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new special forms

• To: mathgroup at yoda.physics.unc.edu
• Subject: new special forms
• From: madler at cco.caltech.edu (Mark Adler)
• Date: 6 May 1994 00:50:47 GMT

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