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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="OrderExcepSequence"></a>
OrderExcepSequence
</h2>

Computes a sequence of exceptional units of maximal length
in a given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := OrderExcepSequence (o);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>exceptional sequence</td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#OrderUnitsExcep">OrderUnitsExcep</a>

<p>

<h3>
Description:
</h3>
Let o be an order over Z and let
omega_1, &hellip; ,omega_m \;(m \ge 2) be a sequence of
elements of o. We say that this sequence is an
exceptional sequence if omega_1 = 0, omega_2 = 1 and all
the mutual differences omega_i - omega_j \;(1 \le i < j
\le m) are units. Note that for such an exceptional
sequence the elements omega_3, &hellip; ,omega_m are
exceptional units in the terminology of T.~Nagell
Nag.\smallskip

The <tt> OrderExcepSequence</tt> function returns an exceptional
sequence of maximal length.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute an exceptional sequence of maximal length
in Z[zeta_7] : 
<pre>

kash> o := Order(Poly(Zx,[1,1,1,1,1,1,1]));
Generating polynomial: x^6 + x^5 + x^4 + x^3 + x^2 + x + 1

kash> OrderExcepSequence(o);
> [ 0, 1, [3, 0, 2, 1, 1, 2], [0, -1, 0, -1, 0, -1], [0, 0, -1, 0, 0, -1], 
  [1, 0, 1, 0, 0, 1], [-2, 0, -2, -1, -1, -2] ]

</pre>

<p>


<hr>

<p>
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