker (70) called with Matrix: | x y |
-- ker (70) returned Module: image {1} | -y |
--                                 {1} | x  |
assert( ker(map(R^1,R^{{-1}, {-1}},{{x,y}})) === (image(map(R^{{-1}, {-1}},R^{{-2}},{{-y}, {x}}))))

o4 = 0 : cokernel | x y |

     1 : image {1} | -y |
               {1} | x  |

o4 : GradedModule