(Originally from math.SE, but might be better here)

I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica:

f[xx_, a_, b_] := 3*xx /. {a -> b} (* f[3*a*b, a, d] gives 9 b d *)


g[exp_] := exp /. {a_[n_] -> a[-n + 2]} (* g[3 b[3 + m]^2] gives 3 b[-1 - m]^2 *)

Is there a mathematical symbol and term to describe such transformations (which is denoted as /. + a substituation list with { someA -> someB } in Mathematica)?

PS: I see that there are two things I use here. First, the mathematica-functions f[xx_, a_, b_] and g[exp_] seem to be functionals (their arguments are functions). And then, there are those symbolic replacement operations denoted by /. { someA -> someB}. I am interested in the mathematically correct name for the second part. Thanks!

  • $\begingroup$ I don't quite think I've seen any words other than "substitution" and "replacement" being used, even in a mathematical context. $\endgroup$ – J. M. will be back soon May 26 '15 at 15:12
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    $\begingroup$ Re: notation, in some contexts, you'll see things like $$f^\prime(a)=\left.\frac{\mathrm d}{\mathrm dx}f(x)\right|_{x=a}$$ which indicate substitution; if there isn't a general one, maybe you can adapt this to what you have. $\endgroup$ – J. M. will be back soon May 26 '15 at 15:18
  • $\begingroup$ Thanks @J.M. That is actually a very good example, I haven't thought about that. I'll try whether all of my methods can be translated in such a way. $\endgroup$ – Mario Krenn May 29 '15 at 22:31
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    $\begingroup$ @J.M. I suppose it is the only part of SE where this is on topic. What do you think about moving your comment to answer? $\endgroup$ – Kuba Dec 18 '15 at 7:42

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