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MathGroup Archive 1994

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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






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