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I want to simplify the arrays of a matrix, first I tried to define my constants then used "FullSimplify" but it does not work. Please see the screen shout.

SetAttributes[Subscript[u, 10], Constant]
SetAttributes[k, Constant]
SetAttributes[a, Constant]

FullSimplify [IndexedExpression[i_,j_,k_]:=HoldForm[Subscript[OverTilde["R"],i,k] TraditionalForm[D[Subscript[OverBar[u],j],Subscript[x,k]]]];

IndexedExpression[j,i,k];
Table[IndexedExpression[a,b,c],{b,1,3},{a,1,3},{c,1,3}];
IndexedExpression[j,i,k]==MatrixForm[Apply[Plus,Table[IndexedExpression[a,b,c],{b,1,3},{a,1,3},{c,1,3}],{2}]]/.{t->SuperStar[t]/(k*Subscript[u, 10]),
Subscript[x, 1]->Subscript[SuperStar[x], 1]/k,Subscript[x, 2]->Subscript[SuperStar[x], 2]/k,Subscript[x, 3]->a* Subscript[SuperStar[x], 3],
Subscript[\!\(\*OverscriptBox[\(u\), \(_\)]\), 1]->(Subscript[u, 10])*Subscript[SuperStar[\!\(\*OverscriptBox[\(u\), \(_\)]\)], 1],Subscript[\!\(\*OverscriptBox[\(u\), \(_\)]\), 2]->(Subscript[u, 10])*Subscript[SuperStar[\!\(\*OverscriptBox[\(u\), \(_\)]\)], 2],Subscript[\!\(\*OverscriptBox[\(u\), \(_\)]\), 3]->(a*k*Subscript[u, 10])*Subscript[SuperStar[\!\(\*OverscriptBox[\(u\), \(_\)]\)], 3],
Subscript[\!\(\*OverscriptBox[\(u\), \(~\)]\), 1]->(Subscript[u, 10])Subscript[SuperStar[\!\(\*OverscriptBox[\(u\), \(~\)]\)], 1],Subscript[\!\(\*OverscriptBox[\(u\), \(~\)]\), 2]->(Subscript[u, 10])Subscript[SuperStar[\!\(\*OverscriptBox[\(u\), \(~\)]\)], 2],Subscript[\!\(\*OverscriptBox[\(u\), \(~\)]\), 3]->(a*k*Subscript[u, 10])Subscript[SuperStar[\!\(\*OverscriptBox[\(u\), \(~\)]\)], 3],
\!\(\*OverscriptBox[\(p\), \(~\)]\)->(\[Rho]*(Subscript[u, 10])^2)* SuperStar[\!\(\*OverscriptBox[\(p\), \(~\)]\)],
Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 1,1]->((Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 1,1],Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 1,2]->((Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 1,2 ],Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 1,3]->(a*k*(Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 1,3],
Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 2,1]->((Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 2,1],Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 2,2]->((Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 2,2 ],Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 2,3]->(a*k*(Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 2,3],
 Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 3,1]->(a*k*(Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 3,1],Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 3,2]->(a*k*(Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 3,2 ],Subscript[\!\(\*OverscriptBox[\("\<R\>"\), \(~\)]\), 3,3]->((a*k*Subscript[u, 10])^2)Subscript[\!\(\*OverscriptBox[\("\<R*\>"\), \(~\)]\), 3,3]}]

enter image description here

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  • $\begingroup$ It seems your equation is already simple. At which place, for instance, you expect simplification? $\endgroup$ Commented May 6, 2024 at 18:59
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    $\begingroup$ The error message is clear. It says "SetAttributes:sym Argument expected to be symbol". The problem is that subscript is not one symbol. That is why it is better to avoid using subscripts in Mathematica. I never use them myself. I assume this is the error you asking about. I did not run your code. $\endgroup$ Commented May 6, 2024 at 19:11
  • $\begingroup$ thank you for your comment . the problem is not only the subscript, the simplify does not work for 'a' and 'k' as well. $\endgroup$ Commented May 6, 2024 at 19:35
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    $\begingroup$ Recommendation: it is just not a good idea to use Subscripts, display-format functions (like TraditionalForm), special formatting and characters (SuperStar[ \!\(\*OverscriptBox[\(u\), \(~\)]\)]), etc., when doing calculations in Mathematica. You just need to change all of your variable names to things like u, u[2], u[1,2], uT[1,2] (for $\tilde{u}$), etc. It is likely that all the errors are due to these things. Especially don't use MatrixForm, because that is for display purposes only: it won't work for multiplying matrices. $\endgroup$ Commented May 7, 2024 at 6:16

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This is too long for a comment and might be off the mark but the way I would handle this type of expression is I would use the symbols straight into the array definitions as dummy functions, do my manipulations and then at the end define a human readable rule to make it into something more palatable or something TeXFormable.

Here, it looks like you have a rank-2 Array[R, {3, 3}], and a Jacobian of a vector field Array[U[#][{x, y, z}] &, 3] which you can symbolically define as D[Array[U[#][{x, y, z}] &, 3], {{x, y, z}, 1}].

So all in all you can achieve the same matrix symbolically with something like:

With[{vars = {x, y, z}, headVar1 = R, headVar2 = U},
 Block[{rArray, uArray, difArray, humanReadableRule, expression},
  rArray = Array[headVar1, {3, 3}];
  uArray = Array[headVar2[#][Sequence @@ vars] &, 3];
  difArray = D[uArray, {vars, 1}];
  humanReadableRule = {headVar1[a_, b_] :> 
     Subscript[ToString@headVar1, ToString[a] <> "," <> ToString[b]], 
    headVar2[c_] :> Subscript[ToString@headVar2, ToString[c]]};
  expression  = difArray . Transpose@rArray;
  expression/. humanRadableRule // TableForm
  ]
 ]

expression is something Mathematica can manipulate, simplify etc but the need for human readable output(after manipulating the symbolic expressions) can be satisfied using the rule humanReadableRule, although I admit it will take a bit of work to get the derivative to look good.

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