// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\n10^2_126\ngeometric_solution  4.41533248\noriented_manifold\nCS_known 0.0000000000000005\n\n2 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n5\n   1    2    1    3 \n 0132 0132 1023 0132\n   1    1    0    0 \n  0  2 -1 -1  1  0  0 -1  1  0  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 -3  1  2 -1  0  0  1 -1 -1  0  2  0 -1  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.471443414326   1.008327689094\n\n   0    4    0    4 \n 0132 0132 1023 1023\n   1    1    0    0 \n  0 -2  0  2 -1  0  1  0  0 -1  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  3  0 -3  1  0 -1  0  0  2  0 -2  1  0 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.455848754475   0.300705204821\n\n   3    0    3    4 \n 1023 0132 0132 0132\n   1    1    0    0 \n  0 -2  0  2  1  0  1 -2  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 -2  0 -1  3 -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 -0.176604982100   1.202820819285\n\n   4    2    0    2 \n 0132 1023 0132 0132\n   1    1    0    0 \n  0 -1  1  0  0  0  1 -1  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  2 -2  0  0  0 -1  1 -2  1  0  1  2  0 -2  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.176604982100   1.202820819285\n\n   3    1    2    1 \n 0132 0132 0132 1023\n   1    1    0    0 \n  0  2 -2  0  0  0  2 -2  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  3  0  0  0 -3  3 -2  0  0  2  2 -2  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.471443414326   1.008327689094\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' : d['1'],
          's_3_3' : d['1'],
          's_3_2' : 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' : d['1'],
          's_2_4' : 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_2' : d['1'],
          's_0_3' : d['1'],
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_4' : d['c_1100_0'],
          'c_1100_1' : negation(d['c_1100_0']),
          'c_1100_0' : d['c_1100_0'],
          'c_1100_3' : d['c_1100_0'],
          'c_1100_2' : d['c_1100_0'],
          'c_0101_4' : d['c_0101_2'],
          '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_4' : d['c_0011_0'],
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          'c_0011_3' : negation(d['c_0011_0']),
          'c_0011_2' : negation(d['c_0011_0']),
          'c_1001_4' : d['c_0101_1'],
          'c_1001_1' : d['c_0101_0'],
          'c_1001_0' : d['c_0101_1'],
          'c_1001_3' : d['c_0101_2'],
          'c_1001_2' : d['c_0101_2'],
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0101_2'],
          'c_0110_2' : d['c_0101_2'],
          'c_0110_4' : d['c_0101_1'],
          'c_1010_4' : d['c_0101_0'],
          'c_1010_3' : d['c_0101_2'],
          'c_1010_2' : d['c_0101_1'],
          'c_1010_1' : d['c_0101_1'],
          'c_1010_0' : d['c_0101_2']})}";
print "PY=EVAL=SECTION=ENDS=HERE";

cputime := Cputime();


// Computation



// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0101_0, c_0101_1, c_0101_2, c_1100_0> := PolynomialRing(RationalField(), 6);
I := ideal<R |
          c_0011_0 * c_1100_0 - c_0101_0 * c_0101_2 + c_0101_1^2,
          c_0011_0 * c_1100_0 + c_0101_0^2 - c_0101_1^2,
          - c_0011_0 * c_1100_0 - c_0101_1 * c_0101_2 + c_0101_2^2,
          - c_0011_0 * c_1100_0 - c_0101_1 * c_0101_2 + c_0101_2^2,
          c_0011_0 * c_1100_0 - c_0101_0 * c_0101_2 + c_0101_1^2,
          - 1 + c_0011_0,
          - 1 + c_0101_0,
          - 1 + c_0011_0 * c_0101_0 * c_0101_1 * c_0101_2 * c_1100_0 * 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);