Re: new special forms
- To: mathgroup at yoda.physics.unc.edu
- Subject: Re: new special forms
- From: withoff (David Withoff)
- Date: Mon, 9 May 1994 13:16:55 -0500
> Mathematica provides ~ for using a function in infix form. However,
> I would like a way to make my own special forms that don't need ~.
> For example, I'd like 3_-5 to mean 3 10^-5. In the quest for a way
> to enter numbers in scientific notation more easily, I came up with
> this kludge:
>
> Unprotect[StringJoin]
> StringJoin[m_?NumberQ,e_?NumberQ] := m 10^e
> Protect[StringJoin]
>
> Then 3<>-5 gives 3 10^-5, and does not interfere with the normal
> operation of <>. This has two drawbacks: a) it's a little cumbersome
> to type and so is only marginally better than blank 10^, and b) the
> precedence is high, but not quite high enough, since something like
> (#^2)& @ 3<>-5 gives 9 10^-5 instead of 9 10^-10.
>
> So, the questions are: is there any way to define my own special form
> with my own specified precedence and operation? Is there a way to
> redefine a higher precedence form like ? or :: (I couldn't find a
> way)? Is there some other completely different approach to this
> problem? Thanks.
>
> mark
The only general way to do this is to write your own parser, which
is certainly a possibility, although it is probably more work than
you had in mind. The current Mathematica parser is not programmable.
The closest available in the current version of Mathematica is
$PreRead, which you could set to a rule that replaces the
characters you enter with the corresponding characters expected
by the parser. Something like
$PreRead = StringReplace[#, {"0_" -> "0*10^", "1_" -> "1*10^",
"2_" -> "2*10^", "3_" -> "3*10^",
"4_" -> "4*10^", "5_" -> "5*10^",
"6_" -> "6*10^", "7_" -> "7*10^",
"8_" -> "8*10^", "9_" -> "9*10^"}] &
In[2]:= 3_x
x
Out[2]= 3 10
In[3]:= 3_-5
3
Out[3]= ------
100000
has many obvious limitations, but will cover generic cases such
as the one you mentioned. Writing a more comprehensive rule would
amount to writing the better part of a parser.
Dave Withoff
Research and Development
Wolfram Research