Re: simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg121863] Re: simplification
• From: Peter Pein <petsie at dordos.net>
• Date: Wed, 5 Oct 2011 04:01:50 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6e693\$kef\$1@smc.vnet.net>

```Am 04.10.2011 07:40, schrieb dimitris:
> 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
>

With a lot of luck:

In[1]:= o1 = 1 + Sqrt[15 + 2*Sqrt[35] + 2*Sqrt[6*(6 + Sqrt[35])]];
ext = Block[{x, poly = RootReduce[o1][[1]]},
Sqrt[Cases[Union @@ Divisors[Abs[CoefficientList[poly[x], x]]],
1 | _?PrimeQ, 1]]]
o2 = ((Rest[#1] / First[#1]) . ext & )[
FindIntegerNullVector[Prepend[ext, -o1]]]

Out[3]= {1, Sqrt[2], Sqrt[3], Sqrt[5], Sqrt[7], Sqrt[19], Sqrt[31]}

Out[4]= 1 + Sqrt[3] + Sqrt[5] + Sqrt[7]

:-)

```

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