// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK14n12557\ngeometric_solution  7.29661154\noriented_manifold\nCS_known 0.0000000000000003\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n9\n   1    2    2    3 \n 0132 0132 3201 0132\n   0    0    0    0 \n  0  0  0  0  1  0 -1  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  0 -1  1 -20  0 20  0  0  0  0  0 19 -20  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.082919899768   1.203812981758\n\n   0    3    4    3 \n 0132 2310 0132 3120\n   0    0    0    0 \n  0  0  0  0 -1  0  0  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 20  0 -1 -19 -19 19  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.206612301459   0.561246339559\n\n   0    0    6    5 \n 2310 0132 0132 0132\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  0  0  0 -1  0  0  1 -20 20  0  0  1  0 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.771627358761   1.907814238281\n\n   1    5    0    1 \n 3120 2031 0132 3201\n   0    0    0    0 \n  0  0  0  0 -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  1 -1  0 19  0  0 -19  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  0.357842979377   0.428159910704\n\n   7    7    8    1 \n 0132 2310 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  0  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  0.643574318689   0.470907573382\n\n   3    8    2    6 \n 1302 3012 0132 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  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  0.261465125353   0.297437788878\n\n   8    5    7    2 \n 1230 2310 3012 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  0  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  0.494925257232   1.639562085808\n\n   4    6    8    4 \n 0132 1230 3120 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  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  0.376585183010   0.597139145511\n\n   5    6    7    4 \n 1230 3012 3120 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  0  0 -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  1.443257448621   0.231469621045\n\n";
print "==TRIANGULATION" cat "=ENDS==";
print "PY=EVAL=SECTION" cat "=BEGINS=HERE";
print "{'variable_dict' : 
     (lambda d, negation = (lambda x:-x): {
          'c_1001_5' : negation(d['c_0011_8']),
          'c_1001_4' : negation(d['c_0101_6']),
          'c_1001_7' : d['c_0011_6'],
          'c_1001_6' : d['c_0011_4'],
          'c_1001_1' : negation(d['c_0011_5']),
          'c_1001_0' : negation(d['c_0011_8']),
          'c_1001_3' : negation(d['c_0110_5']),
          'c_1001_2' : negation(d['c_0110_5']),
          'c_1001_8' : negation(d['c_0011_6']),
          's_2_8' : 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_2_6' : d['1'],
          's_2_7' : d['1'],
          's_0_8' : d['1'],
          's_0_6' : d['1'],
          's_0_7' : 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_8' : negation(d['c_0101_1']),
          'c_1100_5' : negation(d['c_0011_6']),
          'c_1100_4' : negation(d['c_0101_1']),
          'c_1100_7' : negation(d['c_0011_4']),
          'c_1100_6' : negation(d['c_0011_6']),
          'c_1100_1' : negation(d['c_0101_1']),
          'c_1100_0' : d['c_0011_0'],
          'c_1100_3' : d['c_0011_0'],
          'c_1100_2' : negation(d['c_0011_6']),
          'c_1010_7' : d['c_0101_6'],
          'c_1010_6' : negation(d['c_0110_5']),
          'c_1010_5' : negation(d['c_0011_4']),
          'c_1010_4' : negation(d['c_0011_5']),
          'c_1010_3' : d['c_0011_5'],
          'c_1010_2' : negation(d['c_0011_8']),
          'c_1010_1' : negation(d['c_0011_3']),
          'c_1010_0' : negation(d['c_0110_5']),
          'c_1010_8' : negation(d['c_0101_6']),
          's_3_1' : d['1'],
          's_3_0' : d['1'],
          's_3_3' : d['1'],
          's_3_2' : d['1'],
          's_3_5' : d['1'],
          's_3_4' : d['1'],
          's_3_7' : d['1'],
          's_3_6' : d['1'],
          's_3_8' : d['1'],
          's_1_7' : 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' : d['1'],
          's_1_0' : d['1'],
          's_1_8' : d['1'],
          'c_0011_8' : d['c_0011_8'],
          'c_0011_5' : d['c_0011_5'],
          'c_0011_4' : d['c_0011_4'],
          'c_0011_7' : negation(d['c_0011_4']),
          'c_0011_6' : d['c_0011_6'],
          '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_0101_7' : d['c_0101_1'],
          'c_0101_6' : d['c_0101_6'],
          'c_0101_5' : negation(d['c_0011_3']),
          'c_0101_4' : d['c_0011_5'],
          'c_0101_3' : d['c_0101_1'],
          'c_0101_2' : d['c_0011_8'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0011_3'],
          'c_0101_8' : d['c_0011_4'],
          'c_0110_8' : d['c_0011_5'],
          'c_0110_1' : d['c_0011_3'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0011_3'],
          'c_0110_2' : negation(d['c_0011_3']),
          'c_0110_5' : d['c_0110_5'],
          'c_0110_4' : d['c_0101_1'],
          'c_0110_7' : d['c_0011_5'],
          'c_0110_6' : d['c_0011_8']})}";
print "PY=EVAL=SECTION=ENDS=HERE";

cputime := Cputime();


// Computation



// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0011_3, c_0011_4, c_0011_5, c_0011_6, c_0011_8, c_0101_1, c_0101_6, c_0110_5> := PolynomialRing(RationalField(), 10);
I := ideal<R |
          c_0011_0^2 + c_0011_3 * c_0110_5 - c_0011_8 * c_0101_1,
          c_0011_0 * c_0101_1 - c_0011_3 * c_0011_5 + c_0011_3 * c_0101_1,
          c_0011_0 * c_0011_6 + c_0011_3 * c_0110_5 + c_0011_8^2,
          c_0011_0 * c_0011_3 - c_0011_3 * c_0110_5 - c_0011_5 * c_0101_1,
          - c_0011_4 * c_0101_1 + c_0011_5^2 - c_0101_1 * c_0101_6,
          - c_0011_3 * c_0011_4 - c_0011_5 * c_0011_6 - c_0011_8 * c_0110_5,
          c_0011_4 * c_0011_8 - c_0011_6^2 + c_0101_6 * c_0110_5,
          c_0011_4^2 + c_0011_5 * c_0011_6 - c_0101_1 * c_0101_6,
          c_0011_4 * c_0101_6 - c_0011_5 * c_0011_6 - c_0011_8 * c_0101_1,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0011_5 * c_0011_6 * c_0011_8 * c_0101_1 * c_0101_6 * c_0110_5 * t>;


// Value indicating failure
P := -1;

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

if Type(P) eq RngIntElt then
   // Some error occured
   print "PRIMARY=DECOMPOSITION" cat "=FAILED";
else
   // Success
   print "PRIMARY=DECOMPOSITION" cat "=BEGINS=HERE";
   P;
   print "PRIMARY=DECOMPOSITION" cat "=ENDS=HERE";
end if;





print "CPUTIME :", Cputime(cputime);