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

Computes a maximal order of an algebraic function field.

<p><p>

<h3>
Syntax:
</h3>
<pre>o := AlffOrderMaxInfty(F);</pre>

<p>

<table>
<tr>
<td>algebraic function field order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffOrderMaxFinite">AlffOrderMaxFinite</a>, <a href="kashref.html#AlffOrderMaximal">AlffOrderMaximal</a>, <a href="kashref.html#Alff">Alff</a>, <a href="kashref.html#AlffElt">AlffElt</a>

<p>

<h3>
Description:
</h3>
Let R be the valuation ring of the degree valuation of k(T),
that is  R = {g/h |  g,h\in k[T], h\neq 0,
\deg(g) &lt;= \deg(h)}, 
and let F/k(T) be an algebraic function field.
This function computes the R-maximal
order of F. It is the integral closure of R in F.

<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> 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

kash> AlffOrderMaxInfty(F);
> Infinite maximal order of 
Algebraic function field defined by
.1^3 + .2^4 + 1
over
Univariate rational function field over GF(5^2)
Variables: T
given by transformation matrix
[1/T   0   0]
[  0 1/T   0]
[  0   0   1]
with denominator 1/T

</pre>

<p>


<hr>

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