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Re: Why does this pattern fail to match?

• To: mathgroup at smc.vnet.net
• Subject: [mg114171] Re: Why does this pattern fail to match?
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Fri, 26 Nov 2010 05:27:09 -0500 (EST)

Hi kj,

Patterns are Mathematica expressions, and as such, can evaluate. If they do,
this happens one step
before MatchQ evaluates (in your examples). FullForm will tell you what are
the expressions MatchQ
really sees:

In[3]:= FullForm[Times[___,Power[___],___]]

Out[3]//FullForm= Power[BlankNullSequence[],3]

This is because

In[4]:= Times[x,Power[x],x]

Out[4]= x^3

whatever is x (happens to be ___ here). Use HoldPattern to prevent the
pattern from evaluation:

In[5]:= MatchQ[Times[-1,Power[s,-1]],HoldPattern[Times[___,Power[___],___]]]

Out[5]= True

HoldPattern is like Hold, but invisible to a pattern-matcher for
pattern-matching purposes.
It was designed to be used exactly to prevent patterns from evaluation.
I discussed similar issues also here:

http://www.mathprogramming-intro.org/book/node349.html

Another possible solution in this particular case:

In[6]:= MatchQ[Times[-1,Power[s,-1]],Unevaluated[Times[___,Power[___],___]]]

Out[6]= True

I'd still prefer the one with HoldPattern though.

Hope this helps.

Regards,
Leonid


On Thu, Nov 25, 2010 at 1:57 PM, kj <no.email at please.post> wrote:

>
>
>
>
> I'm tearing my hair out over this one.  Could someone please explain
> to me why all the following MatchQ expressions
>
> MatchQ[Times[ -1, Power[s, -1]      ],
>       Times[___, Power[___],    ___]]
>
> MatchQ[Times[ -1, Power[s, -1]],
>       Times[___, Power[___]  ]]
>
> MatchQ[Times[ -1,  Power[s, -1]      ],
>       Times[___, _Power        , ___]]
>
> return False?  (In all cases, s is undefined).  And yet, this succeeds:
>
> MatchQ[Times[ -1,  Power[s, -1]],
>       Times[___, _Power       ]]
>
>
> Is there a systematic way to debug/troubleshoot such pattern matching
> problems? Trace is useless here.
>
> Also, whatever the reason is for the failure of this pattern to
> match, where is this reason documented?  I've gone blind poring
> over the documentation trying to find an answer, without success.
>
> TIA!
>
> ~kj
>
>