use application 'ideal';

use vars '$simpl', '$lambda_simpl', '$F_simpl', '$T_simpl', '$F_sqr', '$sqr', '$lambda_sqr', '$T_sqr', '$hex', '$lambda_hex', '$F_hex', '$T_hex', '$lambda_hex_new', '$lambda_hex_new_2', '$n';

script("./random_solve.script");

$n = 500000;

##### Simplex #####
$simpl = new Matrix<Int>([
[1, 0, 0],
[1, 1, 0],
[1, 2, 0],
[1, 3, 0],
[1, 0, 1],
[1, 1, 1],
[1, 2, 1],
[1, 0, 2],
[1, 1, 2],
[1, 0, 3]
]);

$lambda_simpl = new Vector<Int>([12, 8, 9, 15, 3, 1, 5, 0, 0, 0]);
$F_simpl = polytope::regular_subdivision($simpl, $lambda_simpl);
$T_simpl = new topaz::GeometricSimplicialComplex(COORDINATES=>$simpl->minor(All,~[0]), FACETS=>$F_simpl);

solve_random_wronski($simpl,$lambda_simpl,$n,{file=>'simplex.csv', triangulation=>$T_simpl});



##### Square #####
$sqr = new Matrix<Int>([
[1, 0, 0],
[1, 1, 0],
[1, 2, 0],
[1, 0, 1],
[1, 1, 1],
[1, 2, 1],
[1, 0, 2],
[1, 1, 2],
[1, 2, 2]
]);

$lambda_sqr = new Vector<Int>([5, 4, 9, 4, 0, 3, 9, 3, 3]);
$F_sqr = polytope::regular_subdivision($sqr, $lambda_sqr);
$T_sqr = new topaz::GeometricSimplicialComplex(COORDINATES=>$sqr->minor(All,~[0]), FACETS=>$F_sqr);

solve_random_wronski($sqr,$lambda_sqr,$n,{file=>'square.csv', triangulation=>$T_sqr});

##### Hexagon #####
$hex = new Matrix<Int>([[1,0,0],[1,1,0],[1,2,1],[1,2,2],[1,1,2],[1,0,1],[1,1,1]]);

$lambda_hex = new Vector<Int>([3,1,1,3,1,1,0]);
$lambda_hex_new = new Vector<Int>([10,1,1,10,1,1,0]);
$lambda_hex_new_2 = new Vector<Int>([1000,10,0,0,0,100,1]);
$F_hex = polytope::regular_subdivision($hex, $lambda_hex);
$T_hex = new topaz::GeometricSimplicialComplex(COORDINATES=>$hex->minor(All,~[0]), FACETS=>$F_hex);

solve_random_wronski($hex,$lambda_hex,$n,{file=>'hex.csv', triangulation=>$T_hex});

solve_random_wronski($hex,$lambda_hex_new,$n,{file=>'hex_otherlifting.csv', triangulation=>$T_hex});

solve_random_wronski($hex,$lambda_hex_new_2,$n,{file=>'hex_otherlifting_2.csv', triangulation=>$T_hex});