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

Decompose a rational function field place.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AlffPlaceSplit(F, p);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of places {frak P} above {frak p}</td>
</tr>
<tr>
<td>algebraic function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
<tr>
<td>prime polynomial or 1/T</td>
<td><pre>  p  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffPlaceRam">AlffPlaceRam</a>, <a href="kashref.html#AlffPlaceDeg">AlffPlaceDeg</a>, <a href="kashref.html#AlffPlaceResDeg">AlffPlaceResDeg</a>, <a href="kashref.html#AlffEltValuation">AlffEltValuation</a>

<p>

<h3>
Description:
</h3>
Let F = k(T,y) be an algebraic function field defined by
f(T, y)=0 over k. This function computes the places {frak P}
of
F lying above a place {frak p} of k(T) given by a prime
polynomial of k[T] or 1/T, the later specifying the
place at infinity (degree valuation). A list containing the
places is returned.


<p><p>

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

<pre>

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

kash> L := AlffPlaceSplit(F, 1/T);
[ Alff place < [ 1/T, 0, 0 ], [ w^4/T, w^3/T, (w^4*T + w^4)/T ] >, 
  Alff place < [ 1/T, 0, 0 ], [ (w^4*T + 1)/T, (w*T + w^2)/T, (w^4*T + w^6)/T \
] > ]
kash> L := AlffPlaceSplit(F, T+1);
> [ Alff place < [ T + 1, 0, 0 ], [ w, 1, 0 ] >, 
  Alff place < [ T + 1, 0, 0 ], [ w^2, 1, 0 ] >, 
  Alff place < [ T + 1, 0, 0 ], [ w^4, 1, 0 ] > ]

</pre>

<p>


<hr>

<p>
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