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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: [mg114638] Re: Replacement Rule with Sqrt in denominator. Also Bug in Series; see Semantica / Harris solution
• From: Richard Fateman <fateman at cs.berkeley.edu>
• Date: Sat, 11 Dec 2010 01:54:08 -0500 (EST)

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