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

Calculates the ramification index of a prime ideal.

<p><p>

<h3>
Syntax:
</h3>
<pre>d := IdealRamIndex(I);</pre>

<p>

<table>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td>must be prime</td>
</tr>
<tr>
<td>integer </td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let O a maximal order. Let p be a prime number and \p
a prime O-ideal over this prime number p. The natural
number e which satisfies \p^e  |  pO and \p^{e+1}
\nmid pO is called the ramification index of
\p over p.

<p><p>

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

<pre>

kash> O := OrderMaximal(Order(Poly(Zx,[1,4,1,-4,-3,7])));
Generating polynomial: x^5 + 4*x^4 + x^3 - 4*x^2 - 3*x + 7
Discriminant: 28442269 

kash> P := Factor(6*O)[2][1];
<2, [1, 0, 0, 1, 1]>
kash> IdealDegree(P);
4
kash> IdealRamIndex(P);
> 1

</pre>

<p>


<hr>

<p>
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