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

Returns a lower bound for the regulator of the given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>x := OrderRegLowBound(o);
x := OrderRegLowBound(o, reg);</pre>

<p>

<table>
<tr>
<td>real</td>
<td><pre>  x  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>real</td>
<td><pre>  reg  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let o be an absolute order.

<tt> OrderRegLowBound(o)</tt> computes a lower bound for the
regulator of the order o. \bigskip

<tt> OrderRegLowBound(o, reg)</tt> sets the regulator of the order
o to the value of reg and returns it.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute a lower bound for the regulator of Q(rho) where
rho^4 + 73 rho^2 - 280 rho - 2399 = 0: 
<pre>

kash> O := OrderMaximal (Order (Poly(Zx,[1,0,73,-280,-2399])));
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^4 + 73*x^2 - 280*x - 2399
Discriminant: -997975 

kash> OrderRegLowBound (O); 
2.590616643223093069474635679775415624303102251639

</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>


Set the lower bound to 2.0: 
<pre>

kash> OrderRegLowBound (O, 2.0);
2
kash> OrderRegLowBound (O);
> 2

</pre>

<p>


<hr>

<p>
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