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Jump straight down to Update 2 for the final code. I'll leave the previous iterations here as they explain how that solution developed. This is based on the following definition of similarity: Two expressions are similar if they become identical when all variables are replaced by the same generic variable. For example, both $a+b$ and $b+c$ become ...


1

data = {I (a^2 + b^2) (*1*), a (I b + e) (*2*), b (I a + d) (*3*), b (I a + f) (*4*), a b (*5*), a (I b + f) (*6*), I (b^2 + c^2) (*7*)} systemnames = Names["System`*"]; test[expr_] := Select[{Extract[expr, #], #} & /@ Position[expr, _Symbol, Infinity], MemberQ[systemnames , ToString@(#[[1]])] &] Gather[data, test[#1] == test[#2] ...



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