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

Computes the regulator of a global function
field's finite maximal order's unit group.

<p><p>

<h3>
Syntax:
</h3>
<pre>R := AlffRegulator(o);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  R  </pre></td>
<td></td>
</tr>
<tr>
<td>finite maximal order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffSignature">AlffSignature</a>, <a href="kashref.html#AlffUnitRank">AlffUnitRank</a>, <a href="kashref.html#AlffUnitsFund">AlffUnitsFund</a>

<p>

<h3>
Description:
</h3>
For 1  &lt;=  i  &lt;=  s-1 let \nu_i denote distinct
normalized
valuations of F at the infinite places with
degrees f_i over the degree valuation of k(T).
Let M\inZ^{(s-1)\times (s-1)} be the image of
a basis of the finite maximal order's unit group
in the "logarithm space" obtained by applying
the \nu_i for 1  &lt;=  i  &lt;=  s-1 on each basis element.
The function returns det(M)\prod_{i=1}^rf_i.

<p><p>

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

<pre>

kash> AlffInit(FF(5,1));
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> AlffOrders(y^4+(2*T+3)*y^3+y^2+(3*T+2)*y+1);
"Defining global variables: F, o, oi, one"
kash> AlffUnitsFund(o);
[ [ 1, 1, 0, 0 ], [ 1, 4*T, 4*T + 3, 2 ], [ 3*T + 1, 1, 2*T + 3, 1 ] ]
kash> AlffRegulator(o);
> 1

</pre>

<p>


<hr>

<p>
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