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

Creates an algebraic function field F/k(T).

<p><p>

<h3>
Syntax:
</h3>
<pre>F := Alff(f);</pre>

<p>

<table>
<tr>
<td>algebraic function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
<tr>
<td>polynomial</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffInit">AlffInit</a>, <a href="kashref.html#AlffOrders">AlffOrders</a>, <a href="kashref.html#AlffGenus">AlffGenus</a>, <a href="kashref.html#AlffPlaceSplit">AlffPlaceSplit</a>

<p>

<h3>
Description:
</h3>
Let f\in k[T,y] be an irreducible
polynomial which is separable in y, where
k is a finite field or a number field (represented by
Q or by number field orders). This function defines
the algebraic function field  F := k(T, rho)\;\;
where\;\; f(T, rho) = 0.
In KASH, F is often also considered as a finite extension of
function fields F / k(T) such as in minimal polynomial
computations or in determining the places of F over places
of k(T). For further information, see the KASH\; manual.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
The definition of an algebraic function field:
<pre>

kash> AlffInit(FF(5,2));
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> F := Alff(y^3+T^4+1);
> Algebraic function field defined by
.1^3 + .2^4 + 1
over
Univariate rational function field over GF(5^2)
Variables: T


</pre>

<p>


<hr>

<p>
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