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

Return an ideal basis in upper Hermite normal form.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AlffIdealBasisUpperHNF(I);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td></td>
</tr>
<tr>
<td>alff order ideal</td>
<td><pre>  I  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#AlffIdealBasis">AlffIdealBasis</a>, <a href="kashref.html#AlffIdeal2EltAssure">AlffIdeal2EltAssure</a>

<p>

<h3>
Description:
</h3>
This function returns a list of two entries. The
first entry is a matrix in upper Hermite normal form
representing an ideal basis with respect to the order
basis. The second entry is the denominator of the ideal.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Some computations:
<pre>

kash> AlffInit(FF(5,2));
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> AlffOrders(y^3+T^4+1);
"Defining global variables: F, o, oi, one"
kash> I := T*o;
< [ T, 0, 0 ] >
kash> AlffIdealBasisUpperHNF(I);
[ [T 0 0]
    [0 T 0]
    [0 0 T], 1 ]
kash> a := AlffElt(o, [0, 1, 0]);
[ 0, 1, 0 ]
kash> I := a*o;
< [ 0, 1, 0 ] >
kash> AlffIdealBasisUpperHNF(I);
> [ [   T^4 + 1          0          0]
    [         0          1          0]
    [         0          0          1], 1 ]

</pre>

<p>


<hr>

<p>
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