[back] [prev] [next] [index] [root]

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

Initializes variables for some structures
of an algebraic function field.

<p><p>

<h3>
Syntax:
</h3>
<pre>AlffOrders(f);</pre>

<p>

<table>
<tr>
<td>polynomial in k[T][y]</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function is used for convenience to initialize variables
for some structures of an algebraic function field and is
not recommended for use in programming. It initializes:
<ul>
<li> <tt> F</tt>, the algebraic function field generated by f(T,y)=0,
<li> <tt> o</tt>, the integral closure of k[T] in F,
<li> <tt> oi</tt>, the integral closure of the degree valuation
ring,
<li> <tt> one</tt>, the 1 \in F.
</ul>
The polynomial f is checked to be irreducible and separable.

<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^3+2);
"Defining global variables: F, o, oi, one"
kash> F;
Algebraic function field defined by
.1^3 + .2^3 + 2
over
Univariate rational function field over GF(5^2)
Variables: T

kash> o;
Finite maximal order of 
Algebraic function field defined by
.1^3 + .2^3 + 2
over
Univariate rational function field over GF(5^2)
Variables: T

kash> AlffGlobals.oi;
Infinite maximal order of 
Algebraic function field defined by
.1^3 + .2^3 + 2
over
Univariate rational function field over GF(5^2)
Variables: T

kash> one;
> [ 1, 0, 0 ]

</pre>

<p>


<hr>

<p>
<a href="../kashref.html"><- back</a>[back] [prev] [next] [index] [root]