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

Returns the finite constant field of the Puiseux series
field into which all completions of a global function
field with respect to the infinite valuations can be embedded.

<p><p>

<h3>
Syntax:
</h3>
<pre>k := AlffPuiseuxCoeff(F);</pre>

<p>

<table>
<tr>
<td>finite field</td>
<td><pre>  k  </pre></td>
<td></td>
</tr>
<tr>
<td>global function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffRoots">AlffRoots</a>

<p>

<h3>
Description:
</h3>
Let f(T,y) be a generating irreducible equation
for a global function
field F, of degree n and separable in y.
Let d be a minimal positive integer such that all n distinct
roots of f(T,y) in y can be represented in
FF_{q^d}((T^{-1/e})), where e is the least common multiple
of the ramification
indices of the infinite places and p \nmid e.
The function returns FF_{q^d}.

<p><p>

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

<pre>

kash> AlffInit(FF(5,2));
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> AlffOrders(y^3+T^4+1);
"Defining global variables: F, o, oi, one"
kash> AlffRoots(F);;
kash> AlffPuiseuxCoeff(F);
> Finite field of size 5^2

</pre>

<p>


<hr>

<p>
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