// Setting up the Polynomial ring and ideal

R<t, c_0012_0, c_0012_1, c_0012_3, c_0021_3, c_0102_0, c_0102_2, c_0111_0, c_0111_2, c_0111_3, c_0201_0, c_0201_2, c_1011_0, c_1011_1, c_1101_0, c_1101_1, c_1101_3> := PolynomialRing(RationalField(), 17);
MyIdeal := ideal<R |
          c_0012_0 * c_1101_0 + c_0012_3 * c_0111_0 - c_0102_0 * c_1011_0,
          c_0012_1 * c_0111_2 + c_0012_1 * c_1011_0 - c_0102_2 * c_0111_0,
          c_0012_0 * c_1101_0 + c_0102_2 * c_0111_0 - c_0111_2 * c_0201_0,
          c_0021_3 * c_0111_2 + c_0201_2 * c_1011_0 - c_0201_2 * c_1101_0,
          - c_0012_1 * c_1011_1 + c_0012_1 * c_1101_1 - c_0111_0 * c_0201_2,
          c_0012_0 * c_1101_3 + c_0102_0 * c_1011_1 + c_0111_0 * c_0201_2,
          - c_0012_0 * c_1101_3 - c_0021_3 * c_0111_0 + c_0201_0 * c_1101_1,
          c_0012_3 * c_1011_1 - c_0102_2 * c_1101_1 + c_0102_2 * c_1101_3,
          c_0012_1 * c_1011_1 + c_0102_2 * c_0111_2 + c_0102_2 * c_1011_0,
          c_0012_0 * c_1101_1 - c_0012_3 * c_0111_2 - c_0102_2 * c_1011_0,
          c_0012_1 * c_0111_2 + c_0201_2 * c_1011_1 - c_0201_2 * c_1101_1,
          - c_0012_0 * c_1011_0 - c_0021_3 * c_1011_1 + c_0201_2 * c_1101_1,
          c_0012_3 * c_1101_3 - c_0021_3 * c_0111_3 + c_0111_3 * c_0201_0,
          - c_0012_3 * c_0111_3 + c_0021_3 * c_1101_0 + c_0102_0 * c_0111_3,
          - c_0012_3 * c_1101_0 + c_0102_2 * c_0111_3 + c_0201_0 * c_1101_3,
          - c_0021_3 * c_1101_3 + c_0102_0 * c_1101_0 + c_0111_3 * c_0201_2,
          - 1 + c_0012_0,
          - 1 + c_0111_0,
          - 1 + c_0012_0 * c_0012_1 * c_0012_3 * c_0021_3 * c_0102_0 * c_0102_2 * c_0111_0 * c_0111_2 * c_0111_3 * c_0201_0 * c_0201_2 * c_1011_0 * c_1011_1 * c_1101_0 * c_1101_1 * c_1101_3 * t>;



print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nm045\ngeometric_solution  3.27587164\noriented_manifold\nCS_known -0.0000000000000002\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n4\n   1    2    3    2 \n 0132 0132 0132 1230\n   0    0    0    0 \n  0  1 -1  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  0 -1  1  0  0  0  0 -1  1  0  0  0 -1  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.755773570847   0.474476778007\n\n   0    2    2    3 \n 0132 3201 2031 1302\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  1  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  0.050919524185   0.595835397802\n\n   0    0    1    1 \n 3012 0132 2310 1302\n   0    0    0    0 \n  0 -1  1  0  0  0  0  0  0  0  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  0  0 -1  0  0  1  0  1  0 -1  0 -1  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.857612619218   1.666147573612\n\n   3    3    1    0 \n 1302 2031 2031 0132\n   0    0    0    0 \n  0 -1  0  1  0  0  0  0  1  0  0 -1  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  0  0  0  0  1  0  0 -1  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.701673273758   0.267578043952\n\n";
print "==TRIANGULATION" cat "=ENDS==";
print "PY=EVAL=SECTION" cat "=BEGINS=HERE";
print "{'variable_dict' : 
     (lambda d, negation = (lambda x:-x): {
          'c_1020_2' : d['c_0012_3'],
          'c_1020_3' : d['c_0012_3'],
          'c_1020_0' : d['c_0102_2'],
          'c_1020_1' : d['c_0201_2'],
          'c_0201_0' : d['c_0201_0'],
          'c_0201_1' : d['c_0012_0'],
          'c_0201_2' : d['c_0201_2'],
          'c_0201_3' : d['c_0012_3'],
          'c_2100_0' : d['c_0201_2'],
          'c_2100_1' : d['c_0012_3'],
          'c_2100_2' : d['c_0012_0'],
          'c_2100_3' : d['c_0201_2'],
          'c_2010_2' : d['c_0021_3'],
          'c_2010_3' : d['c_0021_3'],
          'c_2010_0' : d['c_0201_2'],
          'c_2010_1' : d['c_0102_2'],
          'c_0102_0' : d['c_0102_0'],
          'c_0102_1' : d['c_0012_1'],
          'c_0102_2' : d['c_0102_2'],
          'c_0102_3' : d['c_0021_3'],
          'c_1101_0' : d['c_1101_0'],
          'c_1101_1' : d['c_1101_1'],
          'c_1101_2' : d['c_1011_1'],
          'c_1101_3' : d['c_1101_3'],
          'c_1200_2' : d['c_0012_1'],
          'c_1200_3' : d['c_0102_2'],
          'c_1200_0' : d['c_0102_2'],
          'c_1200_1' : d['c_0021_3'],
          'c_1110_2' : d['c_1101_1'],
          'c_1110_3' : d['c_1101_0'],
          'c_1110_0' : d['c_0111_2'],
          'c_1110_1' : d['c_1101_3'],
          'c_0120_0' : d['c_0012_1'],
          'c_0120_1' : d['c_0102_0'],
          'c_0120_2' : d['c_0102_2'],
          'c_0120_3' : d['c_0102_0'],
          'c_2001_0' : d['c_0021_3'],
          'c_2001_1' : d['c_0102_2'],
          'c_2001_2' : d['c_0201_2'],
          'c_2001_3' : d['c_0102_0'],
          'c_0012_2' : d['c_0012_1'],
          'c_0012_3' : d['c_0012_3'],
          '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']),
          'c_0111_2' : d['c_0111_2'],
          'c_0111_3' : d['c_0111_3'],
          'c_0210_2' : d['c_0201_2'],
          'c_0210_3' : d['c_0201_0'],
          'c_0210_0' : d['c_0012_0'],
          'c_0210_1' : d['c_0201_0'],
          'c_1002_2' : d['c_0102_2'],
          'c_1002_3' : d['c_0201_0'],
          'c_1002_0' : d['c_0012_3'],
          'c_1002_1' : d['c_0201_2'],
          'c_1011_2' : negation(d['c_1011_0']),
          'c_1011_3' : d['c_0111_3'],
          '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'],
          'c_0021_2' : d['c_0012_0'],
          'c_0021_3' : d['c_0021_3']})}";
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);