Re: PrimitiveElement doesn't work much.
- To: mathgroup at smc.vnet.net
- Subject: [mg33341] Re: PrimitiveElement doesn't work much.
- From: Alexander Dreyer <dreyer at itwm.fhg.de>
- Date: Sat, 16 Mar 2002 01:40:23 -0500 (EST)
- Organization: Fraunhofer ITWM
- References: <a6rhn6$ep0$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Richard Fateman wrote:
>
> << NumberTheory`PrimitiveElement`
> PrimitiveElement[z, {Sqrt[2], Sqrt[3]}]
> which is the example given, works fine.
>
> but
> PrimitiveElement[z, {2^(1/3), 3^(1/3)}]
> returns unchanged.
>
> There are algebraic numbers other than square roots.
> RJF
Hi,
yes, but 2^(1/3) is not the Mathematica representation of the algebraic
number you desire. You have to think of 2^(1/3) as the first root (the
real root!) of the polynomial x^3-2, which is given by Root[#^3-2,1].
The Mathematica code for your problem is:
PrimitiveElement[z, {Root[#^3-3,1],Root[#^3-2,1]}]
Yours,
Alexander Dreyer
--
/ Alexander Dreyer, Dipl.-Math. - Abteilung Adaptive Systeme \
/ Fraunhofer Institut fuer Techno- und Wirtschaftsmathematik (ITWM) \
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