Identifying the symbol which has a specific value

Question

I'm writing a program that will solve the value of 1 variable in a 4-variable equality equation, but the variable to be solved will depend on the user's input to the program.

This is what I've come up with: Create a Mathematica script that reads in 4 parameters from the commandline. Read in the given 4 values and assign it to 4 variables. The variable that needs to be solved will have a specific value (say -100). I need to identify that variable and Remove it from the Mathematica namespace, so that 3 variables remain.

I can then call the Solve function that contains n variables, but since I've used Remove on 1 of those, Mathematica solves the value for that variable.

The only part that I don't get to work, is to identify which symbol's value is -100 so that I can call Remove on the symbol.

Can anyone suggest a solution? I've tried putting all my variables in a list and find the symbol with value -100 using Position or Case, but it only returns the -100 numerical value and not the symbol name. As so:

(* Values for a, b, c and d have been read from the commandline using *)
(* a = ToExpression[$CommandLine[[4]]] etc  *)

list = {a, b, c, d}
(* {1, 2, 3, -100} *)

Position[list, -100]
(* {{4}} *)

Cases[list, -100]
(* {-100} *)

(* I can't call Remove on the answers given by Position and Cases to remove variable d *)

I've tried some other solutions as well but with no luck. In case it's relevant - I'm new to Mathematica.

Answer 1

Here's one way of doing this:

(* names of variables *)
syms = {"a", "b", "c", "d"}

(* values (these would be from user input in your case) *)
vals = {1, 2, -100, 3}

(* value *not* to assign to a symbol *)
noset = -100

(* clean out our symbols to be safe *)
Remove @@ syms

(* do the appropriate assignments *)
MapThread[If[#2 != noset, Evaluate[ToExpression[#1]] = #2] &, {syms, vals}];

(* what's there? *)
{a, b, c, d}

(* {1, 2, c, 3} *)

(* use them in some solve... *)
Solve[a + b == c + d]

(* {{c -> 0}} *)

Answer 2

syms = {a, b, c, d};
vals = {1, 2, -100, 3};

Table[If[vals[[i]] != -100, syms[[i]] = vals[[i]], syms[[i]]], {i, 1, Range@Length@syms}]

{1, 2, c, 3}

Answer 3

I'd suggest something like...

Block[{a, b, c, d}, 
  With[{a = 1, b = 1, c = 1}, 
    Solve[a + b + c + d == 0, First[Cases[{a, b, c, d}, _Symbol]]]]]

Block localizes the symbols. With gives some of them values. The First[Cases... finds the one without a value.