I am working on creating a function that takes in any physics equation as a string and converts it to an equation that I will then paste into an interactive interface as asked here: How to make an interactive calculator for any mathematical relation?. I am implementing the first answer as a function that accepts any physics equation as a string and does two things before replacing the example of a^2+b^2==c^2.

First I want to replace any instance of "=" with "==" except for an instance of "==". The goal of this is to make a user-friendly function if the user enters an equation with incorrect programming syntax. I will then convert it to an expression.

Second, after it has been converted to an expression I will extract the symbols from the equation using this code, which I got from How to find all symbols in an expression and perform an operation on them?.

Symbols[x_String] := 
 DeleteDuplicates@Cases[ToExpression[x], _Symbol, Infinity]

The function for the first program is as follows:

StringReplace["\!\(\*SuperscriptBox[\(a\), \
\(2\)]\)+\!\(\*SuperscriptBox[\(b\), \
\(2\)]\)==\!\(\*SuperscriptBox[\(c\), \(2\)]\)", 
 Except[{"=="}, "="] -> "=="]

I am trying to base my code off this example

StringReplace["the cat in the hat", 
 Except[Characters["aeiou"], "c"] -> ""]

Unfortunately, this causes an error: enter image description here I am not sure what I am doing wrong here.

EDIT: I have my attempt here: https://www.wolframcloud.com/obj/burbery1/Published/Interactive%20Solver%20Function.nb In the process I came across two more unexpected hurdles: if the variable the user is solving for was already defined in a previous call of Interactive Solver or another piece of program that already executed, the symbol is regarded as a numerical value and not a variable.

The second problem is that the InteractiveSolver function returns a list of Null values when I run it for some reason.

I tried some code provided as an answer to this question and encountered the following error: enter image description here

  • 1
    $\begingroup$ Except is not accepted as a valid string pattern. As a way around, you could first replace all "==" by "=" and then replace all "=" by "==". $\endgroup$ Nov 6, 2021 at 17:05
  • $\begingroup$ The function Symbols will return symbolic numeric constants as well as variables, e.g., look at the result of Symbols["Pi*x + E"]. Either modify the definition to Symbols[x_String] := DeleteDuplicates@Cases[ToExpression[x], _Symbol?(!NumericQ[#]&), Infinity] or use Symbols[x_String] := Variables[Level[x, {-1}]] $\endgroup$
    – Bob Hanlon
    Nov 6, 2021 at 17:13
  • $\begingroup$ I am wondering if I should attach code in the form of a cloud notebook link or paste it directly in Stack Exchange or both. I have a little more than a page of code if you include the code in the question. $\endgroup$ Nov 6, 2021 at 17:18
  • $\begingroup$ Interpreter[] might be fast enough for you: parse = Interpreter["MathFormula"]; parse["a=b^2"]. Parsing takes a little less than a second, so it's not fast. $\endgroup$
    – Michael E2
    Nov 7, 2021 at 16:27
  • $\begingroup$ I don't quite understand how the Interpreter capability of Mathematica can be used to turn any string with only one equations sign into an expression with an equality checking expression (==) instead of assignment (=). Can you provide an example or explain a little bit more how the Interpreter can help me accomplish my goal? $\endgroup$ Nov 8, 2021 at 1:17

1 Answer 1


FWIW, my take on the big problem. I'm not particularly interested in parsing strings, so I can delete if this is unhelpful.

 *  Calculator
     (* displays some data for inspection *)
     Dynamic@{var, formula},
       (* TBD:check input/output of Solve *)
       With[{sol = Solve[ReleaseHold@formula, var]},
        With[{sol0 = 
           sol /. Thread[freevariables -> value /@ freevariables]},
         value[var] = var /. Last[sol0];(* last sol *)
         Grid@Transpose@{sol, sol0} /. Rule -> Equal
     (* parameter inputs *)
        InputField[Dynamic@value@#] & /@ freevariables}
   {{formula, formula}, (* user input = held expression *)
       ({formula, variables, var} = parseFormula[#];
         (value[#] = 1) & /@ variables;
         freevariables = DeleteCases[variables, var];
         ) &],
      Hold@Expression] &},
   {{var, var}, Dynamic@variables, SetterBar, TrackingFunction -> (
      (var = #;
        freevariables = DeleteCases[variables, var]) &)},
   {{variables, variables}, None},
   {{freevariables, freevariables}, None},
   {{parseFormula, parseFormula}, None},
   {{value, value}, None},(* stores values of parameters *)
   Initialization :> (
     (* utility (parses held expression) *)
     parseFormula // ClearAll;
     parseFormula[f_] := Module[{myformula, myvars, myvar},
       myformula = 
        f /. {Set | SetDelayed | Rule | RuleDelayed -> Equal,
          Null -> $Failed}; (* TBD: Handle user error *)
       myvars = Reduce`FreeVariables[ReleaseHold@myformula];
       myvar = Replace[{myformula, myvars},
         {{Hold[v_ == _] /; MemberQ[myvars, v], _} :> v,
          {_, {a_, ___}} :> a,
          {_, v_} :> v (* TBD: Handle user error *)
       myformula = Replace[myformula,
         {eq : Hold[_Equal] :> eq,
          Hold[x_] /; Internal`WouldBeNumericQ[x, Evaluate@myvars] :>
           (myvar = $ans; 
            PrependTo[myvars, $ans];
            Hold[$ans == x]),
          form_ :> (myvars = myvar = $Failed; form)
          }]; (* TBD: Handle user error *)
       {myformula, myvars, myvar}
     (* init *)
     {formula, variables, var} = 
      parseFormula[ToExpression["a^2+b^2==c^2", StandardForm, Hold]];
     freevariables = DeleteCases[variables, var];
     (value[#] = 1) & /@ variables;
  CellContext -> Cell]
  • $\begingroup$ If I try to change the equation or relation inside the box I get an error that I would like to display in a screenshot but don't know how to. $\endgroup$ Nov 8, 2021 at 1:19
  • $\begingroup$ @PeterBurbery What did you type? When I type "a^2 == b^2 - c^2", I get no error. $\endgroup$
    – Michael E2
    Nov 8, 2021 at 2:01
  • $\begingroup$ When I type "a^2=b^2-c^2" I get an error because it is an assignment expression and I would like to make it convert any assignment expressions into equality testing expressions. $\endgroup$ Nov 8, 2021 at 15:22
  • $\begingroup$ @PeterBurbery I get no error if I enter "a^2=b^2-c^2". The code converts = (Set) to == (Equal) when the formula is parsed. It also converts A -> b h to A == b h. Not that a student would think of that, but it's a sort of like an assignment (a substitution Rule technically), so I threw that in. Unfortunately (?) E = m c^2 gets converted to the base of the natural logarithm and E=mc^2 is in terms the single variable mc squared. $\endgroup$
    – Michael E2
    Nov 8, 2021 at 16:34
  • $\begingroup$ I was pressing Shift+Enter every time instead of Enter. It is working now. $\endgroup$ Nov 8, 2021 at 16:42

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