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<p>&nbsp;<p>
<hr noshade size="5">
<h2><a name="Ideal2EltNormalAssure"></a>
Ideal2EltNormalAssure
</h2>

Calculates a 2 element normal representation of an ideal.

<p><p>

<h3>
Syntax:
</h3>
<pre>Ideal2EltNormalAssure(I);</pre>

<p>

<table>
<tr>
<td>ideal </td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>

This is a special represenation to speed up multipication and
inverting an ideal. The two generators are computed if not
already present and then transformed to a normal representation
via a propabilistic algorithm. Multiplying and inverting use
normal representations on appropriate occasions.

<p><p>

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

<pre>

kash> O := OrderMaximal (Order (Poly (Zx, [1,0,0,0,657])));;
kash> I := 5*Elt (O,[345,76,345,46])*O;
<[1725, 380, 1725, 230]>
kash> fac := Filtered (Flat (Factor (I)), IsIdeal);
[ <2, [1, 1, 0, 0]>, <3, [0, 7, 3, 7]>, <5>, <7, [1, 1, 0, 0]>, 
  <41, [3, 1, 0, 0]>, <41, [27, 1, 0, 0]>, <197603671, [39148097, 1, 0, 0]> ]
kash> for I in fac do
> Ideal2EltNormalAssure (I);
> Print (I,"\n");
> od;
> <2, [1, 1, 0, 0]>
<3, [0, 7, 3, 7]>
<5>
<7, [1, 1, 0, 0]>
<41, [3, 1, 0, 0]>
<41, [27, 1, 0, 0]>
<197603671, [39148097, 1, 0, 0]>

</pre>

<p>


<hr>

<p>
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