// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0011_2, c_0101_0, c_0101_1, c_0101_2, c_0101_5, c_0101_6> := PolynomialRing(RationalField(), 8);
MyIdeal := ideal<R |
          - c_0011_0 * c_0101_2 + c_0101_0^2 - c_0101_1^2,
          - c_0011_0^2 + c_0011_2 * c_0101_0 + c_0101_1^2,
          c_0011_0 * c_0101_0 + c_0011_2 * c_0101_2 - c_0101_1 * c_0101_2,
          - c_0011_0 * c_0101_0 - c_0011_2 * c_0101_2 + c_0101_1 * c_0101_2,
          - c_0011_2^2 - c_0101_0 * c_0101_6 + c_0101_2^2,
          - c_0011_2^2 - c_0101_2 * c_0101_5 + c_0101_6^2,
          c_0011_2 * c_0101_6 - c_0011_2^2 + c_0101_5^2,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_2 * c_0101_0 * c_0101_1 * c_0101_2 * c_0101_5 * c_0101_6 * t>;



print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nv1751\ngeometric_solution  5.44367619\noriented_manifold\nCS_unknown\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n7\n   1    1    2    3 \n 0132 2310 0132 0132\n   0    0    0    0 \n  0  0  1 -1  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  1  1 -2  0  0  0  0  0  0  0  0 -1  1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.370840115001   0.616169705448\n\n   0    3    2    0 \n 0132 3012 3012 3201\n   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  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  0.174878595875   1.060198097540\n\n   4    1    3    0 \n 0132 1230 2031 0132\n   0    0    0    0 \n  0  0  1 -1  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  1 -1 -1  0  1  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  0.429523452409   0.710886164351\n\n   1    4    0    2 \n 1230 3201 0132 1302\n   0    0    0    0 \n  0 -1  1  0  0  0  0  0  0  1  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  2 -1  0  0  0  0  0  1  0 -1 -1  1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.429523452409   0.710886164351\n\n   2    5    3    5 \n 0132 0132 2310 1023\n   0    0    0    0 \n  0  0 -1  1  0  0  0  0  0  0  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  0 -1  1  1  0 -1  0  0  0  0  0  0 -1  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.802492079308   1.931535368910\n\n   6    4    6    4 \n 0132 0132 1023 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  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  0.529979101585   0.209429284451\n\n   5    6    5    6 \n 0132 1302 1023 2031\n   0    0    0    0 \n  0  0 -1  1  0  0  0  0  0 -1  0  1  1 -1  0  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  0 -1  0  1  1 -1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.583183385688   0.051148530250\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' : negation(d['1']),
          's_3_0' : negation(d['1']),
          's_3_3' : d['1'],
          's_3_2' : d['1'],
          's_3_5' : d['1'],
          's_3_4' : d['1'],
          's_2_0' : d['1'],
          's_2_1' : d['1'],
          's_2_2' : d['1'],
          's_2_3' : negation(d['1']),
          's_2_4' : d['1'],
          's_2_5' : d['1'],
          's_2_6' : d['1'],
          's_1_6' : d['1'],
          's_1_5' : d['1'],
          's_1_4' : d['1'],
          's_1_3' : d['1'],
          's_1_2' : d['1'],
          's_1_1' : negation(d['1']),
          's_1_0' : negation(d['1']),
          's_0_6' : d['1'],
          's_0_4' : d['1'],
          's_0_5' : d['1'],
          's_0_2' : d['1'],
          's_0_3' : negation(d['1']),
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_6' : d['c_0011_2'],
          'c_1100_5' : negation(d['c_0011_2']),
          'c_1100_4' : d['c_0011_2'],
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0011_0']),
          'c_1100_0' : d['c_0101_2'],
          'c_1100_3' : d['c_0101_2'],
          'c_1100_2' : d['c_0101_2'],
          'c_0101_6' : d['c_0101_6'],
          'c_0101_5' : d['c_0101_5'],
          'c_0101_4' : d['c_0101_0'],
          'c_0101_3' : d['c_0101_1'],
          'c_0101_2' : d['c_0101_2'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_2'],
          'c_0011_4' : negation(d['c_0011_2']),
          'c_0011_6' : negation(d['c_0011_2']),
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          'c_0011_3' : d['c_0011_2'],
          'c_0011_2' : d['c_0011_2'],
          'c_1001_5' : d['c_0101_6'],
          'c_1001_4' : d['c_0101_2'],
          'c_1001_6' : d['c_0101_5'],
          'c_1001_1' : negation(d['c_0011_2']),
          'c_1001_0' : d['c_0101_1'],
          'c_1001_3' : negation(d['c_0101_0']),
          'c_1001_2' : d['c_0011_0'],
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : negation(d['c_0011_0']),
          'c_0110_2' : d['c_0101_0'],
          'c_0110_5' : d['c_0101_6'],
          'c_0110_4' : d['c_0101_2'],
          'c_0110_6' : d['c_0101_5'],
          'c_1010_6' : negation(d['c_0011_2']),
          'c_1010_5' : d['c_0101_2'],
          'c_1010_4' : d['c_0101_6'],
          'c_1010_3' : negation(d['c_0101_2']),
          'c_1010_2' : d['c_0101_1'],
          'c_1010_1' : negation(d['c_0101_1']),
          'c_1010_0' : negation(d['c_0101_0'])})}";
print "PY=EVAL=SECTION=ENDS=HERE";



// Initialize Q to -1 so that we can check whether an error happend
// by checking that Q is still of type integer.
Q := -1;

// Remember start time to calculate computation time
primTime := Cputime();




print "DECOMPOSITION=TYPE: Primary Decomposition of Radical";

P, Q := PrimaryDecomposition(Radical(MyIdeal));



print "IDEAL=DECOMPOSITION" cat "=TIME: ", Cputime(primTime);

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


    print "FREE=VARIABLES=IN=COMPONENTS" cat "=BEGINS=HERE";
    N := Names(R);
    isFirstComp := true;
    freeVarStr := "[";
    for Comp in Q do
    
        if isFirstComp then
            isFirstComp := false;
        else
            freeVarStr := freeVarStr cat ",";
        end if;
        freeVarStr := freeVarStr cat "\n    [ ";
        
        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 "\n]";
    print freeVarStr;
    print "FREE=VARIABLES=IN=COMPONENTS" cat "=ENDS=HERE";
end if;

print "CPUTIME: ", Cputime(primTime);