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

Computes a bound for the number of places of degree one of
a global function field.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := AlffPlacesDegOneNumBound(F);
b := AlffPlacesDegOneNumBound(q, g);</pre>

<p>

<table>
<tr>
<td>global function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  q, g  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let N_q(g) be the maximal number of places of degree one of
a global function field F with genus g over {\Bbb
F}_q. This function calculates the minimum of the Serre
bound and the Ihara bound as an upper bound for N_q(g) from the
given special function field or for given q and g.

<p><p>

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

<pre>

kash> AlffInit(FF(7,2));
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> AlffOrders(y^7+y+T^4+1);
"Defining global variables: F, o, oi, one"
kash> AlffGenus(F);
9
kash> AlffPlacesDegOneNumBound(F);
176
kash> AlffPlacesDegOneNumBound(5, 6);
> 25

</pre>

<p>


<hr>

<p>
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