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

Tests if a column vector is element of the given module.

<p><p>

<h3>
Syntax:
</h3>
<pre>L:=ModuleMember(M,V|EL);</pre>

<p>

<table>
<tr>
<td>list</td>
<td><pre>  L  </pre></td>
<td>see below</td>
</tr>
<tr>
<td>module </td>
<td><pre>  M  </pre></td>
<td></td>
</tr>
<tr>
<td>vector </td>
<td><pre>  V  </pre></td>
<td></td>
</tr>
<tr>
<td>list</td>
<td><pre>  EL  </pre></td>
<td>of n algebraic elements of O</td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
The column vector v is a member of the module iff it is a linear
combination of the columns of the matrix of M with coefficients in the
corresponding coefficient ideals.

This function returns a list of a boolean value (if the element is
indeed a member of the module) and a representation column
vector x where M x = v. x is returned even if its
entries are not members of the corresponding ideals of the
module.

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>

<pre>

kash> O:=OrderMaximal(Poly(Zx,[1,-10,-3,-2]));;
kash> M:=Module([2*O,2*O,1*O],Mat(O,[[1,0,1],[0,1,1],[0,0,1]]));
{<2><2><1>
[1 0 1]
[0 1 1]
[0 0 1]
}

kash> V:=MatTrans(O,[[1,3,1]]);
[1]
[3]
[1]
kash> L:=ModuleMember(M,V);
[ true, [0]
    [2]
    [1] ]
kash> ModuleMatrix(M)*L[2];
> [1]
[3]
[1]

</pre>

<p>


<hr>

<p>
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