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<h2><a name="AlffDivisorLBasis"></a>
AlffDivisorLBasis
</h2>

Computes a basis of a Riemann-Roch space

<p><p>

<h3>
Syntax:
</h3>
<pre>B := AlffDivisorLBasis(D);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  B  </pre></td>
<td>of basis elements</td>
</tr>
<tr>
<td>alff divisor</td>
<td><pre>  D  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Given a divisor D of an algebraic function field F
this function returns a basis for
the k-vector space {cal L}(D), where k denotes the constant
field of definition of F. The basis elements are represented
in the finite maximal order.

<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> AlffDivisorLBasis(D);
[ [ 4*T^3 + 4*T^2 + 2*T + 1, T ] / (T^3 + 4*T^2 + 2*T + 2), 
  [ 4*T^4 + 4*T^3 + 2*T^2 + T, T^2 ] / (T^3 + 4*T^2 + 2*T + 2), 
  [ 4*T^3 + 2*T^2 + 4, 1 ] / (T^3 + 4*T^2 + 2*T + 2), 
  [ 4*T^4 + 2*T^3 + 4*T, T ] / (T^3 + 4*T^2 + 2*T + 2) ]

</pre>

<p>


<hr>

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