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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
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