# Findings powers within strings - Cases function

Any idea which Cases statement will work for both A^2 and CA^4X^36 to find the powers? If I set sym to these two expressions, one requires a curly brackets around the first argument and the other doesn't.

(* Sample 1.  Returns {} *)
Clear[x]; Clear[y];
sym = "A^2";
Cases[ToExpression[sym], x_^y_ -> {x, y}]

(* Sample 2. Returns {{CA,4},{X,36}} - as required*)
Clear[x]; Clear[y];
sym = "CA^4X^36";
Cases[ToExpression[sym], x_^y_ -> {x, y}]

(* Sample 3. Placing brackets around the first argument of the Cases \
function returns {{A,2}}  - as required *)
Clear[x]; Clear[y];
sym = "A^2";
Cases[{ToExpression[sym]}, x_^y_ -> {x, y}]

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You're not finding powers within strings because you convert the strings to expressions before finding powers. Since Cases looks for matches among parts of the input (either a list or an expression), it will not find a match in the expression A^2. Its only parts are A and 2. You can look at FullForm[ToExpression[sym]] to see its structure and confirm what its parts look like. That's why you need {A^2} to make A^2 a part of the input expression for Cases. So you may want to use that {...} wrapper with the other examples too and append , Infinity] to Cases[.... – Jens Jun 5 '13 at 5:02
I think that if you take a look at Cases in the documentation center, under the section heading Scope that the fifth example may be what you are looking for. – Clif Jun 5 '13 at 5:27

Changing the level specifications is what you need here:

Cases[ToExpression["a^2"], x_^y_ :> {x, y}, {0, ∞}]
{{a, 2}}

Cases[ToExpression["CA^4X^36"], x_^y_ :> {x, y}, {0, ∞}]
{{CA, 4}, {X, 36}}


Nevertheless, you might want to consider manipulating the strings directly:

StringCases["a^2", RegularExpression["(\\w+)\\^(\\d+)"] -> {"$1", "$2"}]
{{"a", "2"}}

StringCases["CA^4X^36", RegularExpression["(\\w+)\\^(\\d+)"] -> {"$1", "$2"}]
{{"CA", "4"}, {"X", "36"}}

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Thanks - I spent ages trying to work that out! – MLD Jun 5 '13 at 6:15
@MLD Note that J. M. used :> (RuleDelayed) rather than ->; by doing so x and y are localized and you will not need to use Clear on these symbols. – Mr.Wizard Jun 5 '13 at 6:50
@Mr.Wizard I hadn't noticed that and thank-you for pointing it out. – MLD Jun 6 '13 at 7:00