Re: Re: Orderless indexed functions
- To: mathgroup at smc.vnet.net
- Subject: [mg20906] Re: [mg20891] Re: [mg20874] Orderless indexed functions
- From: "N Monomachoff" <nmonomachoff at email.msn.com>
- Date: Sun, 21 Nov 1999 15:12:50 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Dear Andrzej Kozlowski,
I want to thank you for the extraordinary efforts you've expended on this
problem. Had I appreciated how nontrivial my original question was, I
would have been much more explicit:
Not only do I need pattern matching within the body of the function, I need
to pattern match the index itself, as in the following:
f[n_][x___,f[0][y___]]:=f[n][x,y]
The ability to do this is precisely why I chose the indexed form.
Unfortunately, none of the proposed solutions, not even your last, seems to
allow for such definitions. Apparently the Notation package is unable to
stretch this far. Even a definition as simple as:
\!\(f\_n_ := h[n]\)
doesn't work. On the other hand, I haven't delved into the deeper parts of
the Notation package, so perhaps I'm wrong.
N Monomachoff
nmonomachoff at msn.com
>From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
>Date: Sat, 20 Nov 1999 17:28:49 +0900
>To: Andrzej Kozlowski <andrzej at tuins.ac.jp>, <mathgroup at smc.vnet.net>
>Subject: [mg20906] Re: [mg20891] Re: [mg20874] Orderless indexed functions
>
>I think I have worked out the right solution to your problem, which will
>produce an indexed function with an Orderless attribute. This is what you
>have to do. First, you need to load the Notation package:
>
>In[2]:=
><< Utilities`Notation`
>
>(I was wrong to say you need ot move it inot the Autoload folder since the
>ExtraPackages folder is actually included in $Path )
>
>Okay, now you symbolize "f\[UnderBracket]Subscript\[UnderBracket]i" using
>the Notation palette:
>
>In[4]:=
>\!\(\*
> RowBox[{"Symbolize", "[",
> TagBox[\(f\__\),
> NotationBoxTag,
> TagStyle->"NotationTemplateStyle"], "]"}]\)
>
>
>
>Once you have done this you need a function that will convert f[i] to
>"f\[UnderBracket]Subscript\[UnderBracket]i". The following will work:
>
>
>In[9]:=
>f[i_] := ToExpression[
> "f\[UnderBracket]Subscript\[UnderBracket]" <> ToString[i]]
>
>e.g.
>
>In[10]:=
>f[3]
>Out[10]=
>f\[UnderBracket]Subscript\[UnderBracket]3
>
>Now all you need to do is
>
>In[13]:=
>\!\(SetAttributes[f\_3, Orderless]\)
>
>and you have what you wanted:
>
>In[14]:=
>f[3][a, c, b]
>Out[14]=
>\!\(f\_3[a, b, c]\)
>
>Unlike with all the other solutions that have been proposed (if I didn't
>miss something) you get the benefit of correct behaviour with respect to
>pattern matching:
>
>In[15]:=
>F[f[3][a, b]] + F[f[3][a, c]] + F[f[3][b, d]] /.
>F[f[3][a, x_]] + F[f[3][c, y_]] -> p[x, y]
>Out[15]=
>\!\(F[f\_3[b, d]] + p[b, a]\)
>
>
>
>--
>Andrzej Kozlowski
>Toyama International University
>JAPAN
>http://sigma.tuins.ac.jp
>
>
>> From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
To: mathgroup at smc.vnet.net
>> Date: Sat, 20 Nov 1999 01:07:05 -0500 (EST)
>> To: mathgroup at smc.vnet.net
>> Subject: [mg20906] [mg20891] Re: [mg20874] Orderless indexed functions
>>
>> I just noticed that there is a third way to do what you want, which is
>> possibly the simplest. Just define your function like this:
>>
>> f[1][x__]:= your definition;
>> f[1][x__] /; Not[OrderedQ[{x}]] := f[1][Apply[Sequence, Sort[{x}]]]
>>
>> However, I should also add that only the first of the three approaches I
>> have suggested (the one based on using the Notation package) actually
gives
>> you the full functionality of having the Orderless attribute. All the
>> functions defined in these ways will be "commutative", but they will not
>> behave like Orderless functions for the purpose of Pattern matching. For
>> example, consider the function f, which has a genuine Orderless
attribute:
>>
>> In[4]:=
>> SetAttributes[f, Orderless]
>>
>> Now consider the following example of pattern matching:
>>
>> In[5]:=
>> F[f[a, b]] + F[f[a, c]] + F[f[b, d]] /. F[f[a, x_]] + F[f[c, y_]] -> p[x,
y]
>> Out[5]=
>> F[f[b, d]] + p[b, a]
>>
>> If we use the definition above we won't get this behaviour:
>>
>> In[6]:=
>> F[f[1][a, b]] + F[f[1][a, c]] + F[f[1][b, d]] /.
