Re: Pattern Matching Mathematica 6 versus 5.2?

*To*: mathgroup at smc.vnet.net*Subject*: [mg77483] Re: [mg77424] Pattern Matching Mathematica 6 versus 5.2?*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Sun, 10 Jun 2007 07:17:59 -0400 (EDT)*References*: <200706080934.FAA03584@smc.vnet.net>

That was highly informative. Thank you. On 6/9/07, Oyvind Tafjord <tafjord at wolfram.com> wrote: > Chris Chiasson wrote: > > 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. > > Hi, > > In this case the difference is actually caused by the same bug fix that was > mentioned here: > > http://forums.wolfram.com/mathgroup/archive/2007/Jun/msg00104.html > > E.g., try > > In[1]:= Attributes[f] = {Flat, Orderless, OneIdentity}; > Grading[foo] = 1; > f[x_, x_] /; OddQ[Grading[x]] := 0 > > In[4]:= f[foo, foo] > Out[4]= 0 > > In[5]:= f[foo, foo, foo] > Out[5]= f[0, foo] > > If you try this in 5.2, the last result will be f[foo,foo,foo], because the > condition prevented f's attributes from being taken into account. A simple > workaround in version 5.2 would be use the equivalent form > > f[x_, x_] := 0 /; OddQ[Grading[x]] > > Now the attributes are indeed used. The key difference is that the Head of > the LHS of the definition is f rather than Condition. > > It's true that the automatic DownValues ordering has also been improved in > version 6. It should now never reorder rules that shouldn't be reordered > (although examples of this are usually fairly subtle). The ordering > algorithm used can be controlled by a system option > > SetSystemOptions["DefinitionsReordering" -> val] > > where val is "Default", "Legacy" (5.2 behavior), or "None". The "None" > option can be useful to set temporarily when reading in a file with > thousands of definitions for which you know you don't need reordering. > > Oyvind Tafjord > Wolfram Research > > > > > 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/

**References**:**Pattern Matching Mathematica 6 versus 5.2?***From:*"Michael Weyrauch" <michael.weyrauch@gmx.de>