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

the transformation matrix from the original basis to the
basis in upper HNF

<p><p>

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

<p>

<table>
<tr>
<td>matrix</td>
<td><pre>  M  </pre></td>
<td></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>

<p>

<h3>
Description:
</h3>
This returns the transformation matrix when transforming the
original basis (which can bee seen with IdealBasis) to the
basis in upper HNF (which can bee seen with
IdealBasisUpperHNF). Once computed the transformation
matrix 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> IdealBasis(I)[2]*IdealUpperHNFTrans(I);
[839 755 349 421 449]
[  0   3   0   1   0]
[  0   0   1   0   0]
[  0   0   0   1   0]
[  0   0   0   0   2]
kash> IdealBasisUpperHNF(I);
> [ 1, [839 755 349 421 449]
    [  0   3   0   1   0]
    [  0   0   1   0   0]
    [  0   0   0   1   0]
    [  0   0   0   0   2] ]

</pre>

<p>


<hr>

<p>
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