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

The basis of the ideal transformed in upper HNF.

<p><p>

<h3>
Syntax:
</h3>
<pre>M := IdealBasisUpperHNF(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#IdealBasisLowerHNF">IdealBasisLowerHNF</a>, <a href="kashref.html#IdealUpperHNFTrans">IdealUpperHNFTrans</a>

<p>

<h3>
Description:
</h3>
This returns the basis of the ideal transformed in (right) upper HNF.
Either it is computed from a plain basis (which can be seen with
IdealBasis) or from a 2-element representation.
Once computed the basis in upper HNF is stored in the
ideal data structure so it has not to be computed again.
In most cases IdealBasis and IdealBasisUpperHNF are identical.

<p><p>

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

<pre>

kash> o := Order(Poly(Zx, [1, 6, 6, 6]));;
kash> alpha := Elt(o, [0, 1, 0]);;
kash> I := Ideal(6, alpha);
<6, [0, 1, 0]>
kash> IdealBasisUpperHNF(I);
> [ 1, [6 0 0]
    [0 1 0]
    [0 0 1] ]

</pre>

<p>


<hr>

<p>
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