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Re: Replacement Rule with Sqrt in denominator. Also Bug in Series; see Semantica / Harris solution

• To: mathgroup at smc.vnet.net
• Subject: [mg114673] Re: Replacement Rule with Sqrt in denominator. Also Bug in Series; see Semantica / Harris solution
• From: Yves Klett <yves.klett at googlemail.com>
• Date: Sun, 12 Dec 2010 05:46:18 -0500 (EST)

> Harris' code looks fairly complicated, but can be downloaded free.
> Not like the paper, which appeared in the "Mathematica Journal".

My last info was that the Mathematica Journal is now availabe for free.
Download away.

Yves

Am 11.12.2010 07:54, schrieb Richard Fateman:
> I just came across this, from a link in this newsgroup, 10 years ago or so.
> Jason Harris wrote a package called "Semantica" for pattern matching.
> It rewrites ReplaceAll etc etc etc, and adds a functionality by
> producing new rules if the LHS includes "Semantic" parts. Thus
> 
> 
> f[8] /. f[Semantic[2*x_]] -> g[x]
> 
> returns g[4].
> 
> f[3+4 I] /. f[Semantic[a_+b_ I] -> aha[a,b]
> 
> returns aha[3,4]
> 
>   .. actually, it doesn't quite do that in version 7.0, but
> it almost does.  I don't know if the bug would be exhibited in
> the version of Mathematica current in 1999. It seems to involve
> a disagreement about dynamic binding.
> 
> Harris' code requires the use of Solve when defining rules,
> but often need not use Solve when applying them.
> 
> See
> http://www.mathematica-journal.com/issue/v7i3/features/harris/
> 
> For your information, the first of the rules above, f[Semantic[2*x_]]->g[x]
> is converted to
> {HoldPattern[f[L$10_]] :> With[{x = L$10/2}, g[x] /; True]}
> 
> 
> There are various limitations in the rule transformations, like only
> single-underscore variables are allowed.
> 
> Actually, it doesn't handle the rule  Sqrt[x] -> g.
> 
> but maybe that could be added. Perhaps it could become
> x^(r_) :> With[{L = 2*r}, g^L /; Denominator[r] == 2]
> 
> Harris' code looks fairly complicated, but can be downloaded free.
> Not like the paper, which appeared in the "Mathematica Journal".
> 
> I guess Jason Harris is doing something else now.
> 
> RJF
> 
> 
>