Re: ReplaceList and //.

*To*: mathgroup at smc.vnet.net*Subject*: [mg73616] Re: ReplaceList and //.*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Fri, 23 Feb 2007 04:32:45 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <erjo1u$nn5$1@smc.vnet.net>

Mr Ajit Sen wrote: > Dear Mathgroup, > > Could someone please enlighten me as to when I should > use ReplaceList and when to use //. in pattern > matching. > > Thus, if Y = a x^2/b^3, then > > ReplaceList[Y, a^m_. x^n_. b^p_. :> z > b^(p + 1) a^(m - 1) x^(n - 1)][[1]] > > as well as > > Y //. a^m_. x^n_. b^p_. :> z b^(p + 1) a^(m - 1) > x^(n - 1) > > give the same result. > > However, > > ReplaceList[a*b*c, {(x_)*(y_) -> x^y, (x_)*(y_) > -> x + y}] > > and > a*b*c //. {(x_)*(y_) :> x^y, (x_y)*_ :> x + y} > > yield different outputs. > > What am I missing here? //. applies the transformation rule(s) once, as /. does. When done, //. applies the transformation rule(s) on the resulting expression. If any modifications have been made, //. applies again the rules the new expression; otherwise it stops. Also, keep in mind that /. and //. attempt to match the most general patterns. For instance, a rule such as x_*y_, when applied to a*b*c, will match only a*(b*c) (that is x -> a and y -> b*c) although there are some other interpretations. The built-in function Trace should help you to understand what is going on: In[1]:= Trace[a*b*c /. {(x_)*(y_) -> x^y, (x_)*(y_) -> x + y}] Out[1]= y {a b c /. {(x_) (y_) -> x , (x_) (y_) -> x + y}, b c b c Times[a ], a } In[2]:= Trace[a*b*c //. {(x_)*(y_) -> x^y, (x_y)*_ -> x + y}] Out[2]= {{{{(x_y) _, _ (x_y)}, _ (x_y) -> x + y, _ (x_y) -> x + y}, y {(x_) (y_) -> x , _ (x_y) -> x + y}}, y a b c //. {(x_) (y_) -> x , _ (x_y) -> x + y}, c b c b c b {Times[a ], a }, a } Regards, Jean-Marc