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

Returns the value of the floor function of the Bach bound of the
algebraic number field which is generated by the given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := OrderBach(O);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
The given order o must be maximal, otherwise
an error is returned.

A theorem of Bach asserts (under the assumption of GRH) that all
prime ideals with norm below this bound generate the class group.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Compute the floor of the Bach bound of the algebraic
number field {\Bbb Q}(\sqrt[17]{2}). 
<pre>

kash> o := Order(Z,17,2);
Generating polynomial: x^17 - 2

kash> O := OrderMaximal(o);
Generating polynomial: x^17 - 2
Discriminant: 54214017802982966177103872 

kash> OrderBach(O);
> 42133

</pre>

<p>


<hr>

<p>
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