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I have a system for equations that is structured hierarchically:
- Level 0: these are base variables that I can measure from a process (e.g. a,b,c)
- Level 1: these are variables derived from Level 0 variables (e.g. d=a+b, e=bc)
- Level 2: these are variables derived from Level 1 variables (e.g. f=d
e)

For all Levels >0 I have only expressions that use variables from one level below, but I want to express those in terms of Level 0 variables. In this case, I want to give Mathematica the expressions for a,b,c,d,e,f in the above form and have it show me that f=d*e=abc+b²c.

Thank you so much for any help
- a Mathematica beginner

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Maybe I missed the point, but if you just copy and paste your expressions (and insert spaces to give multiplication) you get:

d = a + b;
e = b c;
f = d e

which gives you b (a + b) c, which is equivalent to your given f. Is this all you were asking?

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I'm guessing you are looking for the list of replacements that need to be made going down to level 0 instead of just showing the level 0 results. Are you looking for something like this?

assignments[d] = a + b;
assignments[e] = b c;
assignments[f] = d e;
assignments[x_] := x;

FixedPointList[Map[assignments, #, {-1}] &, {f}][[;; -2, 1]]

{f, d e, b (a + b) c}

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  • $\begingroup$ It really was that easy, thank you! I thought I had to keep everything in the format d[a_,b_]:=a+b $\endgroup$ – F. E. Apr 17 '15 at 7:10

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