Re: Pattern matching

*To*: mathgroup at smc.vnet.net*Subject*: [mg116241] Re: Pattern matching*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Tue, 8 Feb 2011 05:05:23 -0500 (EST)

No... the rule is never applied to fact[-1]. If it were, there WOULD be an infinite loop, since fact[-1] -> -1 fact[-2] (not -1 times the previous zero). The previous zero, multiplied by fact[-1] (unevaluated) is zero, and there's no rule for zero, so ReplaceRepeated stops. Bobby On Mon, 07 Feb 2011 05:07:14 -0600, Leonid Shifrin <lshifr at gmail.com> wrote: > This is not a bug. The second rule indeed has no chance to execute. The > reason that this does not iterate infinitely is that when the first rule > applies for n = 0, we get zero as a result. The next time the rule is > applied for n = -1, we get zero again, since we multiply -1 and the > previous > zero. Since the two consecutive results are the same, ReplaceRepeated > stops. > > I used a similar example in my book, where I made the same statement > that > we should expect infinite iteration, which is apparently incorrect for > this > particular problem, as you just pointed out. Will add this to a list of > things I have to correct. > > Regards, > Leonid > > > On Sun, Feb 6, 2011 at 1:35 PM, StatsMath <stats.math8 at gmail.com> wrote: > >> Have a question regarding the applicaiton of pattern rules: >> >> fact[4] //. {fact[n_] :> n fact[n-1], fact[0] -> 1} >> >> This is a bug since fact[0] needs to be defined 1st, but I expected >> the above to grind away idefnitely but it returned a a value 0, >> instead of an infininte computation. >> >> Can you help me understand why the above returns 0? >> >> Thanks! >> >> -- DrMajorBob at yahoo.com