Why are scripts not allowed as components of vectors?

Question

In Mathematica, I attempted to construct an arbitrary vector $\vec{a}$ using the Subscript:

a = {Subscript[a, x], Subscript[a, y], Subscript[a, z]}

However, Mathematica returns with the following message:

Hold[{Subscript[a, x],Subscript[a, y], Subscript[a, z]}]

All I would like to do is to perform vector operations with components of a vector denoted by subscript index. This comes across as very odd to me given subscripts are non-protected symbols.

Answer 1

One idea is to automatically change Subscript[a, n] into Subscript[RawBoxes["a"], n] to avoid recursion errors. Both a and RawBoxes["a"] look the same, so you will only notice that they are different by looking at the InputForm/FullForm of an expression (this is an idea I mentioned previously in (137993)). A couple possibilities to do this are:

If you always enter subscripts using control + _, then you can use a MakeExpression rule:

MakeExpression[SubscriptBox["a", n_], StandardForm] := With[
    {v = HoldComplete[RawBoxes["a"]], sub = MakeExpression[n, StandardForm]},
    Thread[Unevaluated @ Subscript[v, sub], HoldComplete]
]

Or, you can add DownValues to Subscript:

Subscript /: Subscript[a, n_] := Subscript[RawBoxes@"a", n]
Subscript /: Set[Subscript[a, n_], rhs_] := Subscript[RawBoxes@"a", n] = rhs

Depending on your workflow, you may need to do both. Note, however, that overriding built-in symbols in this way can lead to trouble. This is why I've written the above code to only work for a, and not for any symbol.

At any rate, now you can do things like:

Solve[a + Subscript[a, 1] == 0, a]
D[a + Subscript[a, 1], a]

{{a -> -Subscript[a, 1]}}

1

as well as your original example:

a = {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}
a // InputForm

{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}

{Subscript[RawBoxes["a"], 1], Subscript[RawBoxes["a"], 2], Subscript[RawBoxes["a"], 3]}

Notice, no recursion errors.