Re: Avoid iteration in pattern test?

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• Subject: [mg132173] Re: Avoid iteration in pattern test?
• From: Carl K Woll <carlw at wolfram.com>
• Date: Thu, 9 Jan 2014 03:51:25 -0500 (EST)
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```You could try:

x /: HoldPattern[Times][f__, x] /; ! FreeQ[Hold[f], d] := "matched"

Carl Woll

On 1/6/2014 1:30 AM, Yi Wang wrote:
> Dear all,
>
> I wonder if one can stop pattern test from unnecessary iteration. For example
>
> ClearAll[x, a, b, c, d, f]
> x /: f_ x := "matched" /; !FreeQ[f, d]
>
> Trace[a b c x]
>
> One can find that Mathematica first tests if a*b*c is free of d. Then it tests if a*b is free of d, if a*c is free of d, ...
>
> However, we know that if a*b*c is free of d, all the sub-sequences are free of d. Thus is it possible to rewrite the above rule, to stop Mathematica from wasting the efforts?
>
> Thanks a lot!
> Yi
>
> PS: currently, I have a workaround -- to hold evolution of x when no match. However, it makes things complicated and less automatic.
>
> x /: f_ x := If[!FreeQ[f, d], "matched", f Hold[x]]
>

```

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