i3 : M = ker F
-- ker (113) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (113) returned CacheFunction: -*a cache function*-
-- ker (113) called with Matrix: | a b d e |
-- | b c e f |
-- ker (113) returned Module: image {1} | cd-be 0 e2-df ce-bf |
-- {1} | -bd+ae e2-df 0 -be+af |
-- {1} | b2-ac -ce+bf -be+af 0 |
-- {1} | 0 cd-be bd-ae b2-ac |
assert( ker(map(R^2,R^{{-1}, {-1}, {-1}, {-1}},{{a,b,d,e}, {b,c,e,f}})) === (image(map(R^{{-1}, {-1}, {-1}, {-1}},R^{{-3}, {-3}, {-3}, {-3}},{{c*d-b*e,0,e^2-d*f,c*e-b*f}, {-b*d+a*e,e^2-d*f,0,-b*e+a*f}, {b^2-a*c,-c*e+b*f,-b*e+a*f,0}, {0,c*d-b*e,b*d-a*e,b^2-a*c}}))))
o3 = image {1} | cd-be 0 e2-df ce-bf |
{1} | -bd+ae e2-df 0 -be+af |
{1} | b2-ac -ce+bf -be+af 0 |
{1} | 0 cd-be bd-ae b2-ac |
4
o3 : R-module, submodule of R
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