// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL8a12\ngeometric_solution  4.85117076\noriented_manifold\nCS_known -0.0000000000000001\n\n2 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n5\n   1    1    2    3 \n 0132 1230 0132 0132\n   0    0    1    0 \n  0  0  0  0  0  0  0  0  0  0  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  1  0 -1  0  0  0  0  0  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  0.339557007896   0.716885059001\n\n   0    4    0    4 \n 0132 0132 3012 1302\n   0    0    0    1 \n  0 -1  0  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  0 -1  0  0 -1  1  2 -2  0  0  0  1 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.460355188452   1.139317680302\n\n   3    2    2    0 \n 3201 1230 3012 0132\n   0    0    0    0 \n  0  0  0  0  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  0  0  0  0  0  0  0  2  0  0 -2  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.086117877114   1.048981610845\n\n   4    4    0    2 \n 0132 1302 0132 2310\n   0    0    0    1 \n  0 -1  0  1  0  0  0  0 -1  1  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  1  1 -2  0  0  0  0  1 -1  0  0  1 -2  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.339557007896   0.716885059001\n\n   3    1    1    3 \n 0132 0132 2031 2031\n   0    0    1    0 \n  0  1  0 -1  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 -1  0  1  0  0  1 -1 -1 -1  0  2 -1  2 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.695123295547   0.754529173144\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_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_1_4' : negation(d['1']),
          's_1_3' : d['1'],
          's_1_2' : d['1'],
          's_1_1' : negation(d['1']),
          's_1_0' : d['1'],
          's_0_4' : negation(d['1']),
          's_0_2' : d['1'],
          's_0_3' : negation(d['1']),
          's_0_0' : negation(d['1']),
          's_0_1' : negation(d['1']),
          'c_1100_4' : d['c_0101_0'],
          'c_1100_1' : negation(d['c_0101_2']),
          'c_1100_0' : d['c_0011_2'],
          'c_1100_3' : d['c_0011_2'],
          'c_1100_2' : d['c_0011_2'],
          'c_0101_4' : negation(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' : d['c_0011_2'],
          'c_1001_4' : negation(d['c_0101_0']),
          'c_1001_1' : negation(d['c_0011_0']),
          'c_1001_0' : d['c_0101_2'],
          'c_1001_3' : d['c_0101_1'],
          'c_1001_2' : negation(d['c_0011_2']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : negation(d['c_0101_2']),
          'c_0110_2' : d['c_0101_0'],
          'c_0110_4' : d['c_0101_1'],
          'c_1010_4' : negation(d['c_0011_0']),
          'c_1010_3' : negation(d['c_0101_0']),
          'c_1010_2' : d['c_0101_2'],
          'c_1010_1' : negation(d['c_0101_0']),
          'c_1010_0' : d['c_0101_1']})}";
print "PY=EVAL=SECTION=ENDS=HERE";

cputime := Cputime();


// Computation



// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0011_2, c_0101_0, c_0101_1, c_0101_2> := PolynomialRing(RationalField(), 6);
I := ideal<R |
          - c_0011_0 * c_0011_2 + c_0101_0 * c_0101_1 + c_0101_1 * c_0101_2,
          c_0011_0 * c_0101_0 + c_0011_0 * c_0101_2 - c_0101_0 * c_0101_1,
          - c_0011_2 * c_0101_0 + c_0011_2^2 - c_0101_2^2,
          c_0011_0 * c_0011_2 + c_0101_0 * c_0101_1 + c_0101_1 * c_0101_2,
          c_0011_0 * c_0101_0 + c_0011_0 * c_0101_2 + c_0101_0 * c_0101_1,
          - 1 + c_0011_0,
          - 1 + c_0101_0,
          - 1 + c_0011_0 * c_0011_2 * c_0101_0 * c_0101_1 * c_0101_2 * 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);