Question

I’m having a very simple but nasty problem with mathematica:

I need/want to enter symbols using a leading zero

\[alpha]^0123

or even simpler just

mysymbol[0123]

which I then transform to my internal representation

(using the Notation package and IntegerDigits[] or Characters[])

==> myrep[{0,1,2,3}]

everything works fine for input without a leading 0.

BUT WHATEVER I TRY (Unevaluated[] or Hold[]), mathematica (it’s overarching evaluator?) will transform the Integer

0123 => 123

so the 0 will be missing from my list

Of course, I could avoid the problem by requiring quotes or commas for the input, but that’s rather unpretty!

ANY IDEAS?

Answer 1

I answered this question in a definitive tone, but I was wrong. Expressions such as 0123, 16^^8b and 1*^6 are not converted during parsing as I had incorrectly recalled. For this reason we would not need to fall back to the heavy duty and unwieldy CellEvaluationFunction but can instead use the much more user-friendly $PreRead.

This is still a little dangerous as once the definition to $PreRead is made it changes all input, even attempts to change $PreRead. For example, if we were to set $PreRead = Null & it would become impossible to enter additional commands until the Kernel was restarted.

To enact your desired behavior as I understand it we may use:

mysymbol[s_String] := myrep[FromDigits /@ Characters@s]

$PreRead = # /. {RowBox[{"mysymbol", "[", digits_String, "]"}] | 
                 RowBox[{digits_String, "//", "mysymbol"}] |
                 RowBox[{"mysymbol", "@", digits_String}] /; 
                 StringMatchQ[digits, DigitCharacter ..] :> 
                 ToBoxes[ mysymbol@digits ]} &;

Testing:

mysymbol[0123]

myrep[{0, 1, 2, 3}]