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

Creation of divisors.

<p><p>

<h3>
Syntax:
</h3>
<pre>D := AlffDivisor(F);
D := AlffDivisor(a);
D := AlffDivisor(P);
D := AlffDivisor(I, J);
D := AlffDivisor(u, v);</pre>

<p>

<table>
<tr>
<td>alff divisor</td>
<td><pre>  D  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
<tr>
<td>alff order element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>alff place</td>
<td><pre>  P  </pre></td>
<td></td>
</tr>
<tr>
<td>alff order ideal</td>
<td><pre>  I  </pre></td>
<td>of the finite maximal order</td>
</tr>
<tr>
<td>alff order ideal</td>
<td><pre>  J  </pre></td>
<td>of the infinite maximal order</td>
</tr>
<tr>
<td>alff order elements</td>
<td><pre>  u,v  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffPlaceSplit">AlffPlaceSplit</a>, <a href="kashref.html#AlffIdealFactor">AlffIdealFactor</a>, <a href="kashref.html#AlffEltMove">AlffEltMove</a>, <a href="kashref.html#Alff">Alff</a>

<p>

<h3>
Description:
</h3>
This function allows the creation of algebraic function field
divisors. There are several possibilities for the arguments:
<ul>
<li> Given the algebraic function field F the
zero divisor is created,
<li> given an alff order element a its principal
divisor is created,
<li> given an alff place frak{P} its prime divisor is created,
<li> given a pair of alff order ideals I, J or alff order elements
u,v in the finite or infinite maximal order, the divisor
corresponding to their ideal factorizations is created.
</ul>

<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^2+T^3+1);
"Defining global variables: F, o, oi, one"
kash> AlffDivisor(F);
Alff divisor
[  ]

kash> a := AlffElt(o, T);
[ T, 0 ]
kash> AlffDivisor(a);
Alff divisor
[ [ Alff place < [ T, 0 ], [ 2, 1 ] >, 1 ],
[ Alff place < [ T, 0 ], [ 3, 1 ] >, 1 ],
[ Alff place < [ 1/T, 0 ], [ 0, 1 ] >, -2 ] ]

kash> l := AlffPlaceSplit(F, T);
[ Alff place < [ T, 0 ], [ 2, 1 ] >, Alff place < [ T, 0 ], [ 3, 1 ] > ]
kash> D := AlffDivisor(l[1]);
Alff divisor
[ [ Alff place < [ T, 0 ], [ 2, 1 ] >, 1 ] ]

kash> l := AlffPlacesDegOne(F);
[ Alff place < [ 1/T, 0 ], [ 0, 1 ] >, Alff place < [ T, 0 ], [ 2, 1 ] >, 
  Alff place < [ T, 0 ], [ 3, 1 ] >, Alff place < [ T + 3, 0 ], [ 1, 1 ] >, 
  Alff place < [ T + 3, 0 ], [ 4, 1 ] >, 
  Alff place < [ T + 1, 0 ], [ 0, 1 ] > ]
kash> 3*Sum(l) + D;
Alff divisor
[ [ Alff place < [ 1/T, 0 ], [ 0, 1 ] >, 3 ],
[ Alff place < [ T, 0 ], [ 2, 1 ] >, 4 ],
[ Alff place < [ T, 0 ], [ 3, 1 ] >, 3 ],
[ Alff place < [ T + 3, 0 ], [ 1, 1 ] >, 3 ],
[ Alff place < [ T + 3, 0 ], [ 4, 1 ] >, 3 ],
[ Alff place < [ T + 1, 0 ], [ 0, 1 ] >, 3 ] ]

kash> 2*D > D;
true
kash> 2*D > D + l[1];
> false

</pre>

<p>


<hr>

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