       Re: Problem with Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg77097] Re: [mg77065] Problem with Mathematica 6
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 3 Jun 2007 06:14:15 -0400 (EDT)
• References: <200706020819.EAA29947@smc.vnet.net> <DFEBF444-FF43-4A1E-8B31-893ABB27F09D@mimuw.edu.pl>

```In my reply I omitted the question of possible reason for the new
behaviour. I did that because when I was replying I had not yet
investigated this problem and, given that this phenomenon involves
unprotecting a built-in function, I did not think the precise reason
was relevant. I have not changed my mind about that, but now I think
that what you have observed is a consequence of changes that have
been made in the pattern matcher, which do not seem to me to involve
any obvious bug and perhaps represent an improvement. To see what I
mean compare these two outputs:

First Mathematica 5.2:

a**b /. (NonCommutativeMultiply[x___] /; (Print[{x}];
Length[{x}] <= 1)) :> f[x]

{a,b}

a**b

Now Mathematica 6:

In:= a ** b /. NonCommutativeMultiply[x___] /; (Print[{x}];
Length[{x}] <= 1) :> f[x]

{a, b}
{a}

Out= f[a] ** b

Note that Mathematica 6.0 actually went inside the expression a**b
and used the attribute Flat to find a match for
NonCommutativeMultiply[x___]/Length[{x}] <= 1), while Mathematica 5.2
looked only at the top level and did not find any match. This
suggests to me that the new behaviour is more likely an improvement
over the old rather than a bug. Anyway, whatever the reason, the
advice not to unprotect built-in functions still stands.

Andrzej Kozlowski

On 2 Jun 2007, at 21:49, Andrzej Kozlowski wrote:

> *This message was transferred with a trial version of CommuniGate
> (tm) Pro*
>
> On 2 Jun 2007, at 17:19, Michael Weyrauch wrote:
>
>> Hello,
>>
>>   the following code fragment runs under Mathematica 5.2 but
>> produces an infinite recursion error in Mathematica 6.0 in certain
>> cases:
>>
>> First I define a number of commands and slightly change the
>> built-in command "NonCommutativeMultiply":
>> Fermion[a__] := ((Grading[#1] = 1) & ) /@ {a};
>> Fermion[a, b];
>>
>> Unprotect[NonCommutativeMultiply];
>> NonCommutativeMultiply[a___] /; (Length[GetGradeds[a]] <= 1) :=
>> Times[a];
>> Protect[NonCommutativeMultiply];
>>
>> If you now e.g. evaluate
>>
>> In:= k ** l
>> Out= k*l
>>
>> or
>>
>> In:= a ** l
>> Out= a*l
>>
>> BUT in Mathematica 6.0:
>>
>> In:= a ** b
>>
>> \$IterationLimit::"itlim" : "Iteration limit of 4096 exceeded. \
>> \!\(\*ButtonBox["\[RightSkeleton]",
>> ButtonData:>"paclet:ref/message/\$IterationLimit/itlim",
>> ButtonFrame->None,
>> ButtonNote->"\$IterationLimit::itlim"]\)"
>> Out= Hold[(Times[a]) ** b]
>>
>> However in Mathematica 5.2 one gets
>>
>> In:= a ** b
>> Out=a**b
>>
>> which is what I expect and I want to have.
>>
>> I.e., whenever I NonCommutativeMultiply two variables which are
>> explicitly declared as fermions by the command Fermion[], I get an
>> infinite recursion error in Mathematica 6.
>>
>> This behaviour of Mathematica 6.0 is rather confusing to me, since
>> I believe that I just use very basic and elementary assignments
>> in my code. Why shouldn't it work  under Mathematica 6.0 if it
>> works under 5.2? It appears that the 6.0 kernel behaves
>> differently than the
>> 5.2 kernel in such basic situations. Very unpleasant!
>>
>> (For anyone who wonders about the purpose of  this (strange) code:
>> It is a small fragment of a package  that implements the handling
>> of Grassmann variables. I just extracted that bit in order to show
>> the Mathematica 6.0 problem.)
>>
>> Furthermore, beyond an explanation of this unexpected behaviour of
>> Mathematica 6, I would like to find a workaround in Mathematica 6
>> such that I get
>> the same result as in Mathematica 5.2.
>>
>> Thanks for any suggestions.
>>
>> Michael Weyrauch
>>
>
> On of the most basic principles in Mathematica programming, stated,
> over the years, a number of times on this list by WRI employees,
> (particularly by David Withoff) is if you choose to Unprotect and
> modify any built-in functions you can only blame yourself for any
> unpleasantness that might occur. The workaround is: don't do it.
>
> One think you can do instead is to do essentially the same thing
> without modifying NonCompputativeMultiply. If you want to use a
> symbol that looks like multiplication you could choose SmallCircle.
> You could then do something like this:
>
> In:= Fermion[a__] := ((Grading[#1] = 1) &) /@ {a};
> In:= Fermion[a, b]
> Out= {1, 1}
> [#1] != 0 &];
> In:= SmallCircle[z___] /; (Length[GetGradeds[z]] <= 1) := Times[z];
> In:= SmallCircle[z___] := NonCommutativeMultiply[z]
>
> In:= SmallCircle[a, l]
> Out= a l
>
> SmallCircle[a,b]
>
> In:= SmallCircle[a, b]
> Out= a ** b
>
> In:= SmallCircle[a, l, m]
> Out= a l m
>
>  Of course instead of writing SmallCircle[a,l,m] you can use as
> input  a escape sc escape l escape sc escape m .
>
> Andrzej Kozlowski

```

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