Revisions to What's an efficient way to relabel multiple dummy indices in a large expression?

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edited Mar 20, 2017 at 4:21

J. M.'s missing motivation

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added longer input example for performance testing

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edited Feb 27, 2017 at 16:44

Jonathan Rayner

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edit: and the desired output of the above would be, in Latex

$ A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} - A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} = 0$

or in my code convention:

Edit: For performance testing

here is some longer input:

test = 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 3]] A[r][\[Nu]] A[r][
 Subscript[\[Omega], 2]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][\[Beta]\[Beta]] A[r][\[Beta]\[Beta]] A[r][\[Nu]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]2, 1], 3]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 4]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 4]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 3]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 3]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 4]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 5]] A[r][\[Nu]] d[
  l][\[Phi], \[Nu]] F[l, l][Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 3]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 5]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 5]] A[r][\[Nu]] d[
  l][\[Phi], \[Nu]] F[l, l][Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[\[Omega], 2]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 5]] F[l, l][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 6]] A[r][\[Nu]] A[r][
 Subscript[\[Omega], 2]] d[l][\[Phi], \[Nu]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][\[Nu]] A[r][\[Nu]] A[r][
 Subscript[\[Omega], 2]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 6]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 8]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 6]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 8]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 7]] A[r][\[Nu]] d[
  l][\[Phi], \[Nu]] F[l, l][Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 7]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 6]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 6]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 7]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 8]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][\[Nu]] A[l][
 Subscript[\[Omega], 2]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 8]] F[l, l][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 2], 3]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 4]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 2], 5]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 3], 
 Subscript[Subscript[\[Rho]2, 2], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 2], 5]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 4]] d[l][\[Phi], \[Nu]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 4], 
 Subscript[Subscript[\[Rho]2, 2], 3]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 3], 
 Subscript[Subscript[\[Rho]2, 2], 5]] + 
 5/6 A[l][\[Nu]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 5]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 4], 
 Subscript[Subscript[\[Rho]2, 2], 3]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 3], 
 Subscript[Subscript[\[Rho]2, 2], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 2], 6]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 7]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 8]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 7], \[Nu]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 6], 
 Subscript[Subscript[\[Rho]2, 2], 8]] - 
 5/6 A[l][\[Nu]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 7]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 8]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 7], 
 Subscript[Subscript[\[Rho]2, 2], 6]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 6], 
 Subscript[Subscript[\[Rho]2, 2], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 3]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]3, 1], 5]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 3], 
 Subscript[Subscript[\[Rho]3, 1], 5]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[\[Omega], 3]] A[r][\[Kappa]\[Kappa]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 1], 5]] F[l, l][
 Subscript[Subscript[\[Rho]3, 1], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 3], 
 Subscript[Subscript[\[Rho]3, 1], 5]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[r][\[Kappa]\[Kappa]] A[r][
 Subscript[\[Omega], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 1], 6]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 8]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 7]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]3, 1], 6]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 8]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 6]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]3, 1], 7]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 8]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 8]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[\[Omega], 3]] F[l, l][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[\[Omega], 3]] A[r][\[Kappa]\[Kappa]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 1], 8]] F[l, l][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[r][\[Kappa]\[Kappa]] A[r][
 Subscript[Subscript[\[Rho]3, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 2], 5]] F[l, l][
 Subscript[Subscript[\[Rho]3, 2], 4], 
 Subscript[Subscript[\[Rho]3, 2], 3]] g[r, r][
 Subscript[Subscript[\[Rho]3, 2], 3], 
 Subscript[Subscript[\[Rho]3, 2], 5]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[r][\[Kappa]\[Kappa]] A[r][
 Subscript[Subscript[\[Rho]3, 2], 7]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 2], 8]] F[l, l][
 Subscript[Subscript[\[Rho]3, 2], 7], 
 Subscript[Subscript[\[Rho]3, 2], 6]] g[r, r][
 Subscript[Subscript[\[Rho]3, 2], 6], 
 Subscript[Subscript[\[Rho]3, 2], 8]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[r][
 Subscript[\[Omega], 1]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][\[Nu], \[Mu]] + 
 5/12 A[l][\[Beta]\[Beta]] A[r][\[Beta]\[Beta]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 2], 3]] A[r][
 Subscript[Subscript[\[Rho]1, 2], 3]] A[r][
 Subscript[Subscript[\[Rho]1, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 2], 4]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] g[r, r][
 Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 3]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] A[r][
 Subscript[\[Omega], 1]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][\[Beta]\[Beta]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] A[r][\[Beta]\[Beta]] d[
  l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] g[r, r][
 Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 2], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 2], 5]] A[r][
 Subscript[Subscript[\[Rho]1, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 2], 4]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[Subscript[\[Rho]1, 2], 3], 
 Subscript[Subscript[\[Rho]1, 2], 5]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[r][
 Subscript[\[Omega], 1]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] S[l, l][Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][\[Nu]] A[r][Subscript[\[Omega], 1]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 7]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] g[r, r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 7]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 7]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 8]] A[r][
 Subscript[\[Omega], 1]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] g[r, r][Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 8]] A[r][
 Subscript[\[Omega], 1]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 7]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 8]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] g[r, r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 7]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 8]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]];

