Re: Inconsistent behaviour of Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg112499] Re: Inconsistent behaviour of Integrate*From*: Peter Pein <petsie at dordos.net>*Date*: Fri, 17 Sep 2010 06:43:18 -0400 (EDT)*References*: <201009140912.FAA16504@smc.vnet.net>

Am Thu, 16 Sep 2010 00:04:46 +0000 (UTC) schrieb Andreas Maier <asmaier78 at googlemail.com>: ... > > P.S.: I still wonder why Factor[17 + 12 Sqrt[2]] doesn't come up with > (1 + Sqrt[2])^4. Can Factor[] only work with expressions involving > variables like x, y...? > ... If you've got an idea what the exponent of the "simpler" Root-expression might be (somewhere between 2 and 6 in this example), you could try: In[1]:= SortBy[Table[{First@SortBy[Root[#^k-(17+12Sqrt[2])&,#]& /@Range[k]//ToRadicals,LeafCount],k},{k,2,6}],LeafCount[#[[1]]]&] Out[1]= {{1+Sqrt[2],4},{(-3-2 Sqrt[2])^(1/3),6},{(17+12 Sqrt[2])^(1/5),5},{(17+12 Sqrt[2])^(1/3),3},{Sqrt[17+12 Sqrt[2]],2}} and if you wish, you can test the result: In[2]:= Expand[Power @@ First[%]] Out[2]= 17 + 12 Sqrt[2] hth, Peter

**References**:**Inconsistent behaviour of Integrate***From:*Andreas Maier <andimai@web.de>