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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



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