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

Reads an order in the FLD format.

<p><p>

<h3>
Syntax:
</h3>
<pre>o := FLDin(name [, n]);
o := FLDin();
o := FLDin(f [, n]);</pre>

<p>

<table>
<tr>
<td>file</td>
<td><pre>  f  </pre></td>
<td>open for reading</td>
</tr>
<tr>
<td>string</td>
<td><pre>  name  </pre></td>
<td>filename</td>
</tr>
<tr>
<td>order</td>
<td><pre>  o  </pre></td>
<td></td>
</tr>
<tr>
<td>integer</td>
<td><pre>  b  </pre></td>
<td>the number of fields to skip. If given, the number</td>
</tr>
<tr>
<td></td>
<td><pre>  of fields is returned.  </pre></td>
<td></td>
</tr>
</table>

<p>


See also:&nbsp;&nbsp;<a href="kashref.html#FLDout">FLDout</a>, <a href="kashref.html#Open">Open</a>

<p>

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

<p><p>

<p>
<hr>
<p>
<h3>
Example:
</h3>
We give an example on how to compute tables using KASH:
First, we will compute a series of orders using a small
program written to check fields generated by polynomials of
the form f = x^3 + p * x^2 + p *x + p for non-trivial
class groups. Of course this is only an example. In
practice you should define a function taking two arguments
(<tt> p</tt> and the bound <tt> c</tt> for p) and the file to write
to. Initialization: 
<pre>

kash> # Open a file for printing the output
kash> outfile := Open("poly.tbl","w");
Filename: poly.tbl / Mode: w / Open (fid): 5
kash> #
kash> p := 3; # start
3
kash> c := 3; # how many fields
3


</pre>

<p>

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

Now do a loop over the first <tt> c</tt> primes:

<pre>

kash> for j in [1..c] do
> p:=NextPrime(p);
> #
> # Assign f and create the corresponding maximal order
> #
> f := Poly(Zx,[1,p,p,p]);
> O := OrderMaximal(Order(f));
> #
> # Compute the class group of o
> #
> clg := OrderClassGroup(O);
> #
> # check if the class group is trivial
> #
> if IsList(clg) then
> Print ("field generated by ", f," has class number: ", clg[1],"\n");
> # print the field in the output file
> FLDout(O, outfile);
> fi;
> od;
field generated by x^3 + 5*x^2 + 5*x + 5 has class number: 1
field generated by x^3 + 7*x^2 + 7*x + 7 has class number: 3
field generated by x^3 + 11*x^2 + 11*x + 11 has class number: 6
kash> # closing the output file
kash> Close(outfile);
true


</pre>

<p>

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

The file should look this:

{\tt(FLD=) 3, 2, 0, 0, 2, 0, 0, 1, 0, 0, 1, -200, *
5 5 5
8 0 0 8
0 8 0 8
4 0 4 8
(FLD=) 3, 1, 1, 0, 2, 0, 0, 3, 0, 0, 1, -3724, *
7 7 7
1 1 1
3 1 3
1
1 2 1 1 0
1
(FLD=) 3, 1, 1, 0, 2, 0, 0, 6, 0, 0, 1, -28556, *
11 11 11
1 1 1
6 1 6
2
1 5 8 1 0
1 2 1 1 0
1 1}\smallskip

Use the output as input to compute fundamental units:
<pre>

kash> #
kash> # Open file for input. Use mode "R" (not "r") to loop
kash> # over the whole file
kash> #
kash> infile := Open("poly.tbl", "R");
Filename: poly.tbl / Mode: R / Open (fid): 5
kash> #
kash> # Read first order
kash> o1 := FLDin(infile);
   F[1]
    |
   F[2]
  /
 /
Q
F  [ 1]     Given by transformation matrix
F  [ 2]     x^3 + 5*x^2 + 5*x + 5
Discriminant: -200 
Class Number 1

kash> OrderUnitsFund(o1);
[ [0, 1, 2] ]
kash> #
kash> # Read second order
kash> o2 := FLDin(infile);
Generating polynomial: x^3 + 7*x^2 + 7*x + 7
Discriminant: -3724 
Class Number 3
Class Group Structure C3
Cyclic Factors of the Class Group:
<2, 2>

kash> OrderUnitsFund(o2);
[ [1, 1, 1] ]
kash> #
kash> # Read third order
kash> o3 := FLDin(infile);
Generating polynomial: x^3 + 11*x^2 + 11*x + 11
Discriminant: -28556 
Class Number 6
Class Group Structure C6
Cyclic Factors of the Class Group:
<10, 10>

kash> OrderUnitsFund(o3);
[ [1, 1, 1] ]
kash> Close(infile);
true

</pre>

<p>


<hr>

<p>
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