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

Index of speciality of alff divisors.

<p><p>

<h3>
Syntax:
</h3>
<pre>i := AlffDivisorLIndex(D);</pre>

<p>

<table>
<tr>
<td>integer</td>
<td><pre>  i  </pre></td>
<td></td>
</tr>
<tr>
<td>divisor</td>
<td><pre>  D  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffDivisorLBasis">AlffDivisorLBasis</a>, <a href="kashref.html#AlffDivisorLDim">AlffDivisorLDim</a>, <a href="kashref.html#AlffDivisorDeg">AlffDivisorDeg</a>, <a href="kashref.html#AlffGenus">AlffGenus</a>, <a href="kashref.html#Alff">Alff</a>

<p>

<h3>
Description:
</h3>
Let F = k(T,y) be an algebraic function field defined by
f(T,y)=0 over k. Given a divisor D of F this
function computes the index of speciality i_k(D) = dim_k
{cal L}(D) - deg_k D + m*(g-1), where g denotes
the genus of F and m the dimension of the exact constant
field over the constant field of definition k, as dimension
over k.

<p><p>

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

<pre>

kash> AlffInit(FF(5,1));;
kash> AlffOrders(y^2+T^3+1);;
kash> infty := AlffPlaceSplit(F, 1/T)[1];
Alff place < [ 1/T, 0 ], [ 0, 1 ] >
kash> l := AlffPlaceSplit(F, T+3);
[ Alff place < [ T + 3, 0 ], [ 1, 1 ] >, 
  Alff place < [ T + 3, 0 ], [ 4, 1 ] > ]
kash> D := 2*infty + 3*l[1] - l[2];
Alff divisor
[ [ Alff place < [ 1/T, 0 ], [ 0, 1 ] >, 2 ],
[ Alff place < [ T + 3, 0 ], [ 1, 1 ] >, 3 ],
[ Alff place < [ T + 3, 0 ], [ 4, 1 ] >, -1 ] ]

kash> AlffDivisorLIndex(D);
> 0

</pre>

<p>


<hr>

<p>
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