[Date Index]
[Thread Index]
[Author Index]
Re: Flat: Problems & Workarounds Sweden.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg8493] Re: Flat: Problems & Workarounds Sweden.
*From*: Robert Villegas <villegas>
*Date*: Tue, 2 Sep 1997 16:15:37 -0400
*Organization*: Wolfram Research
*Sender*: owner-wri-mathgroup at wolfram.com
An additional note regarding the associative function that recognizes
NumericQ arguments in certain positions:
> This is the result from my work trying to construct a associative function.
> Assume I want a associative function h[] which treats numerical arguments
> specially. Starting from the template in Roman Maeders "Programming in
> Mathematica", 3rd ed. I define h[] as
>
> In[3]:= SetAttributes[h,{Flat,OneIdentity}]
> h[x_,y_?NumericQ] := f[y,x]
> h[x_?NumericQ,y_] := f[x,y]
> h[x_] := x
> h[] = 1
The problem was underspecified in that you didn't say exactly how you
wanted nested h expressions treated. Here's an example using the code I
supplied:
In[51]:=
h[h[a, 2], h[a, 3]]
Out[51]=
h[f[2, a], f[3, a]]
It's possible that you expect In[51] to return the same result as the
following, which has h pre-flattened out:
In[52]:=
h[a, 2, a, 3]
Out[52]=
f[3, h[a, 2, a]]
In[51] did what it was supposed to: h isn't HoldAll, so it lets its
arguments fully evaluate first. Thus, h[a, 2] ==> f[2, a] and
h[a, 3] ==> f[3, a].
So the question is, which do you want to occur first: argument evaluation
or argument flattening?
The original code I gave you did the default: evaluation.
If you want flattening to occur first, here is the same code with a couple
additions -- HoldAll and an extra rule -- with the net effect that h forces
its arguments to sit still only long enough to be flattened, then lets them
go.
ClearAll[h];
Attributes[h] = HoldAll;
$hEvaluate = True;
h[elems___] /; MemberQ[Unevaluated[{elems}], _h] :=
Flatten[Unevaluated @ h[elems], Infinity, h];
h[elems___] :=
Block[{$hEvaluate = False},
h @@ {elems}
] /; $hEvaluate;
h[elems__, n_?NumberQ] := f[n, h[elems]];
h[n_?NumberQ, elems__] := f[n, h[elems]];
h[singleton_] := singleton;
h[] = 1;
It still works for the test examples, and pre-flattens nested h:
In[47]:=
{h[], h[1], h[a], h[1, a], h[a, 1], h[a, b], h[2, a, 3], h[2, 3, a],
h[a, 2, 3]}
Out[47]=
{1, 1, a, f[1, a], f[1, a], h[a, b], f[3, f[2, a]], f[2, f[3, a]],
f[3, f[2, a]]}
In[48]:=
h[h[a, 2], h[a, 3]]
Out[48]=
f[3, h[a, 2, a]]
Robby Villegas
Prev by Date:
**Re: Partition List**
Next by Date:
**Loading Standard Packages**
Previous by thread:
**RE: Flat: Problems & Workarounds Sweden.**
Next by thread:
**Re: Flat: Problems & Workarounds Sweden.**
| |