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