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 |