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

Enumeration of lattice points.

<p><p>

<h3>
Syntax:
</h3>
<pre>ok := LatEnum(Lambda);</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  ok  </pre></td>
<td></td>
</tr>
<tr>
<td>lattice</td>
<td><pre>  Lambda  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Please refer to "KASH{} - A User's Guide" for a detailed
description of the <tt> LatEnum</tt> function.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Let rho be a zero of the polynomial x^3+x^2+x-1 \in Z[x].
We will enumerate several elements \alpha \in Z[rho]
with small T_2 norms. Those elements are likely to have a
small norm. By assigning <tt> 4.2</tt> to the
lower bound we avoid enumeration of lattice elements
which correspond to torsion units. 
<pre>

kash> o := Order(Poly(Zx, [1,1,1,-1]));;
kash> Lambda := Lat(o);;
kash> LatEnumLowerBound(Lambda, 4.2);
4.2
kash> LatEnumUpperBound(Lambda, 2*EltT2(OrderBasis(o)[3]));
13.706659122393255422774258033027130293898341365588
kash> while LatEnum(Lambda) do
> elt := EltMove(LatEnumElt(Lambda), o);
> Print(elt, "\t", EltT2(elt), "\t", Norm(elt), "\n");
> od;
> [-2, -2, -1]	12.035720531284966795311115387919719602545072476587	-1
[-1, -2, -1]	9.035720531284966795311115387919719602545072476585	-4
[0, -2, -1]	12.035720531284966795311115387919719602545072476587	-7
[-2, -1, -1]	9.470353793290390217264420480058530559999788639053	-2
[-1, -1, -1]	4.470353793290390217264420480058530559999788639052	-1
[0, -1, -1]	5.470353793290390217264420480058530559999788639052	-2
[1, -1, -1]	12.47035379329039021726442048005853055999978863905	1
[-1, 0, -1]	7.853329561196627711387129016513565146949170682804	-4
[0, 0, -1]	6.853329561196627711387129016513565146949170682794	-1
[1, 0, -1]	11.853329561196627711387129016513565146949170682793	4
[-2, -1, 0]	11.974171252950407036084701722158111814747332940641	-7
[-1, -1, 0]	4.974171252950407036084701722158111814747332940639	-2
[1, -1, 0]	8.974171252950407036084701722158111814747332940643	2
-2	12	-8

</pre>

<p>


<hr>

<p>
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