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MathGroup Archive 2006

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Re: a Quaternion quadratic level Pisot polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68596] Re: a Quaternion quadratic level Pisot polynomial
  • From: Roger Bagula <rlbagula at sbcglobal.net>
  • Date: Fri, 11 Aug 2006 04:40:08 -0400 (EDT)
  • References: <eahtq5$p0b$1@smc.vnet.net> <eakd82$qhf$1@smc.vnet.net> <eaprmm$s40$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks to Peter Pleasants I did solve the golden mean / Fibonacci Pisot
and several others for real roots:
the secret is using :
{t_Real, x_Real, y_Real,  z_Real}

\!\(<< Algebra`Quaternions`\n
  q = Quaternion[t, x, y, z]\n
  q2 = ExpandAll[q ** q]\n
  q3 = \((q2 ** q2)\)\n
  FullSimplify[q2 - q - Quaternion[1, 0, 0, 0]]\n
  NSolve[{\(-1\) + \((\(-1\) + t)\)\ t - x\^2 - y\^2 -
      z\^2 == 0, \((\(-1\) + 2\ t)\)\ x ==
    0, \((\(-1\) + 2\
      t)\)\ y == 0, \((\(-1\) + 2\ t)\)\ z == 0}, {t_Real, x_Real, y_Real,
    z_Real}]\)


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