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

Returns the basis of an ideal.

<p><p>

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

<p>

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

<p>


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

<p>

<h3>
Description:
</h3>
Ideals are given either in Z-basis representation or 2
element representation. If the ideal is given in basis
representation this representation is simply returned. Otherwise it
will be computed. In this case the ideal has got 2 equivalent
representations stored afterwards. This can be of advantage because
some algorithms prefer 2 element representations, others prefer
Z-basis representations.
Once a basis is fixed (entered or calculated)
it will never change even if simplification is possible.

<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> IdealBasis(I);
> [ 1, [6 0 0]
    [0 1 0]
    [0 0 1] ]

</pre>

<p>


<hr>

<p>
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