in reply to Lunch Bunch arrangement problem

Try using the following gp script: 

multable( p, P, g ) =
{
P = Mod(1,p) *  P;
g = Mod( Mod(1,p) *  g, P );
d = poldegree( P );
n = p^d;

/*
    This version makes B[2] = Mod( 1, P ) which is wrong
    B = concat( [0], vector( n-1, i, g^(i-1) ) );

    The following line corrects the mistake
*/

B = concat( [0], vector( n-1, i, Mod( Mod(1,p), P ) * g^(i-1) ) );
R = vector( n );
for( i = 1, n,
    R[ 1 + subst( lift(lift( B[i] )), x, p )] = i-1;
);

for( a = 1, p^d,
     ae = B[a];
    for ( b = 1, p^d,
        be = B[b];
        re = ae * be;
        print1( R[ 1 + subst( lift(lift( re )), x, p )], "\t" );
    );
    print;
);

}

[download]
Save it in a file (say "ff.gp") and then invoke gp (it's an interactive environment for pari). A sample session might be 
$ gp -q
? read ("/tmp/ff.gp")
? multable(2, x^3+x+1, x)
0       0       0       0       0       0       0       0
0       1       2       3       4       5       6       7
0       2       3       4       5       6       7       1
0       3       4       5       6       7       1       2
0       4       5       6       7       1       2       3
0       5       6       7       1       2       3       4
0       6       7       1       2       3       4       5
0       7       1       2       3       4       5       6
?
The arguments to multable are the characteristic, the polynomial generating the field and a generator of the multiplicative group. To generate the addition table, substitute with re = ae + be on the due line.

Cheers

Antonio

The stupider the astronaut, the easier it is to win the trip to Vega - A. Tucket

Update: The mistake for g^0 + g^0 should be corrected now

Replies are listed 'Best First'.
Re: Re: Lunch Bunch arrangement problem
by tall_man (Parson) on May 17, 2003 at 19:03 UTC
    Thanks, Antonio. It looks very close to what I need, but I am getting some errors. For example, when I try for the addition table: 
    ? addtable(2, x^3+x+1, x)
0       1       2       3       4       5       6       7       

1       2       4       7       2       6       5       3       

2       4       0       5       1       3       7       6       

3       7       5       0       6       2       4       1       

4       2       1       6       0       7       3       5       

5       6       3       2       7       0       1       4       

6       5       7       4       3       1       0       2       

7       3       6       1       5       4       2       0

    [download]
    The second entry on the second line is supposed to be 0, not 2. I also tried for 3^2, like this: 
    ? multable(3,x^2+x+1,x)
0       0       0       0       0       0       0       0       0     
+  
0       7       8       6       7       8       6       7       8     
+  
0       8       6       7       8       6       7       8       6     
+  
0       6       7       8       6       7       8       6       7     
+  
0       7       8       6       7       8       6       7       8     
+  
0       8       6       7       8       6       7       8       6     
+  
0       6       7       8       6       7       8       6       7     
+  
0       7       8       6       7       8       6       7       8     
+  
0       8       6       7       8       6       7       8       6

    [download]
    This table doesn't look right at all. What could be going wrong?

    Update:For the 3^2 case, I see that I didn't use a correct primitive polynomial for GF(3). I tried "x^2+2*x+2" and it looks a lot better. Now I just need to find a way to get other primitive polynomials...

    Update2: I found a program than can compute a primitive polynomial of any order for GF(n), here.

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