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

Improves the generators of the ideal given in two element
representation.

<p><p>

<h3>
Syntax:
</h3>
<pre>I1:= IdealImprove(I2);</pre>

<p>

<table>
<tr>
<td>ideal</td>
<td><pre>  I1, I2  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
The ideal can be improved if
<ul>
<li> one of the generators is an rational integer. Then
every basis coefficient of the other generator can be
reduced modulo this integer.
<li> the minimum is given. Coefficients of both generators
can be reduced modulo this integer. This procedure is fast
and simple therefore it does not <b> compute</b> the minimum
of the ideal. For more possible improvement call
<tt> IdealMin</tt> first.
</ul>

<p><p>

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

<pre>

kash> O:=Order(Poly(Zx,[1,0,2,4,58]));
Generating polynomial: x^4 + 2*x^2 + 4*x + 58

kash> E:=Elt(O,[1,2,-1,-2]);
[1, 2, -1, -2]
kash> I:=Ideal(3,E^7);
<3, [-470899145529, -57698441418, 37053141409, 29584796218]>
kash> IdealImprove(I);
> <3, [-470899145529, -57698441418, 37053141409, 29584796218]>

</pre>

<p>


<hr>

<p>
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