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

Returns the gap numbers of a divisor.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AlffGapNumbers( D [, P] );
L := AlffGapNumbers( F [, P] );</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>containing the gap numbers</td>
</tr>
<tr>
<td>alff divisor </td>
<td><pre>  D  </pre></td>
<td></td>
</tr>
<tr>
<td>alff</td>
<td><pre>  F  </pre></td>
<td>equivalent to taking D = 0</td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffWeierstrassPlaces">AlffWeierstrassPlaces</a>, <a href="kashref.html#AlffWronskian">AlffWronskian</a>, <a href="kashref.html#AlffWronskianOrders">AlffWronskianOrders</a>, <a href="kashref.html#AlffDiff">AlffDiff</a>, <a href="kashref.html#AlffDifferentiation">AlffDifferentiation</a>

<p>

<h3>
Description:
</h3>
Let F/k be an algebraic function field,
D a divisor and P a place of degree one. An integer
m  &gt;=  1 is a D-gap number of P if \dim \bigl( D + (m-1)P
\bigr) =
\dim(D + mP) holds. The D-gap numbers m satisfy 1  &lt;=  m
 &lt;=  2g-1-\deg(D) and their cardinality equals the index of
speciality i(D). If P of degree one
is given as argument this function
returns the sequence of its D-gap numbers. The sequences of
D-gap numbers are independent of constant field extensions for
perfect k and are the same for all but a
finite number of places P of degree one
(consider e.g. k algebraically closed). If P is omitted
in the function call, this uniform sequence
is returned. The places P
which have different sequences of D-gap numbers are called
D-Weierstra\ss{} places.
The constant field k is required to be exact.


<p><p>

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

<pre>

</pre>

<p>


<hr>

<p>
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