// Setting up the Polynomial ring and ideal

R<t, c_0013_0, c_0013_1, c_0022_0, c_0103_1, c_0112_0, c_0112_1, c_0202_1, c_0211_0, c_0301_1, c_1012_0, c_1012_1, c_1021_0, c_1021_1, c_1102_0, c_1111_0, c_1111_1, c_1120_0, c_1120_1, c_1201_1, c_1210_0, u> := PolynomialRing(RationalField(), 22);
MyIdeal := ideal<R |
          - c_0013_0 * c_1012_0 + c_0013_0 * c_1102_0 + c_0103_1 * c_0112_0,
          c_0022_0 * c_1111_0 - c_0112_0 * c_1021_0 + c_0112_1 * c_1012_0 * (-u),
          - c_0013_1 * c_1120_0 - c_0103_1 * c_0112_1 * (-u) + c_0103_1 * c_1021_0 * (-u),
          - c_0022_0 * c_1111_0 - c_0112_0 * c_1012_1 + c_0211_0 * c_1102_0,
          c_0112_1 * c_1210_0 * (-u) + c_0202_1 * c_1111_0 * (-1) - c_0211_0 * c_1120_0,
          c_0013_1 * c_0211_0 + c_0013_1 * c_1210_0 - c_0301_1 * c_1012_1 * u,
          c_0202_1 * c_1111_0 - c_1012_0 * c_1021_1 + c_1102_0 * c_1201_1,
          - c_0202_1 * c_1111_0 - c_1021_0 * c_1120_1 * (-u) - c_1120_0 * c_1201_1,
          c_0022_0 * c_1111_0 - c_1012_1 * c_1120_1 * (-u) - c_1021_1 * c_1210_0,
          c_0013_0 * c_1201_1 + c_0301_1 * c_1021_1 - c_0301_1 * c_1120_1 * (-u),
          c_0013_1 * c_0112_1 - c_0013_1 * c_1021_0 - c_0103_1 * c_1012_1,
          c_0022_0 * c_1111_1 + c_0112_0 * c_1012_1 * u - c_0112_1 * c_1021_1,
          c_0013_0 * c_1021_1 * u - c_0013_0 * c_1120_1 + c_0112_0 * c_0301_1 * u,
          c_0112_1 * c_1201_1 - c_0202_1 * c_1111_1 + c_0211_0 * c_1021_0 * (-1),
          c_0022_0 * c_1111_1 * (-1) - c_0112_0 * c_1210_0 * (-u) + c_0211_0 * c_1120_1 * (-1),
          - c_0013_1 * c_1201_1 * (-u) + c_0211_0 * c_0301_1 * (-1) + c_0301_1 * c_1210_0 * (-1),
          c_0022_0 * c_1111_1 + c_1012_0 * c_1012_1 + c_1021_0 * c_1102_0,
          - c_0202_1 * c_1111_1 - c_1021_1 * c_1120_0 * u + c_1102_0 * c_1120_1,
          c_0202_1 * c_1111_1 - c_1012_0 * c_1210_0 * (-1) + c_1120_0 * c_1201_1 * u,
          c_0013_0 * c_1120_0 * u + c_0103_1 * c_1012_0 - c_0103_1 * c_1102_0,
          1 + u^2,
          - 1 + c_0013_0,
          - 1 + c_0022_0,
          - 1 + c_0112_0,
          - 1 + c_1210_0 * t>;



