// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0011_3, c_0011_4, c_0101_0, c_0101_1, c_0101_5> := PolynomialRing(RationalField(), 7);
MyIdeal := ideal<R |
          - c_0011_0 * c_0011_4 + c_0011_3 * c_0101_1 + c_0101_0 * c_0101_5,
          - c_0011_0 * c_0101_1 - c_0101_0^2 + c_0101_1^2,
          - c_0011_0 * c_0011_3 - c_0011_0^2 + c_0101_5^2,
          - c_0011_3 * c_0011_4 + c_0011_3^2 - c_0101_0^2,
          - c_0011_4 * c_0101_1 - c_0011_4^2 + c_0101_5^2,
          - c_0011_0 * c_0011_4 + c_0011_3 * c_0101_1 + c_0101_0 * c_0101_5,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0101_0 * c_0101_1 * c_0101_5 * t>;



print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\ns955\ngeometric_solution  6.08964964\noriented_manifold\nCS_unknown\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n6\n   1    2    3    4 \n 0132 0132 0132 0132\n   0    0    0    0 \n  0 -1  0  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  0  1  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  0.500000000000   0.866025403784\n\n   0    5    1    1 \n 0132 0132 2031 1302\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  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  0.500000000000   0.866025403784\n\n   2    0    2    5 \n 2031 0132 1302 2310\n   0    0    0    0 \n  0  1 -1  0  1  0 -1  0  1  0  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  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  0.500000000000   0.866025403784\n\n   3    3    5    0 \n 1302 2031 0132 0132\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  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  0.500000000000   0.866025403784\n\n   5    4    0    4 \n 2310 1302 0132 2031\n   0    0    0    0 \n  0  0 -1  1  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 -1  1  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  0.500000000000   0.866025403784\n\n   2    1    4    3 \n 3201 0132 3201 0132\n   0    0    0    0 \n  0  0  0  0  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  1  0 -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  0.500000000000   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_3' : d['1'],
          's_3_2' : d['1'],
          's_3_5' : d['1'],
          's_3_4' : d['1'],
          's_3_0' : d['1'],
          's_2_0' : d['1'],
          's_2_1' : d['1'],
          's_2_2' : d['1'],
          's_2_3' : d['1'],
          's_2_4' : d['1'],
          's_2_5' : 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' : d['1'],
          's_1_0' : d['1'],
          's_0_4' : d['1'],
          's_0_5' : d['1'],
          's_0_2' : d['1'],
          's_0_3' : d['1'],
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_5' : negation(d['c_0011_4']),
          'c_1100_4' : negation(d['c_0011_4']),
          'c_1100_1' : d['c_0101_1'],
          'c_1100_0' : negation(d['c_0011_4']),
          'c_1100_3' : negation(d['c_0011_4']),
          'c_1100_2' : d['c_0011_0'],
          'c_0101_5' : d['c_0101_5'],
          'c_0101_4' : d['c_0101_1'],
          'c_0101_3' : negation(d['c_0011_3']),
          'c_0101_2' : d['c_0011_0'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_0'],
          'c_0011_4' : d['c_0011_4'],
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          'c_0011_3' : d['c_0011_3'],
          'c_0011_2' : negation(d['c_0011_0']),
          'c_1001_5' : negation(d['c_0101_1']),
          'c_1001_4' : negation(d['c_0101_5']),
          'c_1001_1' : negation(d['c_0101_0']),
          'c_1001_0' : d['c_0011_3'],
          'c_1001_3' : negation(d['c_0101_0']),
          'c_1001_2' : negation(d['c_0101_5']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0101_0'],
          'c_0110_2' : negation(d['c_0101_5']),
          'c_0110_5' : negation(d['c_0011_3']),
          'c_0110_4' : negation(d['c_0101_5']),
          'c_1010_5' : negation(d['c_0101_0']),
          'c_1010_4' : d['c_0011_4'],
          'c_1010_3' : d['c_0011_3'],
          'c_1010_2' : d['c_0011_3'],
          'c_1010_1' : negation(d['c_0101_1']),
          'c_1010_0' : negation(d['c_0101_5'])})}";
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);