// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK12n242\ngeometric_solution  2.82812209\noriented_manifold\nCS_known -0.0000000000000000\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n3\n   1    2    1    1 \n 0132 0132 2031 0321\n   0    0    0    0 \n  0 -1  1  0 -1  0  1  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 19 -18 -1 18  0 -18  0  0  0  0  0 18  0 -18  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.215079854501   1.307141278682\n\n   0    0    2    0 \n 0132 0321 3120 1302\n   0    0    0    0 \n  0  0  1 -1  1  0  0 -1  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  1 -19 18 -18  0  0 18 -18  0  0 18  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.877438833123   0.744861766620\n\n   2    0    1    2 \n 3201 0132 3120 2310\n   0    0    0    0 \n  0  1  0 -1  1  0  0 -1  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 -19  0 19 -19  0  0 19 -19  0  0 19 -19  0 19  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.337641021378   0.562279512062\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_2' : d['1'],
          's_3_0' : d['1'],
          's_2_0' : d['1'],
          's_2_1' : d['1'],
          's_2_2' : d['1'],
          's_1_2' : d['1'],
          's_1_1' : d['1'],
          's_1_0' : d['1'],
          's_0_2' : d['1'],
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_1' : d['c_0101_0'],
          'c_1100_0' : d['c_1001_1'],
          'c_1100_2' : negation(d['c_0011_0']),
          'c_0101_2' : negation(d['c_0101_0']),
          'c_0101_1' : d['c_0011_0'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          'c_0011_2' : negation(d['c_0011_0']),
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : negation(d['c_0101_0']),
          'c_1001_2' : negation(d['c_1001_1']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0011_0'],
          'c_0110_2' : d['c_0101_0'],
          'c_1010_2' : negation(d['c_0101_0']),
          'c_1010_1' : negation(d['c_1001_1']),
          'c_1010_0' : negation(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_0101_0, c_1001_1> := PolynomialRing(RationalField(), 4);
I := ideal<R |
          - c_0011_0 * c_0101_0 + c_0011_0 * c_1001_1 + c_0101_0 * c_1001_1,
          - c_0011_0 * c_0101_0 + c_0011_0 * c_1001_1 + c_0101_0 * c_1001_1,
          c_0011_0^2 - c_0101_0 * c_1001_1 - c_0101_0^2,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0101_0 * c_1001_1 * 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);