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Re: Question about OneIdentity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88227] Re: [mg88198] Question about OneIdentity
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 29 Apr 2008 06:47:36 -0400 (EDT)
  • References: <200804280838.EAA05888@smc.vnet.net>

You can find a very clear explanation of these matters here:

http://hilbert.math.hr/arhive/mathgroup/2000/01/0323.html

Note also that, although, as you note:

Attributes[f] = Attributes[Times];

MatchQ[1, f[1]]
  False

but

MatchQ[f[1], f[f[1]]]
  True

For the explanation see the above link.

Andrzej Kozlowski





On 28 Apr 2008, at 17:38, Szabolcs Horv=E1t wrote:

>
> (Scroll down for the actual question)
>
> I never really understood Flat and OneIdentity, and unfortunately
> documentation about them is scarce.
>
> =46rom the docs:
>
> """
> OneIdentity is an attribute that can be assigned to a symbol f to
> indicate that f[x], f[f[x]], etc. are all equivalent to x for the
> purpose of pattern matching.
>
> OneIdentity has an effect only if f has attribute Flat.
> """
>
> ** Some comments:
>
> There is also an example, listing the Attributes of Times and showing
> that Times[a] evaluates to a.  However, this is misleading because 
> this
> behaviour cannot be caused by Times's attributes:
>
> In[1]:= Attributes[f] = Attributes[Times]
> Out[1]= {Flat, Listable, NumericFunction,
>          OneIdentity, Orderless, Protected}
>
> In[2]:= f[a]
> Out[2]= f[a]
>
> If we assign the same attributes to f, f[a] will not evaluate to a.  =

> Was
> the technical writer also confused, or is the example supposed to
> illustrate something different than what I understood?
>
>
> ** And now the actual question:
>
> According to the text in the docs (f[x] is considered equivalent to =

> x in
> pattern matching) I would expect
>
> MatchQ[1, f[1]]
>
> to give True after evaluating SetAttributes[f, {Flat, OneIdentity}].
> But it gives False.
>
>
> ** The application:
>
> This came up in the following application:
>
> fun[HoldPattern@Plus[terms__]] := doSomething[{terms}]
>
> This function should handle a single term, too.  Of course, there are
> workarounds, but I couldn't come up with anything as simple as the
> pattern above (which unfortunately does not work).
>



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