/* This file contains a list of examples for which the algortihm of
   "Numerical evidence for a conjectural generalization of Hilbert's Theorem 132"
   can be applied.
*/

 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [5, [5, 0]~, 1, 2, [1, 0]~], 1];
 module = [15, 0; 0, 15];
 subgrp = Mat(3);

K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/



 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [13, [-4, 1]~, 1, 1, [4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [13, [-4, 1]~, 1, 1, [4, 1]~], 1];
 module = [39, 27; 0, 3];
 subgrp = Mat(3);
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [13, [4, 1]~, 1, 1, [-4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [13, [4, 1]~, 1, 1, [-4, 1]~], 1];
 module = [39, 12; 0, 3];
 subgrp = Mat(3);
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [37, [-15, 1]~, 1, 1, [15, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [37, [-15, 1]~, 1, 1, [15, 1]~], 1];
 module = [111, 66; 0, 3];
 subgrp = Mat(3);
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~], [13, [-4, 1]~, 1, 1, [4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [5, [5, 0]~, 1, 2, [1, 0]~], 1; [13, [-4, 1]~, 1, 1, [4, 1]~], 1];
 module = [195, 135; 0, 15];
 subgrp = [3, 1; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~], [13, [4, 1]~, 1, 1, [-4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [5, [5, 0]~, 1, 2, [1, 0]~], 1; [13, [4, 1]~, 1, 1, [-4, 1]~], 1];
 module = [195, 60; 0, 15];
 subgrp = [3, 0; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [13, [-4, 1]~, 1, 1, [4, 1]~], [13, [4, 1]~, 1, 1, [-4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 2; [13, [-4, 1]~, 1, 1, [4, 1]~], 1; [13, [4, 1]~, 1, 1, [-4, 1]~], 1];
 module = [39, 0; 0, 39];
 subgrp = [3, 1; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~]];
 module = Mat([[3, [0, 1]~, 2, 1, [0, 1]~], 3]);
 module = [9, 0; 0, 3];
 subgrp = Mat(3);
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [5, [5, 0]~, 1, 2, [1, 0]~], 1];
 module = [45, 0; 0, 15];
 subgrp = [3, 1; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [5, [5, 0]~, 1, 2, [1, 0]~], 1];
 module = [45, 0; 0, 15];
 subgrp = [3, 2; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/


 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [7, [7, 0]~, 1, 2, [1, 0]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [7, [7, 0]~, 1, 2, [1, 0]~], 1];
 module = [63, 0; 0, 21];
 subgrp = [3, 1; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/

 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [7, [7, 0]~, 1, 2, [1, 0]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [7, [7, 0]~, 1, 2, [1, 0]~], 1];
 module = [63, 0; 0, 21];
 subgrp = [3, 2; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/

 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~], [13, [-4, 1]~, 1, 1, [4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [5, [5, 0]~, 1, 2, [1, 0]~], 1; [13, [-4, 1]~, 1, 1, [4, 1]~], 1];
 module = [585, 135; 0, 15];
 subgrp = [3, 0, 1; 0, 1, 0; 0, 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/

/*********************************************************************/
 f = y^2 - 3;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [5, [5, 0]~, 1, 2, [1, 0]~], [13, [-4, 1]~, 1, 1, [4, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [5, [5, 0]~, 1, 2, [1, 0]~], 1; [13, [-4, 1]~, 1, 1, [4, 1]~], 1];
 module = [585, 135; 0, 15];
 subgrp = [3, 0, 0; 0, 1, 0; 0, 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/

 f = y^2 - 6;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~], [19, [-5, 1]~, 1, 1, [5, 1]~], [19, [5, 1]~, 1, 1, [-5, 1]~]];
 module = [[3, [0, 1]~, 2, 1, [0, 1]~], 3; [19, [-5, 1]~, 1, 1, [5, 1]~], 1; [19, [5, 1]~, 1, 1, [-5, 1]~], 1];
 module = [171, 0; 0, 57];
 subgrp = [3, 0, 1; 0, 1, 0; 0, 0, 1];
 h = x^6 - 132*x^4 - 38*x^3 + 3357*x^2 + 1482*x - 15245;
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/

 f = y^2 - 6;
 l = 3;
 P = [[3, [0, 1]~, 2, 1, [0, 1]~]];
 module = Mat([[3, [0, 1]~, 2, 1, [0, 1]~], 4]);
 module = [9, 0; 0, 9];
 subgrp = [3, 1; 0, 1];
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/*******************************************************************/

 f = y^2 - 6;
 l = 5;
 P = [[5, [-1, 1]~, 1, 1, [1, 1]~], [5, [1, 1]~, 1, 1, [-1, 1]~]];
 module = [[5, [-1, 1]~, 1, 1, [1, 1]~], 2; [5, [1, 1]~, 1, 1, [-1, 1]~], 2];
 module = [25, 0; 0, 25];
 subgrp = Mat(5);
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );

result = Hilbert( K, l, P, module, rcgp, subgrp )[2];

/* STACK OVERFLOW ????????????????????????? */
 
/*******************************************************************/

 f = y^2 - 5;
 l = 5;
 P = [[5, [-1, 2]~, 2, 1, [-1, 2]~], [11, [-5, 2]~, 1, 1, [3, 2]~]];
 module = [[5, [-1, 2]~, 2, 1, [-1, 2]~], 2; [11, [-5, 2]~, 1, 1, [3, 2]~], 1];
 module = [55, 15; 0, 5];
 subgrp = Mat(5);
K = bnfinit( f );
rcgp = bnrinit( K, module, 1 );