edit: and the desired output of the above would be, in Latex

$ A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} - A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} = 0$

or in my code convention:

edit: the desired output of the above would be, in my code convention:

Edit: For performance testing

here is some longer input:

test = 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 3]] A[r][\[Nu]] A[r][
 Subscript[\[Omega], 2]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][\[Beta]\[Beta]] A[r][\[Beta]\[Beta]] A[r][\[Nu]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]2, 1], 3]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 4]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 4]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 3]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 3]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 4]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 5]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 5]] A[r][\[Nu]] d[
  l][\[Phi], \[Nu]] F[l, l][Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 3]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 5]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 5]] A[r][\[Nu]] d[
  l][\[Phi], \[Nu]] F[l, l][Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[\[Omega], 2]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 5]] F[l, l][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 3], 
 Subscript[Subscript[\[Rho]2, 1], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 6]] A[r][\[Nu]] A[r][
 Subscript[\[Omega], 2]] d[l][\[Phi], \[Nu]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][\[Nu]] A[r][\[Nu]] A[r][
 Subscript[\[Omega], 2]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 6]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 8]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][Subscript[\[Omega], 2]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 6]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 8]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 7]] A[r][\[Nu]] d[
  l][\[Phi], \[Nu]] F[l, l][Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 7]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 6]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 6]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 7]] F[l, l][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 8]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] + 
 5/6 A[l][\[Nu]] A[l][
 Subscript[Subscript[\[Rho]2, 1], 8]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[\[Omega], 2]] F[l, l][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][\[Nu]] A[l][
 Subscript[\[Omega], 2]] A[r][\[Nu]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 1], 8]] F[l, l][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[\[Omega], 2], 
 Subscript[Subscript[\[Rho]2, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]2, 1], 6], 
 Subscript[Subscript[\[Rho]2, 1], 8]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 2], 3]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 4]] F[l, l][\[Nu], 
 Subscript[Subscript[\[Rho]2, 2], 5]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 3], 
 Subscript[Subscript[\[Rho]2, 2], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 2], 5]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 4]] d[l][\[Phi], \[Nu]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 4], 
 Subscript[Subscript[\[Rho]2, 2], 3]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 3], 
 Subscript[Subscript[\[Rho]2, 2], 5]] + 
 5/6 A[l][\[Nu]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 5]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 4], 
 Subscript[Subscript[\[Rho]2, 2], 3]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 3], 
 Subscript[Subscript[\[Rho]2, 2], 5]] - 
 5/6 A[l][Subscript[Subscript[\[Rho]2, 2], 6]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 7]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 8]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 7], \[Nu]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 6], 
 Subscript[Subscript[\[Rho]2, 2], 8]] - 
 5/6 A[l][\[Nu]] A[r][\[Nu]] A[r][
 Subscript[Subscript[\[Rho]2, 2], 7]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]2, 2], 8]] F[l, l][
 Subscript[Subscript[\[Rho]2, 2], 7], 
 Subscript[Subscript[\[Rho]2, 2], 6]] g[r, r][
 Subscript[Subscript[\[Rho]2, 2], 6], 
 Subscript[Subscript[\[Rho]2, 2], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 3]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]3, 1], 5]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 3], 
 Subscript[Subscript[\[Rho]3, 1], 5]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[\[Omega], 3]] A[r][\[Kappa]\[Kappa]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 1], 5]] F[l, l][
 Subscript[Subscript[\[Rho]3, 1], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 3], 
 Subscript[Subscript[\[Rho]3, 1], 5]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[r][\[Kappa]\[Kappa]] A[r][
