Re: How to get an answer as a Root object?
- To: mathgroup at smc.vnet.net
- Subject: [mg57299] Re: How to get an answer as a Root object?
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 24 May 2005 05:12:36 -0400 (EDT)
- Organization: The University of Western Australia
- References: <200505170520.BAA25934@smc.vnet.net> <200505190708.DAA13114@smc.vnet.net> <acbec1a405051916553ad63c12@mail.gmail.com> <200505200843.EAA00645@smc.vnet.net> <d6mlqh$g9o$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <d6mlqh$g9o$1 at smc.vnet.net>, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > Mathod 1 is of course classical (discussed for example in 1991 Henri > Cohen's "A Course in Computational Algebraic Number Theory" on page > 100) Thanks for the ref. I've used this idea regularly since I first encountered the Recognize package but have not seen it in the literature (though I knew it would be classical). > but I don't like the fact that you have to (or at least it seems > to me you have to) guess the degree of the polynomial used in > Recognize. You can increment the degree and determine the minimal degree (using FixedPoint or somesuch). expr = (-1 + Sqrt[2] - Sqrt[(1 + 2 Sqrt[2] - s) (-1 + s)] + s) * (-1 - Sqrt[2] + Sqrt[2] s - Sqrt[-1 - 2 Sqrt[2] + 2 (2 + Sqrt[2] - s) s]) - (-1 - Sqrt[2] + Sqrt[2] s + Sqrt[-1 - 2 Sqrt[2] + 2 (2 + Sqrt[2] - s) s]) (-2 - 2 Sqrt[2] + 2 s + 2 Sqrt[1 - (1/4) (-1 - Sqrt[2] + Sqrt[(1 + 2 Sqrt[2] - s) (-1 + s)] + s)^2]); << NumberTheory` x = Chop[s /. FindRoot[expr == 0, {s, 2.5}, WorkingPrecision -> 100]] Table[{n, Last[FactorList[Recognize[x, n, t]]]}, {n, 10, 20}] Also, you can verify the solution by back-substitution: RootReduce[expr /. s -> Root[Function[t, 256 t^12 - 3072 t^11 + 15872 t^10 - 46080 t^9 + 81425 t^8 - 86152 t^7 + 43568 t^6 + 10832 t^5 - 32136 t^4 + 21024 t^3 - 6112 t^2 + 512 t + 64], 8]] Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul http://InternationalMathematicaSymposium.org/IMS2005/
- References:
- How to get an answer as a Root object?
- From: "David W. Cantrell" <DWCantrell@sigmaxi.org>
- Re: How to get an answer as a Root object?
- From: Daniel Lichtblau <danl@wolfram.com>
- Re: Re: How to get an answer as a Root object?
- From: Daniel Lichtblau <danl@wolfram.com>
- How to get an answer as a Root object?