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

Installs an embedding from the first given order into the second
given order.

<p><p>

<h3>
Syntax:
</h3>
<pre>OrderInstallHom(o1,o2,alpha);
OrderInstallHom(o1,o2,b);</pre>

<p>

<table>
<tr>
<td>order</td>
<td><pre>  o1  </pre></td>
<td></td>
</tr>
<tr>
<td>order</td>
<td><pre>  o2  </pre></td>
<td></td>
</tr>
<tr>
<td>algebraic element</td>
<td><pre>  alpha  </pre></td>
<td></td>
</tr>
<tr>
<td>boolean</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
Installs the embedding given via the image of the primitive
element of o|1 in o|2 which is defined to be \alpha in case
o|1 is an equation order. If the third
argument is a boolean instead of an algebraic element,
the corresponding number fields are assumed to be isomorphic,
iff the boolean is `true` and this will be used in the sequel.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Moving of an element from an absolute extension into a relative one. 
<pre>

kash> o1 := Order (Z,2,3);;
kash> o2 := Order (o1,2,2);
      F[1]
        /
       /
   E1[1]
  /
 /
Q
F  [ 1]     x^2 - 2
E 1[ 1]     x^2 - 3

kash> gen1 := OrderBasis (OrderEquationOrder (o1))[2];
[0, 1]
kash> gen2 := OrderBasis (OrderEquationOrder (o2))[2];
[0, 1]
kash> gen := EltMove (gen1, o2) + gen2;
[[0, 1], 1]
kash> o3 := Order (MatMinPoly (EltRepMat(gen, Z)[2]));
Generating polynomial: x^4 - 10*x^2 + 1

kash> OrderInstallHom (o3, o2, gen);
kash> EltMove (Elt (o3, [1,2,3,4]), o2);
[[16, 38], [46, 6]]
kash> EltMove (Elt (o3, [1,2,3,4]/2), o2);
> [[8, 19], [23, 3]]

</pre>

<p>


<hr>

<p>
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