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<p>&nbsp;<p>
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<h2><a name="AlffIdealFactor"></a>
AlffIdealFactor
</h2>

Return the factorization of an ideal.

<p><p>

<h3>
Syntax:
</h3>
<pre>L := AlffIdealFactor(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>in maximal order</td>
</tr>
</table>

<p>


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

<p>

<h3>
Description:
</h3>
This function computes the factorization of an ideal I
in its order which must be maximal. The return value
is a list of pairs consisting of prime ideals {frak P}_i
and exponents e_i such that I = \prod {frak P}_i^{e_i}.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Factor some ideals:
<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> AlffIdealFactor((T+w^3)*o);
[ [ < [ T + w^3, 0, 0 ], [ 0, 1, 0 ] >, 3 ] ]
kash> a := AlffElt(o, [0, 1, 0]);
[ 0, 1, 0 ]
kash> I := (T + w^3)*o + a*o;
< 
[ T + w^3        0        0]
[       0        1        0]
[       0        0        1]
/ 1
 >
kash> AlffIdealFactor(I);
> [ [ < [ T + w^3, 0, 0 ], [ 0, 1, 0 ] >, 1 ] ]

</pre>

<p>


<hr>

<p>
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