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

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

<p><p>

<h3>
Syntax:
</h3>
<pre>M:=IdealLowerHNFTrans(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#IdealBasisLowerHNF">IdealBasisLowerHNF</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 lower HNF (which can bee seen with
IdealBasisLowerHNF). 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]*IdealLowerHNFTrans(I);
[   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]
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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