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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