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I have the following expression:

Subscript[x, i] + (-Subscript[x, -1 + i] + Subscript[x, 
    i]) Subscript[\[Zeta], 
  1 + i] + ((Subscript[gf, -1 + i] + Subscript[gh, 
     i]) Subscript[\[Zeta], 1 + i] - 
  Subscript[gf, 
   i] (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 1 + i]) - 
  Subscript[gh, 
   1 + i] (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 1 + i]))/
 L

i.e., enter image description here

And I want to collect the terms in a manner so that I get the following equivalent form of the last expression:

enter image description here

What would be the Mathematica command to go from expression 1 to expression 2?

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2 Answers 2

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2
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There is no single command for this. You must do this by hand. "Coefficient" is your friend here.

First we get the different coefficients:

c1 = Coefficient[ex, (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 1 + i])];
c2 = Coefficient[ex - (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 
       1 + i]) c1, (Subscript[gf, -1 + i] + Subscript[gh, i])];
c3 = Coefficient[ex - (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 
       1 + i]) c1 - (Subscript[gf, -1 + i] + Subscript[gh, i]) c2, 
   Subscript[\[Zeta], 1 + i]];
c4 = ex - (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 
       1 + i]) c1 - (Subscript[gf, -1 + i] + Subscript[gh, i]) c2 - 
    Subscript[\[Zeta], 1 + i] c3 // Simplify;

Then we assemble the wanted expression:

{1, Subscript[\[Zeta], 1 + i], (Subscript[gf, -1 + i] + Subscript[gh, i]), (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 1 + i])} . {c4, c3, 
  c2, c1}

enter image description here

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  • $\begingroup$ That is a great solution, thanks Daniel! $\endgroup$
    – TDH
    Commented Apr 29, 2022 at 12:27
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Consider the TreeForm of expr:

expr = Subscript[x, 
   i] + (-Subscript[x, -1 + i] + Subscript[x, i]) Subscript[\[Zeta], 
    1 + i] + ((Subscript[gf, -1 + i] + 
        Subscript[gh, i]) Subscript[\[Zeta], 1 + i] - 
     Subscript[gf, 
       i] (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 1 + i]) -
      Subscript[gh, 
       1 + i] (1 + Subscript[\[Zeta], 1 + i] + 
        Subscript[\[Eta], 1 + i]))/L

enter image description here

I have labeled the Tree such that the L in the denominator is marked as "p" and this branch needs to appear with "q". As well as "p" needs to appear as a multiplier for the simplified form of "r" and "s".

The following step is required:

Subscript[gf, 
   i] (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 1 + i]) - 
  Subscript[gh, 
   1 + i] (1 + Subscript[\[Zeta], 1 + i] + Subscript[\[Eta], 
     1 + i]) // Simplify

$$\left(\text{gf}_i-\text{gh}_{i+1}\right) \left(\zeta _{i+1}+\eta _{i+1}+1\right)$$

Initially I wanted to MapAt the function Simplify at this location but I am still struggling with it so some rule-therapy is in order:

expr /. Times[Power[p_], Plus[q_, r_, s_]] :> Plus[
   Times[Power[p], q], Times[Power[p], Simplify[Plus[r, s]]]]

$$-\frac{\left(\text{gf}_i+\text{gh}_{i+1}\right) \left(\zeta _{i+1}+\eta _{i+1}+1\right)}{L}+\frac{\zeta _{i+1} \left(\text{gf}_{i-1}+\text{gh}_i\right)}{L}+\zeta _{i+1} \left(x_i-x_{i-1}\right)+x_i$$

enter image description here

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