Construct a function with subindices

Question

I'm constructing a function that gives me subindices in output.
The function is HAt.

For example:

HAt[u == u0, t -> 0]

The function is constructed following:

HAt/:MakeBoxes[HAt[eq_, x_-> n_], StandardForm]:=
  RowBox[
    {SubscriptBox[
      RowBox[{"", ToBoxes[eq[[1]]], ")"}], 
      RowBox[{ToBoxes[x], "=", ToBoxes[n]}]], 
   "\[Equal]", 
   SubscriptBox[
      RowBox[{"(", ToBoxes[eq[[2]]], ")"}], 
      RowBox[{ToBoxes[x],"=",ToBoxes[n]}]]}]

So, the problema is when the right-hand (or left-hand) of my equation is a number. For example, if I put:

HAt[u == 0, t -> 0]

But I want some like this:

I think the ideia is put some condition at eq[[2]] when this term is a numerical term, some like that:

HAt/:MakeBoxes[HAt[eq_, x_ -> n_] /; eq[[2]]_Numeric, StandardForm] := 
  RowBox[
    {SubscriptBox[
       RowBox[{"(",ToBoxes[eq[[1]]],")"}], 
       RowBox[{ToBoxes[x], "=", ToBoxes[n]}]], 
       "\[Equal]",
       ToBoxes[eq[[2]]]}]

But the above doesn't work. How do I write the condition I want to enforce correctly?

Answer 1

When playing with typesetting the most important thing is to keep your input unevaluated. In cases like Hold @ HAt[...] MakeBoxes won't know that Hold is there.

There are several things that can cause evaluation leaks:

• ToBoxes[x] will evaluate x, use MakeBoxes

• eq[[1]] will evaluate eq, use lhs_ == rhs_ to match your equations

• ?NumericQ will evaluate as well as opposed to e.g. _Real but the latter is not general enough. Fortunately there is System`Dump`HeldNumericQ :)

Here is how I'd do this:

HAt // ClearAll;
HAt /: MakeBoxes[HAt[lhs_ == rhs_, x_ -> n_], fmt : StandardForm] := With[
  { subscript = SubscriptBox[RowBox[{"(", #, ")"}], RowBox[{MakeBoxes[x, fmt], "=", MakeBoxes[n, fmt]}]] &
  }
, RowBox[{
    subscript @ MakeBoxes[lhs, fmt]
  , "\[Equal]"
  , If[System`Dump`HeldNumericQ[rhs], Identity, subscript] @ MakeBoxes[rhs, fmt]
  }]
]