\r stu.gp
\r listen.gp

/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(5))
    of degree l=5 and coductor module = 11*P_41, where P_41 is 
    a prime of K above 41.
*****************************************************************************/
\p 50

print("Verification of ETNC for all extensions of K = Q(sqrt(5))");
print("of degree l=5 and coductor module = 11*P_41, where P_41 is");
print("a prime of K above 41.");
print("\n\n");

p = [11,  41];
l = 5; d = 5;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

P = vector( length( p ), i, idealprimedec( K, p[i])[1] );
P = concat(P, [idealprimedec( K, p[1])[2]]);
module = 1;
for( i = 1, length(P), module = idealmul( K, module, P[i] ) );

rcgp = bnrinit( K, module, 1 );
sgl = findsubgroup( rcgp, l );

result = vector(length(sgl), i, etnc( K, l, E, rcgp, sgl[i]));


/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(3))
    of degree l=3 and r=2 ramified primes, each of norm at most 50
*****************************************************************************/
print("Verification of ETNC for all extensions of K = Q(sqrt(3))");
print("of degree l=3 and r=2 ramified primes, each of norm at most 50");
print("\n\n");

d = 3; l = 3;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

PListe = PrimeList(d, 50, l);

r = 2;
EnumSubSets(PListe, K, E, l, r);


/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(3))
    of degree l=3 and r=3 ramified primes, each of norm at most 30
*****************************************************************************/
print("Verification of ETNC for all extensions of K = Q(sqrt(3))");
print("of degree l=3 and r=3 ramified primes, each of norm at most 30");
print("\n\n");

d = 3; l = 3;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

PListe = PrimeList(d, 30, l);

r = 3;
EnumSubSets(PListe, K, E, l, r);

/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(5))
    of degree l=3 and r=2 ramified primes, each of norm at most 30
*****************************************************************************/
print("Verification of ETNC for all extensions of K = Q(sqrt(5))");
print("of degree l=3 and r=2 ramified primes, each of norm at most 30");
print("\n\n");

d = 5; l = 3;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

PListe = PrimeList(d, 30, l);

r = 2;
EnumSubSets(PListe, K, E, l, r);



/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(5))
    of degree l=5 and r=1 ramified primes, each of norm at most 500
*****************************************************************************/
print("Verification of ETNC for all extensions of K = Q(sqrt(5))");
print("of degree l=5 and r=1 ramified primes, each of norm at most 500");
print("\n\n");

d = 5; l = 5;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

PListe = PrimeList(d, 500, l);

r = 1;
EnumSubSets(PListe, K, E, l, r);


/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(5))
    of degree l=5 and r=2 ramified primes, each of norm at most 50
*****************************************************************************/
print("Verification of ETNC for all extensions of K = Q(sqrt(5))");
print("of degree l=5 and r=2 ramified primes, each of norm at most 50");
print("\n\n");

d = 5; l = 5;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

PListe = PrimeList(d, 50, l);

r = 2;
EnumSubSets(PListe, K, E, l, r);

/****************************************************************************
    Verification of ETNC for all extensions of K = Q(sqrt(5))
    of degree l=2 and r=1 ramified primes, each of norm at most 3000
*****************************************************************************/
print("Verification of ETNC for all extensions of K = Q(sqrt(5))");
print("of degree l=2 and r=1 ramified primes, each of norm at most 3000");
print("\n\n");

\p  100
d = 2; l = 7;
poly = y^2 - d;
K = bnfinit( poly );
zykpol = ( x^l - 1 )/( x - 1 );
E = bnfinit( zykpol );

PListe = PrimeList(d, 2000, l);

r = 1;
v = EnumSubSets(PListe, K, E, l, r);