Re: perplexed by blank sequence in pattern replacement

*To*: mathgroup at smc.vnet.net*Subject*: [mg68721] Re: perplexed by blank sequence in pattern replacement*From*: dimmechan at yahoo.com*Date*: Thu, 17 Aug 2006 04:18:28 -0400 (EDT)*References*: <ebuj5d$6f5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Dear Blake, I think you can see where is the problem by applying the Trace function with the option TracOriginal activated to True. In[52]:= Trace[Replace[a*b*c,Times[mysequence__]\[RuleDelayed]{mysequence}],\ TraceOriginal\[Rule]True]//InputForm Out[53]= {Replace[a b c,Times[mysequence__]\[RuleDelayed]{mysequence}],{Replace},{a b c,{Times},{a},{b},{ c},a b c},{Times[mysequence__]\[RuleDelayed]{mysequence},{RuleDelayed},{\ Times[mysequence__],{Times},{ mysequence__,{Pattern},{__},mysequence__},Times[mysequence__], mysequence__}, mysequence__\[RuleDelayed]{mysequence},mysequence__\[RuleDelayed]{\ mysequence},{RuleDelayed},{mysequence__},mysequence__\[RuleDelayed]{\ mysequence}},Replace[a b c,mysequence__\[RuleDelayed]{mysequence}],{a b c},{List},{a b c},{a b c}} If I am not wrong, the problem is that pattern Times[mysequence__] is evaluated to mysequence__ before application of the rule. An idea to avoid this is the followg command: In[59]:= Replace[a*b*c,Times[x_,y___]:>{x,y}] Out[59]= {a,b,c} You can see why this pattern matching gives what you want below. In[60]:= Trace[Replace[a*b*c,Times[x_,y___]:>{x,y}],TraceOriginal\[Rule]True] Out[60]= {Replace[a b c,x_ y___\[RuleDelayed]{x,y}],{Replace},{a b c,{Times},{ a},{b},{c},a b c},{x_ y___\[RuleDelayed]{x,y},{RuleDelayed},{x_ \ y___,{Times},{x_,{ Pattern},{_},x_},{y___,{Pattern},{___},y___},x_ y___},x_ y___\[RuleDelayed]{x, y},x_ y___\[RuleDelayed]{x,y},{RuleDelayed},{x_ y___},x_ y___\ \[RuleDelayed]{x,y}},Replace[a b c,x_ y___\[RuleDelayed]{ x,y}],{a,b,c},{List},{a},{b},{c},{a,b,c}} Cheers, Jim Î?/Î? Blake ÎÎ³Ï?Î±Ï?Îµ: > Dear MathGroup: > > I have been blithely using blank sequences in pattern matching for some > time. In persuit of a bug in a package of mine, I was quite alarmed to > find that I don't really understand how to use the blank sequence, as > expressed in the following simplified example: > > In[1]:=Replace[a*b*c,Times[mysequence__]:>{mysequence}] > > Out[1]={a b c} > > I expected Out[1]={a,b,c}, from a naieve reading of the full form of > a*b*c > > In[2]:=FullForm[a*b*c] > > Out[2]//FullForm=Times[a,b,c] > > Will someone PLEASE tell me why In[1] does not yield the results I > expected? (I can readily use a work-around, what I am concerned with is > a correct understanding of pattern matching). > > Blake Laing > thesis slave > University of Oklahoma