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adjoint.m2
-- * Usage:adjoint'(f,G,H) -- * Inputs: -- * f, a matrix, a homomorphism F --> Hom(G,H) between free modules -- * G, a module, a free module -- * H, a module, a free module -- * Outputs: -- * a matrix, the adjoint homomorphism F ** G --> H R = QQ[x] F = G = H = R^1 f = map(G**H,F,{{x}},Degree=>1) assert isHomogeneous f f' = adjoint'(f,dual G,H) assert isHomogeneous f' assert (source f' === F ** dual G) assert (target f' === H) F = R^{2} G = R^{3} H = R^{7} f = map(G**H,F,{{x}},Degree=>-7) assert isHomogeneous f f' = adjoint'(f,dual G,H) assert isHomogeneous f' assert (source f' === F ** dual G) assert (target f' === H) -- * Usage:adjoint(f,F,G) -- * Inputs: -- * f, a matrix, a homomorphism F ** G --> H between free modules -- * F, a module, a free module -- * G, a module, a free module -- * Outputs: -- * a matrix, the adjoint homomorphism F --> (dual G) ** H F = G = H = R^1 f = map(H,F**G,{{x}},Degree => 1) assert isHomogeneous f assert isHomogeneous adjoint(f,F,G) F = R^{2} G = R^{3} H = R^{7} f = map(H,F**G,{{x}},Degree => -1) assert isHomogeneous f f' = adjoint(f,F,G) assert isHomogeneous f' assert (source f' === F) assert (target f' === dual G ** H)
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