Re: Just another Mathematica "Gotcha", and HoldForm

• To: mathgroup at smc.vnet.net
• Subject: [mg120843] Re: Just another Mathematica "Gotcha", and HoldForm
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 12 Aug 2011 05:06:52 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j1r5d3\$fi4\$1@smc.vnet.net> <j1tnpf\$pnu\$1@smc.vnet.net> <201108110909.FAA07141@smc.vnet.net>
• Reply-to: murray at math.umass.edu

```But in the first two examples, you have only one "postifx" operator in
each case, whereas in the second two you have two such. Only there you
have to deal with precedence, really.

Also, I find nothing especially difficult about looking up Mathematica's
syntax and operator precedence with respect, at least, to this issue.

On 8/11/11 5:09 AM, Richard Fateman wrote:
> Why one might be confused
>
> In[6]:= A + B /. x_ ->  M[x]
> Out[6]= M[A + B]
>
> In[7]:= A + B // M
> Out[7]= M[A + B]
>
> In[8]:= A + B /. x_ ->  M[x] // F
> Out[8]= F[M[A + B]]
>
> In[9]:= A + B // M /. x_ ->  F[x]
> Out[9]= F[M][A + B]
>
>
> Note the identicality of Out[6] and Out[7].
> Note that Out[8] and Out[9] are different.
>
> Since neither //  nor /. are "traditional" mathematical
> syntax, one's intuition may be unreliable. Simple examples
> such as 6,7 above, might lead one to believe they have
> equal precedence and are treated nominally from left to right.
>
> Reading up on the details by looking at Mathematica's
> description of syntax and operator precedence is difficult,
> since it is simultaneously daunting and incomplete.
> One is therefore left with experimentation. Simple experiments
> are not enough, though, as shown by 6, which suggests that
> /. applies rule(s) to everything to the left, and 7 which
> suggests that // applies an operator to everything
> to the left.  Both of these are false. See a=b/.f;  a=b//f.
>

--
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            fax   413 545-1801
Amherst, MA 01003-9305

```

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