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

The basis of the ideal transformed in lower HNF

<p><p>

<h3>
Syntax:
</h3>
<pre>M:=IdealBasisLowerHNF(I);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  M  </pre></td>
<td>two elements, the denominator and the basis matrix</td>
</tr>
<tr>
<td>ideal</td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This returns the basis of the ideal transformed in lower HNF.
The basis is computed from the actual (which can be seen
with IdealBasis). Once computed the basis in lower HNF is
stored in the ideal data structure so it has not to be
computed again.

<p><p>

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

<pre>

kash> O:=OrderMaximal(Order(Poly(Zx,[1,4,1,-4,-3,7])));
Generating polynomial: x^5 + 4*x^4 + x^3 - 4*x^2 - 3*x + 7
Discriminant: 28442269 

kash> I:=Ideal(O,Mat(Z,[[1,2,1,4,6],[3,8,4,6,2],[6,4,3,3,8],
> [3,2,7,9,5],[0,2,8,8,4]]),1);
<
[1 2 1 4 6]
[3 8 4 6 2]
[6 4 3 3 8]
[3 2 7 9 5]
[0 2 8 8 4]
>

kash> IdealBasisLowerHNF(I);
> [ 1, [   1    0    0    0    0]
    [   0    1    0    0    0]
    [   0    0    1    0    0]
    [   0    1    0    3    0]
    [ 512  910  858 1672 1678] ]

</pre>

<p>


<hr>

<p>
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