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

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

Creates an element of an algebraic function field F/k(T).

<p><p>

<h3>
Syntax:
</h3>
<pre>a := AlffElt(o, s);
a := AlffElt(o, b);
a := AlffElt(o, L);</pre>

<p>

<table>
<tr>
<td>algebraic function field element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic function field order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>finite field element, rational or order element</td>
<td><pre>  s  </pre></td>
<td>a constant</td>
</tr>
<tr>
<td>polynomial or quotient field element</td>
<td><pre>  b  </pre></td>
<td>a rational function</td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of above s or b of length n</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Let o be an alff order
in F of rank n with basis b_1, &hellip; ,b_n.
Invoked with s or b these arguments will be embedded into
k(T) \subseteq F. Invoked with a list
<tt> L</tt> :=[c_1, &hellip; ,c_n] of length n the element
\sum_{i=1}^n c_i b_i will be returned. The c_i have to be
of the same type as s or b.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Define an element of the finite maximal order:
<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> a := AlffElt(o, [0, 1, 0]);
[ 0, 1, 0 ]
kash> a^3+T^4+1;
> [ 0, 0, 0 ]

</pre>

<p>


<hr>

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