[Date Index]
[Thread Index]
[Author Index]
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
Prev by Date:
**Re: basic complex number question**
Next by Date:
**Re: Elementary workbench question**
Previous by thread:
**How to find Minimal Poly of a possible algebraic number?**
Next by thread:
**Re: How to find Minimal Poly of a possible algebraic number?**
| |