// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL8a18\ngeometric_solution  6.55174329\noriented_manifold\nCS_known 0.0000000000000002\n\n3 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n7\n   1    2    3    4 \n 0132 0132 0132 0132\n   2    1    0    1 \n  0  1 -1  0  0  0 -1  1  1  0  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  3 -4  1  0  0 -2  2  1 -1  0  0  3 -3  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.101839048370   1.191670795605\n\n   0    2    4    5 \n 0132 0213 0213 0132\n   2    1    1    0 \n  0  0  0  0  0  0  0  0 -1  1  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  0  0  0  0  0  0 -3  3  0  0 -1  0  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.581706428681   0.452396594283\n\n   4    0    1    3 \n 0213 0132 0213 0132\n   2    1    1    0 \n  0 -1  0  1  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 -3  0  3  0  0 -3  3 -3  3  0  0 -1  1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.403346547516   0.535156087905\n\n   6    5    2    0 \n 0132 0321 0132 0132\n   2    1    1    1 \n  0  0 -1  1  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 -1 -3  4  1  0 -3  2  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  0.163412857361   0.904793188566\n\n   2    1    0    5 \n 0213 0213 0132 0321\n   2    1    1    0 \n  0  0  0  0  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  0 -1  1  3  0 -2 -1  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  0.403346547516   0.535156087905\n\n   6    4    1    3 \n 2103 0321 0132 0321\n   2    1    1    1 \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  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  0.550919524185   0.595835397802\n\n   3    6    5    6 \n 0132 1302 2103 2031\n   1    1    1    1 \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  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  0.454266071701   1.130991485707\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' : 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' : negation(d['1']),
          's_2_2' : d['1'],
          's_2_3' : d['1'],
          's_2_4' : negation(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' : negation(d['1']),
          's_1_3' : d['1'],
          's_1_2' : d['1'],
          's_1_1' : d['1'],
          's_1_0' : 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' : d['1'],
          's_0_0' : negation(d['1']),
          's_0_1' : negation(d['1']),
          'c_1100_6' : d['c_0011_3'],
          'c_1100_5' : d['c_1001_0'],
          'c_1100_4' : d['c_1001_5'],
          's_3_6' : d['1'],
          'c_1100_1' : d['c_1001_0'],
          'c_1100_0' : d['c_1001_5'],
          'c_1100_3' : d['c_1001_5'],
          'c_1100_2' : d['c_1001_5'],
          'c_0101_6' : d['c_0101_0'],
          'c_0101_5' : d['c_0101_0'],
          'c_0101_4' : negation(d['c_0011_0']),
          'c_0101_3' : d['c_0011_5'],
          'c_0101_2' : negation(d['c_0011_0']),
          'c_0101_1' : negation(d['c_0011_0']),
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_5'],
          'c_0011_4' : negation(d['c_0011_0']),
          'c_0011_6' : negation(d['c_0011_3']),
          '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' : d['c_1001_5'],
          'c_1001_4' : d['c_1001_1'],
          'c_1001_6' : d['c_0011_5'],
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : d['c_1001_0'],
          'c_1001_3' : d['c_1001_0'],
          'c_1001_2' : d['c_1001_1'],
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : negation(d['c_0011_0']),
          'c_0110_3' : d['c_0101_0'],
          'c_0110_2' : d['c_0011_5'],
          'c_0110_5' : negation(d['c_0011_3']),
          'c_0110_4' : negation(d['c_0011_5']),
          'c_0110_6' : d['c_0011_5'],
          'c_1010_6' : negation(d['c_0011_3']),
          'c_1010_5' : d['c_1001_0'],
          'c_1010_4' : d['c_1001_0'],
          'c_1010_3' : d['c_1001_0'],
          'c_1010_2' : d['c_1001_0'],
          'c_1010_1' : d['c_1001_5'],
          'c_1010_0' : d['c_1001_1']})}";
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_5, c_0101_0, c_1001_0, c_1001_1, c_1001_5> := PolynomialRing(RationalField(), 8);
I := ideal<R |
          - c_0011_0 * c_1001_0 - c_0011_0 * c_1001_5 + c_0101_0 * c_1001_1,
          c_0011_0 * c_1001_0 + c_0011_0 * c_1001_5 - c_0101_0 * c_1001_1,
          c_0011_0 * c_1001_0 - c_0011_0 * c_1001_5 + c_0011_5 * c_1001_1,
          c_0011_3 * c_1001_5 - c_0011_5 * c_1001_0 + c_0101_0 * c_1001_0,
          - c_0011_0 * c_1001_0 + c_0011_0 * c_1001_5 - c_0011_5 * c_1001_1,
          - c_0011_3 * c_1001_5 + c_0011_5 * c_1001_0 - c_0101_0 * c_1001_0,
          c_0011_3 * c_0101_0 - c_0011_3^2 + c_0011_5^2,
          - 1 + c_0011_0,
          - 1 + c_0101_0,
          - 1 + c_1001_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_5 * c_0101_0 * c_1001_0 * c_1001_1 * c_1001_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);