[back] [prev] [next] [index] [root]

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

Checks the results of class group computations done by using
the Euler product.

<p><p>

<h3>
Syntax:
</h3>
<pre>OrderClassGroupCheck(o, [[lb,] ub ]  |  [p, "pmax"]);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  ub  </pre></td>
<td>upper resp.~ lower bound</td>
</tr>
<tr>
<td>integer</td>
<td><pre>  p  </pre></td>
<td>prime number</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function checks the computed class group to be the ideal
class group generated by all prime ideals with norm below
the used ideal bound. The units are proved to be
fundamental. You may specify by <tt> lb</tt> and <tt> ub</tt> a
lower and upper bound for primes p for which the units are
checked to be p-maximal.

In this way you may compute a
class group using the option "fast" first and then perform
this test later on. This function returns after quite a while
if the results are wrong. It is therefore sometimes convenient to
switch on output using the <tt> PRINTLEVEL</tt> function.

The last calling sequence is used to ensure that subsequently
computed S-units are p-maximal (special case of the
previous calling sequences).

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Of Q(\sqrt[6]{-13}) we check the results:
<pre>

kash> o := OrderMaximal(x^6+13);;
kash> OrderClassGroup(o, 500, fast);
[ 6, [ 6 ] ]
kash> OrderClassGroupCheck(o);
> true

</pre>

<p>


<hr>

<p>
<a href="../kashref.html"><- back</a>[back] [prev] [next] [index] [root]