 Subscript[\[Omega], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 1], 6]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 8]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 7]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]3, 1], 6]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 8]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 6]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[Subscript[\[Rho]3, 1], 7]] F[l, l][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 8]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[Subscript[\[Rho]3, 1], 8]] A[r][\[Kappa]\[Kappa]] d[
  l][\[Phi], Subscript[\[Omega], 3]] F[l, l][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[l][
 Subscript[\[Omega], 3]] A[r][\[Kappa]\[Kappa]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 1], 8]] F[l, l][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[\[Omega], 3], 
 Subscript[Subscript[\[Rho]3, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]3, 1], 6], 
 Subscript[Subscript[\[Rho]3, 1], 8]] - 
 5/12 A[l][\[Kappa]\[Kappa]] A[r][\[Kappa]\[Kappa]] A[r][
 Subscript[Subscript[\[Rho]3, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 2], 5]] F[l, l][
 Subscript[Subscript[\[Rho]3, 2], 4], 
 Subscript[Subscript[\[Rho]3, 2], 3]] g[r, r][
 Subscript[Subscript[\[Rho]3, 2], 3], 
 Subscript[Subscript[\[Rho]3, 2], 5]] + 
 5/12 A[l][\[Kappa]\[Kappa]] A[r][\[Kappa]\[Kappa]] A[r][
 Subscript[Subscript[\[Rho]3, 2], 7]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]3, 2], 8]] F[l, l][
 Subscript[Subscript[\[Rho]3, 2], 7], 
 Subscript[Subscript[\[Rho]3, 2], 6]] g[r, r][
 Subscript[Subscript[\[Rho]3, 2], 6], 
 Subscript[Subscript[\[Rho]3, 2], 8]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[r][
 Subscript[\[Omega], 1]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][\[Nu], \[Mu]] + 
 5/12 A[l][\[Beta]\[Beta]] A[r][\[Beta]\[Beta]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 2], 3]] A[r][
 Subscript[Subscript[\[Rho]1, 2], 3]] A[r][
 Subscript[Subscript[\[Rho]1, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 2], 4]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] g[r, r][
 Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 3]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 3]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] A[r][
 Subscript[\[Omega], 1]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][\[Beta]\[Beta]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] A[r][\[Beta]\[Beta]] d[
  l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] d[l][\[Phi], 
 Subscript[\[Omega], 1]] g[r, r][\[Nu], \[Mu]] g[r, r][
 Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 4]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 3]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[\[Omega], 1]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 5]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 4]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 3], 
 Subscript[Subscript[\[Rho]1, 1], 5]] S[l, l][\[Nu], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 2], 3]] A[l][
 Subscript[Subscript[\[Rho]1, 2], 5]] A[r][
 Subscript[Subscript[\[Rho]1, 2], 4]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 2], 4]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[Subscript[\[Rho]1, 2], 3], 
 Subscript[Subscript[\[Rho]1, 2], 5]] S[l, l][\[Nu], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[r][
 Subscript[\[Omega], 1]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] S[l, l][Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][\[Nu]] A[r][Subscript[\[Omega], 1]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] S[l, 
  l][Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 7]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] g[r, r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 7]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[r][
 Subscript[Subscript[\[Rho]1, 1], 6]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 7]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 8]] A[r][
 Subscript[\[Omega], 1]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] g[r, r][Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] + 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 8]] A[r][
 Subscript[\[Omega], 1]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][Subscript[Subscript[\[Rho]1, 1], 6]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 7]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 8]] d[l][\[Phi], \[Nu]] g[r, 
  r][\[Nu], \[Mu]] g[r, r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]] - 
 5/12 A[l][\[Nu]] A[l][Subscript[Subscript[\[Rho]1, 1], 7]] A[l][
 Subscript[Subscript[\[Rho]1, 1], 8]] d[l][\[Phi], 
 Subscript[Subscript[\[Rho]1, 1], 6]] g[r, r][\[Nu], \[Mu]] g[r, 
  r][Subscript[\[Omega], 1], 
 Subscript[Subscript[\[Rho]1, 1], 7]] g[r, r][
 Subscript[Subscript[\[Rho]1, 1], 6], 
 Subscript[Subscript[\[Rho]1, 1], 8]] S[l, l][
 Subscript[\[Omega], 1], \[Mu]];

