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

Extends a system of units of the given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>B := OrderUnitsMerge(o,eta);
B := OrderUnitsMerge(o,eta,"append");</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  B  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  eta  </pre></td>
<td>a unit in o</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
The OrderUnitsMerge function performs a MLLL reduction
to expand the current unit group of the given absolute order
o by merging \eta in it.
If the rank of the unit group increases <tt> OrderUnitsMerge</tt> will
return TRUE. Otherwise it will return FALSE.

<tt> OrderUnitsMerge(o,eta,"append")</tt> just appends the unit
\eta to the system of units of the order o, MLLL is not
performed.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Extending a system of units of an order. 
<pre>

kash> o := Order (Poly (Zx,[1,0,-186,0,13097,0,-412704,0,4946176]));
Generating polynomial: x^8 - 186*x^6 + 13097*x^4 - 412704*x^2 + 4946176

kash> O := OrderMaximal (o);;
kash> OrderUnitsMerge (O,Elt (O,[-14, 5, 1, 0, -1, 1, 3, -5]));
true
kash> OrderUnitsMerge (O,Elt (O,[177, -301, 26, -31, 39, -74, -190, 377]));
true
kash> OrderReg (O);
Error, no maximal set of independent units known
kash> OrderUnitsMerge (O,Elt (O,[227, -555, 57, -63, 74, -140, -361, 714]));
true
kash> a := Elt (O,[-14, 5, 1, 0, -1, 1, 3, -5]);;
kash> b := Elt (O,[227, -555, 57, -63, 74, -140, -361, 714]);;
kash> OrderUnitsMerge (O,a*b);
false
kash> OrderReg (O);
> 121.297795062765195428716897829517493027623458635

</pre>

<p>


<hr>

<p>
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