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Re: OneIdentity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg103646] Re: OneIdentity
  • From: Chris Osborn <chrisosb at gmail.com>
  • Date: Thu, 1 Oct 2009 06:38:59 -0400 (EDT)
  • References: <200909240352.XAA13458@smc.vnet.net> <h9vfkq$e6g$1@smc.vnet.net>

On Sep 30, 6:32 am, "Kurt TeKolste" <tekol... at fastmail.us> wrote:
> You have misread the definition of OneIdentity.  OneIdentity declares
> key to be what mathematicians call "idempotent,"  i.e. you get the
> answer after one application and no change occurs with repeated
> application.  The usual example of an idempotent operator is projection
> in linear algebra: the result of projecting to the x-axis a projection
> to the x-axis is the same
>
>   xProjection[xProjection[{x,y}]] = xProjection[{x,y}] = {x,0}
>
> Note, however that
>
>    xProjectionn[{x,y}] == {x,y}  is false in general
>
> On Wed, 23 Sep 2009 23:52 -0400, "Chris Osborn" <chris... at gmail.com>
> wrote:
>
>
>
> > I do not understand why I get "False" instead of "True" here:
>
> > In[773]:= ClearAll[key];
> > SetAttributes[key, OneIdentity];
>
> > MatchQ[13, key[_]]
>
> > Out[775]= False
>
> > According to 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.
>
> > Thanks in advance,
> > Chris
>
> Regards,
> Kurt Tekolste

As I see it, the function description implies that for purposes of
pattern matching,
every input to "key" is a fixed point (i.e.  key[x] = x) which is a
bit stronger
than idempotence (key[key[x_]] = key[x]).

But, OneIdentity does not seem to correspond to Idempotence, either,
e.g.:

In[1568]:= ClearAll[key];
SetAttributes[key, OneIdentity];

MatchQ[key[13], key@key[13]]

Out[1570]= False



Chris


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