// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK8n1\ngeometric_solution  4.12490325\noriented_manifold\nCS_known 0.0000000000000002\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n5\n   1    2    3    4 \n 0132 0132 0132 0132\n   0    0    0    0 \n  0  0  1 -1  0  0  0  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  1 -2  1  0  0  0  0  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 -0.165924414224   1.354819388892\n\n   0    4    3    2 \n 0132 0321 0321 2310\n   0    0    0    0 \n  0  1  0 -1  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 -1  0  1  0  0 -1  1  0  2  0 -2  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.369908768847   0.281337020237\n\n   1    0    3    4 \n 3201 0132 3201 0321\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 -1  1  0  2  0  0 -2 -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  1.099771252721   1.129446753864\n\n   2    4    1    0 \n 2310 2031 0321 0132\n   0    0    0    0 \n  0  1  0 -1  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 -2  0  2  0  0  0  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  0.364931241937   0.424054866813\n\n   3    2    0    1 \n 1302 0321 0132 0321\n   0    0    0    0 \n  0  0  1 -1  0  0  0  0 -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  0 -1  1  0  0  0  0  2  0  0 -2 -1  2 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.077606503681   0.878533758687\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_3' : d['1'],
          's_3_2' : d['1'],
          's_3_4' : d['1'],
          's_3_0' : 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_1001_1'],
          'c_1100_1' : negation(d['c_0011_0']),
          'c_1100_0' : d['c_1001_1'],
          'c_1100_3' : d['c_1001_1'],
          'c_1100_2' : negation(d['c_0011_3']),
          'c_0101_4' : negation(d['c_0011_3']),
          'c_0101_3' : d['c_0011_3'],
          'c_0101_2' : negation(d['c_0101_0']),
          'c_0101_1' : negation(d['c_0011_3']),
          'c_0101_0' : d['c_0101_0'],
          'c_0011_4' : d['c_0011_4'],
          '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_4' : negation(d['c_0011_3']),
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : d['c_0011_4'],
          'c_1001_3' : negation(d['c_0011_0']),
          'c_1001_2' : negation(d['c_0011_3']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : negation(d['c_0011_3']),
          'c_0110_3' : d['c_0101_0'],
          'c_0110_2' : negation(d['c_0011_4']),
          'c_0110_4' : d['c_0011_0'],
          'c_1010_4' : d['c_0011_4'],
          'c_1010_3' : d['c_0011_4'],
          'c_1010_2' : d['c_0011_4'],
          'c_1010_1' : d['c_0011_4'],
          'c_1010_0' : negation(d['c_0011_3'])})}";
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_0101_0, c_1001_1> := PolynomialRing(RationalField(), 6);
I := ideal<R |
          c_0011_0 * c_1001_1 - c_0011_3 * c_0011_4 + c_0011_3 * c_0101_0,
          c_0011_0^2 + c_0011_3 * c_0011_4 + c_0101_0 * c_1001_1,
          c_0011_0 * c_0011_3 + c_0011_3 * c_0011_4 + c_0011_4 * c_0101_0,
          - c_0011_0 * c_0101_0 - c_0011_3 * c_0011_4 + c_0011_3 * c_1001_1,
          - c_0011_0 * c_0011_3 + c_0011_3 * c_0011_4 + c_0011_4 * c_1001_1,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * 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);