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Re: RE: Prefix notation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg40734] Re: [mg40574] RE: [mg40530] Prefix notation
  • From: Murray Eisenberg <murraye at attbi.com>
  • Date: Tue, 15 Apr 2003 03:59:50 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200304100741.DAA24268@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

Perhaps an even nicer thing to do for such examples -- although it takes 
a bit of effort to set up -- is to make use of the Notation package so 
as to employ the traditional mathematical symbol for composition (the 
little circle).


David Park wrote:
> Bobby,
> 
> Another nice use for the prefix notation, @, is in writing compositions. It
> even looks a little like the composition symbol.
> 
> Here is an example. Suppose we define translations T[v] and rotations
> R[angle, center] in the complex plane.
> 
> T[v_][z_] := z + v
> R[theta_, a_][z_] := E^(I*theta)*(z - a) + a
> 
> Then to perform a rotation of Pi/4 about 1, followed by a translation of 1,
> followed by a rotation of Pi/4 about 0 we write the composition...
> 
> R[Pi/4, 0]@T[1 + I]@R[Pi/4, 1]@z
> 
> E^((I*Pi)/4)*(2 + I + E^((I*Pi)/4)*(-1 + z))
> 
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
> 
> 
> From: Dr Bob [mailto:majort at cox-internet.com]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> 
> 
> 
>>>You make judicious use of what I guess is "infix" notation.
>>>Maybe you're minimizing the number of keystrokes one uses.
> 
> 
> It's actually called prefix notation.  I just discovered functions called
> Infix, Prefix, and Postfix whose help entries make this clear.
> 
> I like "@" when there's only one argument because, when I see "[", it's
> often hard to tell where the matching "]" is, and vice-versa.  If I avoid
> some brackets by using "@" or "//", that makes it easier to visually match
> the remaining brackets, and "@" does save a keystroke, after all.  I
> generally don't like "//", but it's handy for applying a function of one
> argument to a long and complicated mess.
> 
> Sometimes, if the argument needs parentheses, I use f[arg] instead of
> f@(arg).
> 
> I tend to use [] if there may be other arguments added later, even though
> there's only one argument at the moment.
> 
> Evaluate the following:
> 
> parabola[zero_] := (# - zero)^2 &
> parabola@3
> parabola[3][x]
> parabola[3]@x
> parabola@3@x
> (parabola@3)@x
> x // parabola@3
> (3 // parabola)@x
> 3 // parabola // x
> 
> -- and you'll see that evaluation order might not be what we want or expect
> sometimes.
> 
> In this example, I think "parabola[3]@x" might be easiest to read and
> write.
> 
> I often use my patented (not really) "multi-click" method to decide what
> the evaluation order will be.  In x // parabola@3, for instance, click
> three or four times in "parabola" and you'll see the selection expand
> (under Windows, anyway) in a way that corresponds to evaluation order.
> 
> The "multi-click" method works for finding matching brackets too, if you
> already have them where they belong.  Prefix notation helps me get them
> right, by eliminating some.
> 
> Bobby
> 
> On Tue, 8 Apr 2003 15:58:29 -0400 (EDT), Stewart Mandell
> <stewart at rentec.com> wrote:
> 
> 
>>thanks for pointing out ComplexExpand to me.
>>
>>You answer lots of queries on the Mathematica NewsGroup.
>>You make judicious use of what I guess is "infix" notation.
>>Maybe you're minimizing the number of keystrokes onw uses.
>>I have to get use to this.
>>
>>regards, Stewart
>>
> 
> 
> 
> 
> --
> majort at cox-internet.com
> Bobby R. Treat
> 
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street
Amherst, MA 01375



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