Re: simplification
- To: mathgroup at smc.vnet.net
- Subject: [mg121847] Re: simplification
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Wed, 5 Oct 2011 03:58:56 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <j6e693$kef$1@smc.vnet.net>
"dimitris" <dimmechan at yahoo.com> schrieb im Newsbeitrag news:j6e693$kef$1 at smc.vnet.net... > Hello. > > Let > > o1 = 1 + Sqrt[15 + 2*Sqrt[35] + 2*Sqrt[6*(6 + Sqrt[35])]]; > o2 = 1 + Sqrt[3] + Sqrt[5] + Sqrt[7]; > > o1 is equal to o2. > > o1 == o2 // FullSimplify > True > > The question is how to make Mathematica to simplify o1 to o2. > > Thanks > Dimitris > There are even simpler examples which seem to bring Mathematica to its limits very soon. Consider this sequence In[95]:= Simplify[Sqrt[1 + a + 2*Sqrt[a]], {a > 0}] Out[95]= 1 + Sqrt[a] In[96]:= Simplify[Sqrt[a^2 + b + 2*a*Sqrt[b]], {a > 0, b > 0}] Out[96]= a + Sqrt[b] In[97]:= Simplify[Sqrt[a + b + 2*Sqrt[a*b]], {a > 0, b > 0}] Out[97]= Sqrt[a + b + 2*Sqrt[a*b]] Maybe Mathematica does not like radicals. If we help a little bit, it works out fine In[126]:= Simplify[Sqrt[a + b + 2*Sqrt[a*b]] /. {a -> u^2, b -> v^2}, {u > 0, v > 0}] /. {u -> Sqrt[a], v -> Sqrt[b]} Out[126]= Sqrt[a] + Sqrt[b] The example o1 provided can be treated by Factor using the option Extension like this ... In[140]:= f = Factor[Sqrt[15 + 2*Sqrt[35] + 2*Sqrt[6*(6 + Sqrt[35])]], Extension -> {Sqrt[3], Sqrt[5], Sqrt[7]}] Out[140]= Root[3481 - 3180*#1^2 + 782*#1^4 - 60*#1^6 + #1^8 & , 8] In[141]:= N[%] Out[141]= 6.613870096133257 ... but this seems to lead to nothing useful. Wolfgang