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

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

Compute the valuation of an algebraic element or an integer.

<p><p>

<h3>
Syntax:
</h3>
<pre>val := EltValuation(P, alpha);</pre>

<p>

<table>
<tr>
<td></td>
<td><pre>  val}{integer}{returned value.  </pre></td>
<td></td>
</tr>
<tr>
<td></td>
<td><pre>  P}{ideal}{a prime ideal.  </pre></td>
<td></td>
</tr>
<tr>
<td></td>
<td><pre>  alpha}{algebraic element or integer}{number to evaluate.  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function returns the valuation of an algebraic element
or an integer at a prime ideal.

<p><p>

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

<pre>

kash> o := OrderMaximal(Order(Z,2,3));
Generating polynomial: x^2 - 3
Discriminant: 12 

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

kash> P := Factor(2*o)[1][1];
<2, [0, 1, 0]>
kash> EltValuation (P, 3);
0
kash> EltValuation (P, 2);
3
kash> EltValuation (P, 2^7);
21
kash> EltValuation (P, 2^40);
> 120

</pre>

<p>


<hr>

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