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