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MathGroup Archive 2007

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Re: Pattern Matching Mathematica 6 versus 5.2?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77472] Re: [mg77424] Pattern Matching Mathematica 6 versus 5.2?
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Sat, 9 Jun 2007 05:41:19 -0400 (EDT)
  • References: <200706080934.FAA03584@smc.vnet.net>

I have noticed that the 6.0 pattern matcher is a bit better at
properly ordering DownValues when a more general (but earlier-defined)
DownValue would block a less general (later-defined) DownValue. By
default, DownValues are supposed to be used in decreasing order of
generality, but if the pattern matcher can't determine which rule to
apply first, then the order is "first come first serve."

In other words, perhaps you should check to see what order the
DownValues of Grading and NonCommutativeMultiply have in 6.0 and
reorder your code so that it defines them in that order.

On 6/8/07, Michael Weyrauch <michael.weyrauch at gmx.de> wrote:
> Hello,
>
>   I encounter the following different behaviour of the Mathematica pattern matcher
> version 6 versus 5.2.
>
> I give to both versions the following rules (which should implement a simple
> Grassmann algebra):
>
> Grading[_Symbol] = 0;
> Grading[_Integer] = 0;
> Grading[_Rational] = 0;
> Grading[_Complex] = 0;
> Grading[_Real] = 0;
> Fermion[a_, b___] := ((Grading[a] = 1); Fermion[b]);
>
> Unprotect[NonCommutativeMultiply];
> NonCommutativeMultiply[x_, y_ /; EvenQ[Grading[y]]] := x y;
> NonCommutativeMultiply[y_ /; EvenQ[Grading[y]], x_] := x y;
> NonCommutativeMultiply[x_, x1_ y_ /; EvenQ[Grading[y]]] := y (x ** x1);
> NonCommutativeMultiply[x_ y_ /; EvenQ[Grading[y]], x1_] := y (x ** x1);
> NonCommutativeMultiply[x_, x_] /; OddQ[Grading[x]] := 0;
> NonCommutativeMultiply[y_ /; OddQ[Grading[y]], x_ /; OddQ[Grading[x]]] /; (! OrderedQ[{y, x}]) := -x ** y;
> Protect[NonCommutativeMultiply];
>
> Now in version 6 I get e.g.
>
> In[11]:= Fermion[f1, f2, f3, f4]
> Out[11]= Fermion[]
>
> In[13]:= f1 ** f2 ** f1 ** f4
> Out[13]= 0
>
> which is as expected, since there a two equal factors.
>
> BUT in version 5.2
>
> In[3]:=Fermion[f1, f2, f3, f4]
> Out[3]=Fermion[]
>
> In[5]:=f1**f2**f1**f4
> Out[5]=f1**f2**f1**f4
>
> which is NOT as it should be.  Mathematica 5.2 fails to simplify this automatically to zero.
>
> I implemented the above rules on the advice of David Bailey, who tried to convince me that the Mathematica pattern matcher makes
> full use of the attributes Flat and OneIdentity, which are given to NonCommuativeMultiply. This means that it should be only
> necessary to deal explicitly with the 2-argument case (as I do above).
>
> >From the results given above , I am not so sure that this holds in version 5.2? Do I misunderstand something? Or is my code buggy?
> Can it be changed that in 5.2 it runs as in 6.0?
>
> Thanks for hints,   Michael
>
>
>


-- 
http://chris.chiasson.name/


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