Re: Replacement Rule with Sqrt in denominator

*To*: mathgroup at smc.vnet.net*Subject*: [mg114433] Re: Replacement Rule with Sqrt in denominator*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Sat, 4 Dec 2010 06:14:00 -0500 (EST)*References*: <ic5igm$44p$1@smc.vnet.net> <ic8ad7$81f$1@smc.vnet.net> <id7t95$lh1$1@smc.vnet.net> <idagbn$js7$1@smc.vnet.net>

On 12/3/2010 2:21 AM, Richard Fateman wrote: ... snip ... I hesitate to follow up on my own posting, but.. Here's a much nicer rule with LCM, that you might like. qq = (a_^r_ b_^s_ /; (lcm = PolynomialLCM[Denominator[s], Denominator[r]]) =!= 1 :> (a^( lcm r) b^(lcm s))^(1/lcm)) although it uses a global variable lcm, which, in a better formulation might be put inside a module, but I don't know how this would work inside a pattern in Mathematica. a^(a_^r_ b_^s_ /; (lcm = PolynomialLCM[Denominator[s], Denominator[r]]) =!= 1 :> (a^( lcm r) b^(lcm s))^(1/lcm) a^(r/s)*b^(p/3/s) /. qq comes out as (a^(3 r) * b^p) ^(1/(3 s)) and Sqrt[u]*Sqrt[v^3]^5 /. qq comes out as Sqrt[u*v^15]. Again, that is assuming you want to make that transformation. Notice the distinct lack of "FullForm" or "Rational" RJF