# Changing variable names

In Mathematica, I am doing computations involving polynomials with variables like

p[0,1,2]


In the end, I will need to put these equations in to another program. This other program does not allow brackets or commas in variable names. So, I need to send the above variable to

p012


Ultimately, I need my entire list of polynomials to be in input form which I can copy and paste into the other program. I have tried writing something like

StringVar[i_, j_, k_] := StringForm["p", i, j, k]


And then using Simplify to substitute the variables. But, when I use InputForm on the entire list of polynomials I get these funny expressions

StringForm["p", 0, 1, 2]


instead of the variables p012 that I would like. How do I make Mathematica treat these as variables?

I think the simplest approach is to give p a Format:

Format[p[a__Integer], InputForm] := SequenceForm[p,a]


Here is an example polynomial, and what it looks like when converted to InputForm:

poly = 2 p[0,1,2]^2 + p[1,2,3]^3
% //InputForm


This is a common trap with using StringForm[]. But before discussing the pitfall, let me offer slightly simpler code:

With[{expr = p[0, 1, 2]},
StringForm["12", Head[expr], StringJoin[ToString /@ (List @@ expr)]]]
p012


Looks good so far, but let's see what InputForm[] says:

InputForm[%]
StringForm["12", p, "012"]


Certainly not a string!

So, you need an additional ToString[]:

ToString[%] // InputForm
"p012"


The alternative in newer versions of Mathematica is StringTemplate[], which produces a genuine string. Observe:

With[{expr = p[0, 1, 2]},
StringTemplate["headargs"] @
<|"head" -> Head[expr], "args" -> StringJoin[ToString /@ (List @@ expr)]|>]
"p012"

• ...and you can then use Symbol["p012"] much later if you really want symbols instead of strings. – J. M. will be back soon Oct 3 '17 at 1:29

If I understand what you're trying to do, this is the replacement rule you're looking for:

rule = p[i_, j_, k_] :> ToExpression[StringJoin @@ (ToString /@ {"p", i, j, k})]


You might also consider using Format and/or \$PrePrint to have the expressions automatically formatted.