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

Creates a finite field.

<p><p>

<h3>
Syntax:
</h3>
<pre>F := FF(p);
F := FF(p, d);
F := FF(f);</pre>

<p>

<table>
<tr>
<td>finite field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  p  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  d  </pre></td>
<td></td>
</tr>
<tr>
<td>polynomial</td>
<td><pre>  f  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#FFElt">FFElt</a>, <a href="kashref.html#FFGenerator">FFGenerator</a>, <a href="kashref.html#FFPrimitiveElt">FFPrimitiveElt</a>

<p>

<h3>
Description:
</h3>
A finite field can be created in three different ways:
<ul>
<li> <tt> FF(p)</tt> returns the finite field FF_p where
p is a prime.
<li> <tt> FF(p, d)</tt> returns the finite field FF_{p^d}
where p is a prime and d a positive integer.
<li> <tt> FF(f)</tt> returns an extension field of a
finite field: f is a monic, irreducible polynomial
over a finite field FF_q (q a prime power) of degree
l>1; FF_{q^l} is returned.
</ul>

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
Creation of finite fields: 
<pre>

kash> F2 := FF(2);
Finite field of size 2
kash> F2x := PolyAlg(F2);
Univariate Polynomial Ring in x over GF(2)

kash> f := Poly(F2x, [1, 1, 1]);
x^2 + x + 1
kash> F4 := FF(f);
Finite field of size 2^2
kash> F9 := FF(3, 3);
> Finite field of size 3^3

</pre>

<p>


<hr>

<p>
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