[back] [prev] [next] [index] [root]

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

Returns the Weierstra\ss{} places of a divisor.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AlffWeierstrassPlaces( D );
L := AlffWeierstrassPlaces( F );</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>containing the Weierstra\ss{} places</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#AlffGapNumbers">AlffGapNumbers</a>, <a href="kashref.html#AlffRamDivisor">AlffRamDivisor</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 of
P satisfy 1  &lt;=  m
 &lt;=  2g-1-\deg(D) and their cardinality equals the index of
speciality i(D).
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). The places P
of degree one
which have different sequences of D-gap numbers are called
D-Weierstra\ss{} places. \par This function returns a list
of all places of F/k (having not necessarily degree
one) which are lying below D-Weierstra\ss{}
places of
F \bar{k} / \bar{k} (k perfect).
The constant field k is required to be exact. Remark:
If the characteristic of F is positive this function
is currently very slow for large genus
because of <tt> AlffDifferentiation()</tt>.


<p><p>

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

<pre>

</pre>

<p>


<hr>

<p>
<a href="../kashref.html"><- back</a>[back] [prev] [next] [index] [root]