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<h2><a name="GaloisMSumPol"></a>
GaloisMSumPol
</h2>

Computing of a polynomial of degree {n choose k} which
roots are sums of k distinct roots of f.

<p><p>

<h3>
Syntax:
</h3>
<pre>g:= GaloisMSumPol(f, k);</pre>

<p>

<table>
<tr>
<td>int</td>
<td><pre>  k  </pre></td>
<td>must be positive</td>
</tr>
<tr>
<td>polynomial</td>
<td><pre>  f,g  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#GaloisGlobals">GaloisGlobals</a>, <a href="kashref.html#GaloisGroupsPossible">GaloisGroupsPossible</a>, <a href="kashref.html#GaloisModulo">GaloisModulo</a>, <a href="kashref.html#GaloisTree">GaloisTree</a>, <a href="kashref.html#GaloisRoots">GaloisRoots</a>, <a href="kashref.html#GaloisNumberToName">GaloisNumberToName</a>, <a href="kashref.html#GaloisBlocks">GaloisBlocks</a>

<p>

<h3>
Description:
</h3>
Let f be a monic polynomial of degree n in Q,Q(x) or a
simple
relative order.This function computes a primitive polynomial
of degree {n choose k}. The roots of <tt> GaloisMSumPol</tt> are the
sums of k distinct roots of f.

<p><p>

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

<pre>

kash> o := OrderMaximal(Z, 2, 2);
Generating polynomial: x^2 - 2
Discriminant: 8 

kash> ox := PolyAlg(o);
Univariate Polynomial Ring in x over Generating polynomial: x^2 - 2
Discriminant: 8 

kash> f := Poly(ox, [Elt(o,1), Elt(o,[74,-16] / 73), Elt(o,[5988,-2368]
> / 5329), Elt(o, [160667739, -69612720] / 133432831), Elt(o,
> [98807254537, -54032137568] / 68184176641)]);
x^4 + [74, -16] / 73*x^3 + [5988, -2368] / 5329*x^2 + [160667739, -69612720] /\
 133432831*x + [98807254537, -54032137568] / 68184176641
kash> g := GaloisMSumPol(f,2);
> x^6 + (222/73*.1 - 48/73*.2)*x^5 + (29940/5329*.1 - 11840/5329*.2)*x^4 + (\
2594440/389017*.1 - 1355200/389017*.2)*x^3 + (42642475310/68184176641*.1 - \
42196712560/68184176641*.2)*x^2 + (-16578528081908/4977444894793*.1 + 988909\
5753408/4977444894793*.2)*x - 35497382888701141/17804320388674561*.1 + 22361\
191523984800/17804320388674561*.2

</pre>

<p>


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