added specific examples of desired outputs

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edited Feb 27, 2017 at 16:16

Jonathan Rayner

246
1
6

Theedit: and the desired output of the above would be, in Latex

$ A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} - A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} = 0$

or in my code convention:

(* A[r][Subscript[\[Tau], 1]] A[r][Subscript[\[Tau], 2]] F[l, l][
Subscript[\[Tau], 2], Subscript[\[Tau], 3]] F[l, r][
Subscript[\[Tau], 1], Subscript[\[Tau], 3]]
- 
A[r][Subscript[\[Tau], 1]] A[r][Subscript[\[Tau], 2]] F[l, l][
Subscript[\[Tau], 2], Subscript[\[Tau], 3]] F[l, r][
Subscript[\[Tau], 1], Subscript[\[Tau], 3]]
= 0 *)

That is, the goal would be to search for expressions that have repeated indices and relabel these indices according to a common list that is as long as the number of pairs of repeated indices.

The goal would be to search for expressions that have repeated indices and relabel these indices according to a common list that is as long as the number of pairs of repeated indices.

edit: and the desired output of the above would be, in Latex

$ A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} - A^{\tau_1} A^{{\tau_2}} F_{{\tau_2} {\tau_3}} {F_{\tau_1}}^{{\tau_3}} = 0$

or in my code convention:

(* A[r][Subscript[\[Tau], 1]] A[r][Subscript[\[Tau], 2]] F[l, l][
Subscript[\[Tau], 2], Subscript[\[Tau], 3]] F[l, r][
Subscript[\[Tau], 1], Subscript[\[Tau], 3]]
- 
A[r][Subscript[\[Tau], 1]] A[r][Subscript[\[Tau], 2]] F[l, l][
Subscript[\[Tau], 2], Subscript[\[Tau], 3]] F[l, r][
Subscript[\[Tau], 1], Subscript[\[Tau], 3]]
= 0 *)

That is, the goal would be to search for expressions that have repeated indices and relabel these indices according to a common list that is as long as the number of pairs of repeated indices.

Formatted code

Source Link

edited Feb 27, 2017 at 4:49

MarcoB

68k
19
100
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added some more thoughts on a solution/clarification of what isn't a solution

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edited Feb 27, 2017 at 3:38

Jonathan Rayner

246
1
6

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asked Feb 27, 2017 at 3:04

Jonathan Rayner

246
1
6

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