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

Creates an algebraic number.

<p><p>

<h3>
Syntax:
</h3>
<pre>a := Elt(O,L);
a := Elt(O,L/d);
a := Elt(O,h/d);
a := Elt(O,h);</pre>

<p>

<table>
<tr>
<td>algebraic element</td>
<td><pre>  a  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  O  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>of coefficients</td>
</tr>
<tr>
<td>integer</td>
<td><pre>  h  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Let o be an order with coefficient order c. Denote by
Quo(o) and Quo(c) the quotient field of o,
respectively c. Let omega_1, &hellip; ,omega_n be the
Quo(c) basis of Quo(o) which belongs to the order
o. Each algebraic number a in o is of a form
 a = a_1 omega_1 + cdots + a_n omega_n 
with coefficients a_1, &hellip; ,a_n \in Quo(c).\smallskip

To create a in <sf> KASH</sf> the coefficients of a must be
passed to the <tt> Elt</tt> function as a list <tt> L</tt> of length
n. The entries of <tt> L</tt> correspond to the coefficients
a_i of a. Each entry <tt> l</tt> of <tt> L</tt> is either an
algebraic number in c or it has to be a valid argument
for the function call <tt> Elt(c,l)</tt>. In the special case
that c equals Z the <tt> Elt</tt> function requires that
the entries of <tt> L</tt> are rational integers. \bigskip

<tt> Elt(o,L)</tt>
creates the element a = a_1omega_1 + cdots + a_nomega_n.
\medskip

<tt> Elt(O,L/d)</tt>
creates the element a = frac{a_1}{d}omega_1 +
cdots + frac{a_n}{d}omega_n. \medskip

<tt> Elt(O,h)</tt>
creates the algebraic number which corresponds to the
rational integer h. \medskip

<tt> Elt(O,h/d)</tt>
creates the algebraic number which corresponds to the
rational frac{h}{d}.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Create some algebraic elements: 
<pre>

kash> o1 := Order (Poly(Zx,[1,0,73,-280,-2399]));;
kash> u := Elt (o1,[1,2,3,4]/2);
[1, 2, 3, 4] / 2
kash> v := Elt (o1,2);
2
kash> u*v;
[1, 2, 3, 4]

kash> o2 := Order (o1,2,2);;
kash> o3 := Order (o2,2,3);
         F[1]
           /
          /
      E2[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^2 - 3
E 2[ 1]     x^2 - 2
E 1[ 1]     x^4 + 73*x^2 - 280*x - 2399

kash> a := Elt (o3,[1,2]);
[1, 2]
kash> b := Elt (o3,[[[1,1,1,1],1/2],2]);
[[[2, 2, 2, 2], 1], 4] / 2
kash> c := Elt (o3,[[[1,1,1,1],1/2],[1/3,[4,5,6,8]/4]]);
[[[12, 12, 12, 12], 6], [4, [12, 15, 18, 24]]] / 12
kash> d := Elt (o3,1/2);
> 1 / 2

</pre>

<p>


<hr>

<p>
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