// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0101_0> := PolynomialRing(RationalField(), 3);
MyIdeal := ideal<R |
          c_0011_0 * c_0101_0 + c_0011_0^2 - c_0101_0^2,
          c_0011_0 * c_0101_0 + c_0011_0^2 - c_0101_0^2,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0101_0 * t>;



print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nm003\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 2103 0321 1023\n   0    0    0    0 \n  0 -1  0  1  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  1  0  1  0  0 -1  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  0.500000000000   0.866025403784\n\n   0    0    0    0 \n 0132 2103 0321 1023\n   0    0    0    0 \n  0  0  0  0  0  0  1 -1 -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  0 -1  1 -1  0  1  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  0.500000000000   0.866025403784\n\n";
print "==TRIANGULATION" cat "=ENDS==";
print "PY=EVAL=SECTION" cat "=BEGINS=HERE";
print "{'variable_dict' : 
     (lambda d, negation = (lambda x:-x): {
          's_3_1' : d['1'],
          's_3_0' : d['1'],
          'c_0101_1' : negation(d['c_0101_0']),
          'c_1010_1' : negation(d['c_0101_0']),
          's_2_0' : d['1'],
          's_2_1' : d['1'],
          'c_1010_0' : d['c_0101_0'],
          'c_1100_1' : negation(d['c_0011_0']),
          'c_1100_0' : d['c_0011_0'],
          'c_1001_0' : negation(d['c_0011_0']),
          'c_1001_1' : d['c_0011_0'],
          'c_0101_0' : d['c_0101_0'],
          's_1_1' : d['1'],
          's_1_0' : d['1'],
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : negation(d['c_0101_0']),
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          's_0_0' : d['1'],
          's_0_1' : d['1']})}";
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;