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

Returns the ramification divisor of a divisor.

<p><p>

<h3>
Syntax:
</h3>
<pre>A := AlffRamDivisor(D);
A := AlffRamDivisor(F);</pre>

<p>

<table>
<tr>
<td>alff divisor</td>
<td><pre>  A  </pre></td>
<td>the ramification divisor of D</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#AlffWronskian">AlffWronskian</a>, <a href="kashref.html#AlffWronskianOrders">AlffWronskianOrders</a>, <a href="kashref.html#AlffWeierstrassPlaces">AlffWeierstrassPlaces</a>, <a href="kashref.html#AlffGapNumbers">AlffGapNumbers</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, x a separating
variable and D a divisor. The ramification divisor
of D is defined to be  i(D)  ( W - D ) + \bigl(
W_x(D) \bigr) + \nu  (dx),
where W is a canonical divisor of F/k, W_x(D) is
the determinant
of the Wronksi matrix of D with respect to x and \nu is the
sum of the Wronski orders of D with respect to x. It is positive
and consists of the 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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