// Setting up the Polynomial ring and ideal

R<t, c_0012_0, c_0012_1, c_0102_1, c_0111_0, c_0201_1, c_1011_0, c_1011_1, c_1110_0, u> := PolynomialRing(RationalField(), 10);
MyIdeal := ideal<R |
          - c_0012_0 * c_1011_0 + c_0012_0 * c_1011_1 + c_0102_1 * c_0111_0,
          c_0012_1 * c_1110_0 - c_0102_1 * c_0111_0 + c_0102_1 * c_1011_0 * u^2,
          c_0012_1 * c_0111_0 - c_0012_1 * c_1110_0 + c_0201_1 * c_1011_1 * u,
          c_0012_0 * c_1011_0 - c_0201_1 * c_1011_1 + c_0201_1 * c_1110_0,
          - c_0012_1 * c_0111_0 * u + c_0012_1 * c_1011_0 - c_0102_1 * c_1011_1,
          c_0012_0 * c_1011_1 * u - c_0012_0 * c_1110_0 * u + c_0111_0 * c_0201_1 * u,
          c_0012_1 * c_1011_0 * u^2 - c_0111_0 * c_0201_1 * u + c_0201_1 * c_1110_0 * u,
          - c_0012_0 * c_1110_0 * u - c_0102_1 * c_1011_0 + c_0102_1 * c_1011_1,
          1 + u + u^2,
          - 1 + c_0012_0,
          - 1 + c_0111_0,
          - 1 + c_0012_0 * c_0012_1 * c_0102_1 * c_0111_0 * c_0201_1 * c_1011_0 * c_1011_1 * c_1110_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_1020_0' : d['c_0102_1'],
          'c_1020_1' : d['c_0201_1'],
          'c_0201_0' : d['c_0012_1'],
          'c_0201_1' : d['c_0201_1'],
          'c_2100_0' : d['c_0012_0'],
          'c_2100_1' : d['c_0102_1'],
          'c_2010_0' : d['c_0201_1'],
          'c_2010_1' : d['c_0102_1'],
          'c_0102_0' : d['c_0012_0'],
          'c_0102_1' : d['c_0102_1'],
          'c_1101_0' : d['c_1011_1'],
          'c_1101_1' : d['c_1011_0'],
          'c_1200_0' : d['c_0012_1'],
          'c_1200_1' : d['c_0201_1'],
          'c_1110_0' : d['c_1110_0'],
          'c_1110_1' : negation(d['c_1110_0']) * d['u'] ** 1,
          'c_0120_0' : d['c_0102_1'] * d['u'] ** 2,
          'c_0120_1' : d['c_0012_0'] * d['u'] ** 1,
          'c_2001_0' : d['c_0201_1'],
          'c_2001_1' : d['c_0012_0'],
          'c_0012_0' : d['c_0012_0'],
          'c_0012_1' : d['c_0012_1'],
          'c_0111_0' : d['c_0111_0'],
          'c_0111_1' : negation(d['c_0111_0']) * d['u'] ** 1,
          'c_0210_0' : d['c_0201_1'] * d['u'] ** 1,
          'c_0210_1' : d['c_0012_1'] * d['u'] ** 2,
          'c_1002_0' : d['c_0102_1'],
          'c_1002_1' : d['c_0012_1'],
          'c_1011_0' : d['c_1011_0'],
          'c_1011_1' : d['c_1011_1'],
          'c_0021_0' : d['c_0012_1'],
          'c_0021_1' : d['c_0012_0']}),
 'non_trivial_generalized_obstruction_class' : True}";
print "PY=EVAL=SECTION=ENDS=HERE";



// Value indicating failure
P := -1;

// Computing the primary decomposition
P,Q := PrimaryDecomposition(MyIdeal);

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";
end if;