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

Tests whether the current unit system of the given order is known
to be fundamental or not.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := OrderUnitsAreFund(o);
b := OrderUnitsAreFund(o,c);</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  b, c  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
The order o must be an absolute order.
The <tt> OrderUnitsAreFund</tt> function can be used to check whether
the current unit system of the order o is known to
be fundamental.

Additionally, the <tt> OrderUnitsAreFund</tt> function makes it
possible to set an internal flag in the order o which
indicates that the current unit system is known to be fundamental.
This can be achieved by invoking the <tt> OrderUnitsAreFund</tt>
function with second optional argument c.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
In a CM field it is quite easy to compute fundamental units. 
<pre>

kash> O := OrderMaximal (Order (x^3 + x^2 - 16*x - 8));;
kash> units := OrderUnitsFund (O);
[ [1, 2, -1], [1, 2, 1] ]
kash> Ox := PolyAlg (O);;
kash> f := Poly (Ox, [1,1,1]);
x^2 + x + 1
kash> O2 := OrderMaximal (OrderAbs (Order (f)));
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^6 + 5*x^5 - 20*x^4 - 95*x^3 + 136*x^2 + 465*x + 475
Discriminant: -502020288 


</pre>

<p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
 The fundamental units of O are moved to O|2, the index of
the lifted group in U(O|2) is shown not to be divisible by 2.

<pre>

kash> Apply (units, u -> EltMove (u, O2));
kash> for u in units do OrderUnitsMerge (O2, u); od;
kash> OrderReg (O2);
28.915447106812858929100272734448621763738691622816
kash> OrderUnitsPFund (O2, 2);
[ [6, -1, -1, 1, 1, -1], [-8, 1, 1, -1, -1, 1] ]
kash> OrderReg (O2);
28.915447106812858929100272734448621763738691622816
kash> OrderUnitsAreFund (O2);
false
kash> # Mark the units as fundamental
kash> OrderUnitsAreFund (O2,true);
> true

</pre>

<p>


<hr>

<p>
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