Variable number of function arguments Lua 5.1

Luis's answer is right, if terser than a beginner to the language might hope for. I'll try to elaborate on it a bit, hopefully without creating additional confusion.

Your question is in the context of Lua embedded in a specific model of TI calculator. So there will be details that differ from standalone Lua, but mostly those details will relate to what libraries and functions are made available in your environment. It is unusual (although since Lua is open source, possible) for embedded versions of Lua to differ significantly from the standalone Lua distributed by its authors. (The Lua Binaries is a repository of binaries for many platforms. Lua for Windows is a batteries-included complete distribution for Windows.)

Your sample code has a confounding factor the detail that it needs to interface with a class system provided by the calculator framework. That detail mostly appears as an absence of connection between your equation object and the equation:init() function being called. Since there are techniques that can glue that up, it is just a distraction.

Your question as I understand it boils down to a confusion about how variadic functions (functions with a variable number of arguments) are declared and implemented in Lua. From your comment on Luis's answer, you have been reading the online edition of Programming in Lua (aka PiL). You cited section 5.2. PiL is a good source for background on the language. Unfortunately, variadic functions are one of the features that has been in flux. The edition of the book on line is correct as of Lua version 5.0, but the TI calculator is probably running Lua 5.1.4.

In Lua 5, a variadic function is declared with a parameter list that ends with the symbol ... which stands for the rest of the arguments. In Lua 5.0, the call was implemented with a "magic" local variable named arg which contained a table containing the arguments matching the .... This required that every variadic function create a table when called, which is a source of unnecessary overhead and pressure on the garbage collector. So in Lua 5.1, the implementation was changed: the ... can be used directly in the called function as an alias to the matching arguments, but no table is actually created. Instead, if the count of arguments is needed, you write select("#",...), and if the value of the nth argument is desired you write select(n,...).

A confounding factor in your example comes back to the class system. You want to declare the function equation:init(...). Since this declaration uses the colon syntax, it is equivalent to writing equation.init(self,...). So, when called eventually via the class framework's use of the __call metamethod, the real first argument is named self and the zero or more actual arguments will match the ....

As noted by Amr's comment below, the expression select(n,...) actually returns all the values from the nth argument on, which is particularly useful in this case for constructing self.answers, but also leads to a possible bug in the initialization of self.pipe.

Here is my revised approximation of what you are trying to achieve in your definition of equation:init(), but do note that I don't have one of the TI calculators at hand and this is untested:

function equation:init(...)
    self.equation = select(1, ...)
    self.pipe = { (select(1,...)) }
    self.selected = 1
    self.answers = { select(2,...) }
end

In the revised version shown above I have written {(select(1,...))} to create a table containing exactly one element which is the first argument, and {select(2,...)} to create a table containing all the remaining arguments. While there is a limit to the number of values that can be inserted into a table in that way, that limit is related to the number of return values of a function or the number of parameters that can be passed to a function and so cannot be exceeded by the reference to .... Note that this might not be the case in general, and writing { unpack(t) } can result in not copying all of the array part of t.

A slightly less efficient way to write the function would be to write a loop over the passed arguments, which is the version in my original answer. That would look like the following:

function equation:init(...)
    self.equation = select(1, ...)
    self.pipe = {(select(1,...))}
    self.selected = 1

    -- Loop arguments to add answers.
    local t = {}
    for i = 2, select("#",...) do
        t[#t+1] = select(i,...)
    end
    self.answers = t
end