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programming - Prevent iterator name from being confused with symbol passed into function body


I have a massive amount of code with lots of Table and Sum inside a Module. Each with their own iterators, and I have completely lost track of all of them. But if the user calls the function with an argument matching the name of the iterator, the code no long works as intended.


An example is this function that is supposed to return a list of three repeated symbols:



function[x_] := 
Module[{},
  answer = Table[x, {i, 1, 3}];
  Return[answer];
]

For example:


function[a]
(*{a,a,a}*)


But this can be broken by


function[i]
(*{1,2,3}*)

Obviously, Table is confusing the input x=i with its own iterator i. What is the fool-proof fix for this? Is there a solution without:




  1. Finding the names of all the iterators and listing them all as private variables inside Module?





  2. Finding all the iterators and renaming them longAndComplicated1, longAndComplicated2, etc.?





Answer



Make use of Module's capability to localize variables.


f[x_] := Module[{i}, Table[x, {i, 1, 3}]]
f[i]


{i, i, i}


Also, with i localized, you don't need to use distinct iterator names in different iteration constructs.


g[x_] :=
  Module[{i, a, b},
    a = Table[x, {i, 3}];
    b = Table[x^3, {i, 2}];
    {a, b}]
{g[i], g[a], g[b]}



{{{i, i, i}, {i^3, i^3}}, 
 {{a, a, a}, {a^3, a^3}}, 
 {{b, b, b}, {b^3, b^3}}

Further, note that you don't need to use Return if you use the semicolon ( ; ) operator properly. (Yes, semicolon is an operator in Mathematica, not a terminator.) See this answer for more information on the semicolon operator. Actually, it likely you will benefit from all answers given on the page I have linked to.


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