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On the basis of $A$ being defined as posted: adef[g_List, h_] := Module[{n = Length[g]}, gs = ArrayFlatten[Table[g, {n}]]; hs = ArrayFlatten[ ReplacePart[ConstantArray[0, {n, n}], {i_, i_} :> h]]; hs - gs] To illustrate: adefex[g_List, h_] := Module[{n = Length[g]}, gs = ArrayFlatten[Table[g, {n}]]; hs = ArrayFlatten[ ...


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The command InverseFunction[a Tanh[d (# - g)] + a/2 (Tanh[d (m + g)] - Tanh[d (m - g)]) &][y] gives the output $$ \frac{\tanh ^{-1}\left(\frac{a \tanh (d (m-g))-a \tanh (d (g+m))+2 y}{2 a}\right)+d g}{d}$$ together with the warning that $\tanh^{-1}$ is a multivalued function.



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