[back] [prev] [next] [index] [root]

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

Returns whether a function field is an absolute extension.

<p><p>

<h3>
Syntax:
</h3>
<pre>b := AlffIsAbs(F);</pre>

<p>

<table>
<tr>
<td>boolean</td>
<td><pre>  b  </pre></td>
<td></td>
</tr>
<tr>
<td>function field</td>
<td><pre>  F  </pre></td>
<td></td>
</tr>
</table>

<p>


<h3>
Description:
</h3>
<i>no detailed description available yet</i>

<p><p>

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

<pre>

kash> k := FF(3);
Finite field of size 3
kash> AlffInit(k);
"Defining global variables: k, w, kT, kTf, kTy, T, y, AlffGlobals"
kash> f := y^3-y^2*(T+1)+2*y*T-T^5;
y^3 + (2*T + 2)*y^2 + 2*T*y + 2*T^5
kash> F:=Alff(f);
Algebraic function field defined by
.1^3 + 2*.1^2*.2 + 2*.1^2 + 2*.1*.2 + 2*.2^5
over
Univariate rational function field over GF(3)
Variables: T

kash> AlffIsAbs(F);
true
kash> AlffOrders(f);
"Defining global variables: F, o, oi, one"
kash> a1:=AlffElt(o,[1,3,T]);
[ 1, 0, T ]
kash> a2:=AlffElt(o,[T,T^2,0]);
[ T, T^2, 0 ]
kash> a3:=AlffElt(o,[1,3,0]);
[ 1, 0, 0 ]
kash> L:=[a3,a2,a1];
[ [ 1, 0, 0 ], [ T, T^2, 0 ], [ 1, 0, T ] ]
kash> A:=PolyAlg(o);
Univariate Polynomial Ring in x over Finite maximal order of 
Algebraic function field defined by
.1^3 + 2*.1^2*.2 + 2*.1^2 + 2*.1*.2 + 2*.2^5
over
Univariate rational function field over GF(3)
Variables: T
given by transformation matrix
[T 0 0]
[0 T 2]
[0 0 1]
with denominator T

kash> g:=Poly(A,L);
x^2 + [ T, T^2, 0 ]*x + [ 1, 0, T ]
kash> G:=Alff(g);
Algebraic function field defined by
.1^2 + .1*.2*.3^2 + .1*.3 + .2^2 + 2*.2 + 1
over
Algebraic function field defined by
.1^3 + 2*.1^2*.2 + 2*.1^2 + 2*.1*.2 + 2*.2^5
over
Univariate rational function field over GF(3)
Variables: T

kash> AlffIsAbs(G);
> false

</pre>

<p>


<hr>

<p>
<a href="../kashref.html"><- back</a>[back] [prev] [next] [index] [root]