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

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

Checks whether an ideal is a prime ideal. Returns <tt> true</tt> or
<tt> false</tt>.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := IdealIsPrime(I);</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td>integral</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
The order over which the prime ideal is defined must be maximal.

<p><p>

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

<pre>

kash> o := OrderMaximal (Order (Poly (Zx,[1,6,6,6])));
Generating polynomial: x^3 + 6*x^2 + 6*x + 6
Discriminant: -1836 

kash> IdealIsPrime (5*o);
false
kash> Factor (5*o);
[ [ <5, [1, 1, 0]>, 1 ], [ <5, [2, 1, 0]>, 1 ], [ <5, [3, 1, 0]>, 1 ] ]
kash> IdealIsPrime (11*o);
true
kash> Factor (11*o);
> [ [ <11>, 1 ] ]

</pre>

<p>


<hr>

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