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

Return an inverse prime element for a place.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := AlffPlaceBeta(P);</pre>

<p>

<table>
<tr>
<td>alff element</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
<tr>
<td>alff place</td>
<td><pre>  P  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffEltValuation">AlffEltValuation</a>, <a href="kashref.html#AlffPlacePrimeElt">AlffPlacePrimeElt</a>, <a href="kashref.html#AlffPlaceMin">AlffPlaceMin</a>

<p>

<h3>
Description:
</h3>
Let a finite (infinite) place frak{P} of the algebraic
function field F/k be given and let p be the minimum
of frak{P}.
This function returns an element \beta \in F such that
\beta / p is integral
at all finite (infinite) places different from frak{P} and
satisfies v_{frak{P}}(\beta / p) = -1.

<p><p>

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

<pre>

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

kash> P := AlffPlacesDegOne(E)[2];
Alff place < [ T, 0 ], [ 0, 1 ] >
kash> p := AlffPlaceMin(P);
T
kash> b := AlffPlaceBeta(P);
[ 1, 1 ]
kash> AlffDivisor(b/p);
> Alff divisor
[ [ Alff place < [ T, 0 ], [ 0, 1 ] >, -1 ],
[ Alff place < [ T + 1, 0 ], [ 1, 1 ] >, 2 ],
[ Alff place < [ 1/T, 0 ], [ 0, 1 ] >, -1 ] ]


</pre>

<p>


<hr>

<p>
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