print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nm004\ngeometric_solution  2.02988321\noriented_manifold\nCS_known 0.0000000000000000\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n2\n   1    1    1    1 \n 0132 1230 2310 2103\n   0    0    0    0 \n  0  0  0  0  0  0  0  0 -1  1  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0 -1  0  1  1  0 -1  0  0  1  0 -1 -1  0  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.500000000000   0.866025403784\n\n   0    0    0    0 \n 0132 3201 3012 2103\n   0    0    0    0 \n  0  0  0  0  0  0  0  0  0  0  0  0  1  0 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0 -1  0  1 -1  0  1  0  1  0  0 -1  0  1 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.500000000000   0.866025403784\n\n";
print "==TRIANGULATION" cat "=ENDS==";
print "PY=EVAL=SECTION" cat "=BEGINS=HERE";
print "{'variable_dict' : 
     (lambda d, negation = (lambda x:-x): {
          'c_0022_1' : d['c_0022_0'],
          'c_3100_0' : negation(d['c_0013_0']),
          'c_0301_1' : d['c_0301_1'],
          'c_0301_0' : negation(d['c_0013_1']),
          'c_0031_0' : negation(d['c_0013_1']),
          'c_3001_0' : d['c_0301_1'],
          'c_2101_1' : d['c_1012_0'],
          'c_3100_1' : negation(d['c_0103_1']),
          'c_2011_1' : d['c_1102_0'],
          'c_0022_0' : d['c_0022_0'],
          'c_0103_1' : d['c_0103_1'],
          'c_0103_0' : d['c_0013_0'],
          'c_1120_0' : d['c_1120_0'],
          'c_0202_1' : d['c_0202_1'],
          'c_0202_0' : d['c_0022_0'],
          'c_1120_1' : d['c_1120_1'],
          'c_1021_0' : d['c_1021_0'],
          'c_1201_1' : d['c_1201_1'],
          'c_1201_0' : negation(d['c_1012_1']),
          'c_0220_0' : d['c_0202_1'] * d['u'] ** 2,
          'c_0220_1' : d['c_0022_0'] * d['u'] ** 2,
          'c_1102_0' : d['c_1102_0'],
          'c_3010_1' : negation(d['c_0103_1']),
          'c_3010_0' : d['c_0301_1'],
          'c_3001_1' : negation(d['c_0013_0']),
          'c_2110_0' : negation(d['c_1120_1']) * d['u'] ** 3,
          'c_0121_1' : d['c_0112_0'] * d['u'] ** 1,
          'c_0121_0' : d['c_0112_1'] * d['u'] ** 3,
          'c_0031_1' : negation(d['c_0013_0']),
          'c_2200_0' : d['c_0022_0'],
          'c_1012_1' : d['c_1012_1'],
          'c_1012_0' : d['c_1012_0'],
          'c_0013_1' : d['c_0013_1'],
          'c_0013_0' : d['c_0013_0'],
          'c_2200_1' : d['c_0202_1'],
          'c_2101_0' : negation(d['c_1021_1']),
          'c_2002_1' : d['c_0022_0'],
          'c_2002_0' : d['c_0202_1'],
          'c_2011_0' : negation(d['c_1201_1']),
          'c_1102_1' : negation(d['c_1021_0']),
          'c_0211_1' : negation(d['c_0211_0']) * d['u'] ** 2,
          'c_0211_0' : d['c_0211_0'],
          'c_1003_1' : d['c_0013_1'],
          'c_1003_0' : d['c_0103_1'],
          'c_1210_1' : negation(d['c_1210_0']) * d['u'] ** 2,
          'c_1210_0' : d['c_1210_0'],
          'c_1300_1' : negation(d['c_0301_1']),
          'c_1300_0' : d['c_0013_1'],
          'c_1030_1' : negation(d['c_0301_1']),
          'c_1030_0' : d['c_0103_1'],
          'c_1021_1' : d['c_1021_1'],
          'c_0130_1' : d['c_0013_0'] * d['u'] ** 1,
          'c_0130_0' : d['c_0103_1'] * d['u'] ** 3,
          'c_2110_1' : negation(d['c_1120_0']) * d['u'] ** 1,
          'c_0112_1' : d['c_0112_1'],
          'c_0112_0' : d['c_0112_0'],
          'c_0310_1' : negation(d['c_0013_1']) * d['u'] ** 3,
          'c_0310_0' : d['c_0301_1'] * d['u'] ** 1,
          'c_2020_1' : d['c_0202_1'],
          'c_2020_0' : d['c_0202_1']}),
 'non_trivial_generalized_obstruction_class' : True}";
print "PY=EVAL=SECTION=ENDS=HERE";



// Value indicating failure
P := -1;

// Computing the primary decomposition
primTime := Cputime();
P, Q := PrimaryDecomposition(MyIdeal);
print "PRIMARY_DECOMPOSITION_TIME: ", Cputime(primTime);

if Type(P) eq RngIntElt then
    // Some error occured
    print "PRIMARY=DECOMPOSITION" cat "=FAILED";
    exit;
else
    // Success
    print "PRIMARY=DECOMPOSITION" cat "=BEGINS=HERE";
    P;
    print "PRIMARY=DECOMPOSITION" cat "=ENDS=HERE";


    print "FREE=VARIABLES=IN=COMPONENTS" cat "=BEGINS=HERE";
    N := Names(R);
    isFirstComp := true;
    freeVarStr := "[";
    for Comp in P do
    
        if isFirstComp then
            isFirstComp := false;
        else
            freeVarStr := freeVarStr cat ",";
        end if;
        freeVarStr := freeVarStr cat "
    [ ";
        
        D, Vars := Dimension(Comp);

        isFirstVar := true; 
        for Var in Vars do
            if isFirstVar then
                isFirstVar := false;
            else
                freeVarStr := freeVarStr cat ", ";
            end if;
 
            freeVarStr := freeVarStr cat "\"" cat N[Var] cat "\"";
        end for;

        freeVarStr := freeVarStr cat " ]";
    end for;
    freeVarStr := freeVarStr cat "
]";
    print freeVarStr;
    print "FREE=VARIABLES=IN=COMPONENTS" cat "=ENDS=HERE";
end if;

print "CPUTIME: ", Cputime(primTime);