>> F[f[1][a, x_]] + F[f[1][c, y_]] -> p[x, y]
>> Out[6]=
>> F[f[1][a, b]] + F[f[1][a, c]] + F[f[1][b, d]]
>>
>> The second method I gave in my first reply is even worse, as you can
check
>> yourself. So if you need your functions to be really orderless for the
>> purpose of pattern matching I can only suggest using subscripts and the
>> Notation package.
>>
>>
>>> From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
To: mathgroup at smc.vnet.net
>> To: mathgroup at smc.vnet.net
>>> Date: Fri, 19 Nov 1999 15:12:49 +0900
>>> To: <nmonomachoff at email.msn.com>, <mathgroup at smc.vnet.net>
>>> Subject: [mg20906] [mg20891] [mg20874] Orderless indexed functions
>>>
>>> I can think of two approaches. If you are willing to abandon the
notation
>>> f[k] and instead use subscripts than probably the simplest way to get
what
>>> you want is to use the Notation package, which you can find in the
>>> ExtraPackages folder in the AddOns folder (you will have ot move it to
>>> somewhere like the AutoLoad folder to make things work as in y example
>>> below)
>>>
>>> In[23]:= << Utilities`Notation`
>>>
>>> In[27]:= Symbolize[NotationBoxTag[\(f\__\)]]
>>>
>>> In[28]:= SetAttributes[f\[UnderBracket]Subscript\[UnderBracket]2,
Orderless]
>>>
>>> In[29]:= f\[UnderBracket]Subscript\[UnderBracket]2[b, c, a]
>>> Out[29]= f\[UnderBracket]Subscript\[UnderBracket]2[a, b, c]
>>>
>>> If, on the other hand, you insist on the f[k] notation or you find the
>>> Notation package just too much bother (as I do) you could try something
like
>>> this.
>>> Suppose you want to define a function of the form: f[1][x__]:=B[x]
(where B
>>> is the body of your function) and give it the attribute Orderless. The
>>> following code will do it for you:
>>>
>>> f[1][x__] := Unevaluated[(Function[y, B[Sequence @@ y],
>>> {Orderless}])[x]] /. y -> Table[Unique[z],{Length[{x}]}]
>>>
>>> e.g.
>>>
>>> In[5]:=
>>> f[1][b, c, a, d]
>>> Out[5]=
>>> B[a, b, c, d]
>>>
>>>
>>> --
>>>
>>>
>>>> From: "N Monomachoff" <nmonomachoff at email.msn.com>
To: mathgroup at smc.vnet.net
>> To: mathgroup at smc.vnet.net
>>>> Date: Thu, 18 Nov 1999 20:46:23 -0500 (EST)
>>>> To: mathgroup at smc.vnet.net
>>>> Subject: [mg20906] [mg20891] [mg20874] Orderless indexed functions
>>>>
>>>> Hello,
>>>>
>>>> I need to use 'indexed functions' like f[0][x__] and f[1][x__].
>>>> It's important that the functions be Orderless, but
>>>>
>>>> SetAttributes[f[0],Orderless]
>>>>
>>>> isn't accepted because f[0] isn't a symbol, and
>>>>
>>>> SetAttributes[f,Orderless]
>>>>
>>>> doesn't affect the ordering in the second set of brackets.
>>>> How does one make a nonsymbolic head orderless?
>>>>
>>>> Thanks for any help.
>>>>
>>>> N Monomachoff
>>>> nmonomachoff at msn.com
>>>>
>>>>
>>>>
>>>
>>
>>
>
>