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Re: How to find Minimal Poly of a possible algebraic number?

• To: mathgroup at smc.vnet.net
• Subject: [mg72130] Re: [mg72094] How to find Minimal Poly of a possible algebraic number?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 13 Dec 2006 06:39:24 -0500 (EST)
• References: <200612110955.EAA07198@smc.vnet.net>

On 11 Dec 2006, at 18:55, titus_piezas at yahoo.com wrote:

> Hello all,
>
> Given x which you think is an algebraic number. Can you use  
> Mathematica
> to find its minimal poly?
> The number I would like to test is:
>
> x = 19.05962891397391285670091722808301086216...
>
> I believe this is the root of either a quadratic or a quintic poly
> P(x). Of course, with an approximate number x one can always find a
> P(x) with large enough coefficients such that x is a root, but if you
> can find one with "small" coefficients, then that might be it.
>
> Any help will be appreciated.
>
> P.S. I tried the "Integer Relations" applet at
> http://www.cecm.sfu.ca/~aszanto/IntegerRelations/ but either there was
> a glitch in the server or my comp and I couldn't access it.  :-(
>
> -Titus
>

You can always try:

<< numbertheory`

Table[Recognize(x, n, t), {n, 2, 15}]


Looking at that I would choose


%[[13]]


t^14 - 8*t^13 - 207*t^12 - 72*t^11 + 8*t^10 - 252*t^9 - 60*t^8 +  
69*t^7 - 165*t^6 - 117*t^5 - 9*t^4 - 143*t^3 + 201*t^2 + 318*t - 313

as that would make your number integral over the integers.

Andrzej Kozlowski

• References:
  • How to find Minimal Poly of a possible algebraic number?
    • From: titus_piezas@yahoo.com