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

Computes the p maximal overgroup of the units in the
given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>OrderUnitsPFund (O,p);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td></td>
</tr>
<tr>
<td>rational prime</td>
<td><pre>  p  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
The given absolute order O must be maximal.
This function computes the p maximal overgroup of
the units given in O.
If no units have been computed so far, an arbitrary system of
independent units is computed in advance.
For further information we refer the reader to Wi1.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Let rho be a root of t^3+15 t^2 + 15 t + 15. We consider the
order {Z}[rho], which is already maximal with
signature [1,1].\newline
2729 + 573 rho + 27 rho ^2 is a unit in this order. 
<pre>

kash> O := OrderMaximal(Order(Poly(Zx,[1,15,15,15])));
Generating polynomial: x^3 + 15*x^2 + 15*x + 15
Discriminant: -110700 

kash> a := Elt(O,[2729, 573, 27]);
[2729, 573, 27]
kash> OrderUnitsMerge(O,a);
true
kash> OrderReg(O);
15.630874731280170083241764717443071385772563284107
kash> OrderUnitsPFund(O,2);
[ [2729, 573, 27] ]
kash> OrderUnitsPFund(O,3);
[ [-14, -1, 0] ]
kash> OrderReg(O);
> 5.210291577093390027747254905814357128590623830734

</pre>

<p>


<hr>

<p>
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