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

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

Lifts an element from a modulo m approximation to
an element with rational coefficients

<p><p>

<h3>
Syntax:
</h3>
<pre>alpha := EltReconstruct (gamma, m);</pre>

<p>

<table>
<tr>
<td>false or algebraic element</td>
<td><pre>  alpha  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  gamma  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  m  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
Given an element \gamma = c_1omega_1+ &hellip; +c_nomega_n in an order
over Z with coefficients less than the positive integer m, the
function
<tt> EltReconstruct</tt> computes an element \alpha in the same order
which is equal to the element q_1omega_1+ &hellip; +q_nomega_n, where
the q_i are the reconstructed rationals from c_i and m
(q_i = frac{a_i}{b_i} such that a_i \equiv b_i c_i \bmod m and
0 \le |a_i|,b_i < \sqrt{frac{m}{2}}, b_i \neq 0, if such a pair
exists).
Otherwise <tt> false</tt> is returned.

<p><p>

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

<pre>

kash> O := Order(Z,2,3);
Generating polynomial: x^2 - 3

kash> gamma := Elt(O,[17,4]);
[17, 4]
kash> EltReconstruct(gamma,49);
> [2, 12] / 3

</pre>

<p>


<hr>

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