Function Repository Resource:

SubscriptedSymbols

Retrieves all symbols in subscript format from a given expression

Contributed by: E. Chan-López, Víctor Castellanos & Jorge Luis Ramos Castellano

ResourceFunction["SubscriptedSymbols"][expr]

gives all symbols already in subscript format for a given expr.

Details and Options

ResourceFunction["SubscriptedSymbols"] looks for symbols with represents as subscripts anywhere within the expression expr.

ResourceFunction["SubscriptedSymbols"] treats the constant C[i] as symbol in subscript format and retrieves them.

Similar to Variables, ResourceFunction["SubscriptedSymbols"] also has the Modulus option.

Each unique subscript is included in the result only once.

Examples

Basic Examples (3)

Use SubscriptedSymbols with a simple expression:

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Use SubscriptedSymbols with a list of simple expressions:

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Use SubscriptedSymbols with a list of expressions that don't contain any symbols in subscript format:

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$ResourceFunction[ "SubscriptedSymbols"] /@ {a*t1, b*x, c*s, d*x1, e*\[Pi]}$

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Scope (8)

Use SubscriptedSymbols with an expression that contains derivatives of any order:

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$ResourceFunction["SubscriptedSymbols"][ Subscript[x, 1]'[t] + Subscript[x, 2]''[t] + \!$\*SuperscriptBox[ SubscriptBox[\(x$, $3$], TagBox[ RowBox[{"(", RowBox[{"1", ",", "1"}], ")"}], Derivative], MultilineFunction->None]\)[t, s]]$

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Use SubscriptedSymbols with a list of simple expressions:

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Use SubscriptedSymbols with a list of more complicated expressions:

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$ResourceFunction[ "SubscriptedSymbols"]@{(Subscript[x, 1]^(1 + n) + Subscript[x, 2]) (Subscript[x, 3]^(-2 + m) - x4), Sqrt[ Subscript[\[Alpha], \[Beta]][t] + Subscript[\[Theta], \[Psi]][t]], Power[(Subscript[x, 4][t, s] + 2 Subscript[w, 3][t, s])^3, (5)^-1]}$

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Use SubscriptedSymbols with a non-linear system of differential equations:

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$ResourceFunction[ "SubscriptedSymbols"][{Subscript[x, 1]'[t] == -Subscript[x, 1][t]^2 - Subscript[x, 2][t], Subscript[x, 2]'[t] == 2 Subscript[x, 1][t] - Subscript[x, 2][t]^3}]$

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Use SubscriptedSymbols with a hyperbolic partial differential equation with non-rational coefficients:

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$ResourceFunction["SubscriptedSymbols"][ D[Subscript[u, 1][x, y], {x, 2}] - 2 Sin[x] D[Subscript[u, 1][x, y], x, y] - Cos[x]^2 D[Subscript[u, 1][x, y], {y, 2}] - Cos[x] D[Subscript[u, 1][x, y], y] == 0]$

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Use SubscriptedSymbols with a tensor product of matrices involving C[i]:

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Use SubscriptedSymbols with a univariate polynomial:

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Use SubscriptedSymbols with a polynomial in two variables:

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Options (2)

Modulus (2)

Find subscripted symbols present after reducing coefficients modulo 2:

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For polynomials, SubscriptedSymbols and Variables gives the same results:

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Applications (5)

Use SubscriptedSymbols to define a simple function that transforms symbols, already in subscript format, into symbols that can be converted to subscript format within a given expression:

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$ToSymbolFormat[expr_] /; SameQ[Head[expr], Subscript] := ToExpression[StringJoin@(ToString /@ Level[expr, {-1}])] ToSymbolFormat[expr_] /; SameQ[Head[expr], C] := expr /. C[s_Integer?NonNegative] :> ToExpression[ToString[C] <> ToString[s]] ToSymbolFormat[expr_] := expr /. Thread[ ResourceFunction["SubscriptedSymbols"][expr] -> ToSymbolFormat /@ ResourceFunction["SubscriptedSymbols"][expr]]$

Use ToSymbolFormat with a tensor of rank 3:

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$MatrixForm@ ToSymbolFormat@ D[{Subscript[x, 1]^2 Subscript[y, 1] + Subscript[x, 1], -Subscript[y, 1] Subscript[x, 1]^3 - 2 Subscript[x, 1]}, {{Subscript[x, 1], Subscript[y, 1]}, 2}]$

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Use ToSymbolFormat with a polynomial in two variables:

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Use ToSymbolFormat with a function:

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$ToSymbolFormat[Function[{x, y}, C[1]*E^(-x^2 - y^2) + C[2]]]$

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Use ToSymbolFormat with an expression involving nested subscripts:

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$ToSymbolFormat[ Cos[Subscript[x, Subscript[\[Alpha], \[Beta]]]] + Sin[Subscript[x, Subscript[\[Psi], \[CurlyPhi]]]]]$

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Properties and Relations (3)

Unlike Variables, SubscriptedSymbols looks for subscripted variables in non-polynomial expressions:

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Use SubscriptedSymbols with a list of functions:

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$ResourceFunction[ "SubscriptedSymbols"] /@ {Function[{x, y}, C[1]*E^(-x^2 - y^2) + C[2]], Function[{x, t}, C[3] + x^2/6 + C[4][t - 1/6 (1 + Sqrt[13]) x]]}$