// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK12n725\ngeometric_solution  5.91674574\noriented_manifold\nCS_known -0.0000000000000002\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n7\n   1    2    3    4 \n 0132 0132 0132 0132\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  0  1 -1 19  0  0 -19 -18 18  0  0  0 -1  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.371203969528   1.485813591345\n\n   0    5    4    2 \n 0132 0132 2310 2310\n   0    0    0    0 \n  0  0  0  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 -1  0  1 -19  0 19  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  0.264735293101   0.426160869693\n\n   1    0    6    3 \n 3201 0132 0132 0132\n   0    0    0    0 \n  0  0  0  0  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  0  0  0  0  0  0  0 -1  1  0  0  0 -18 18  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.371203969528   1.485813591345\n\n   6    5    2    0 \n 0213 0213 0132 0132\n   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  0  0  0  0  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 -0.158266616674   0.633491851959\n\n   5    1    0    6 \n 0132 3201 0132 0132\n   0    0    0    0 \n  0 -1  0  1  1  0 -1  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 18  1 -19 -19  0 19  0  0  0  0  0 19 -19  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.329130699918   0.726942705993\n\n   4    1    3    6 \n 0132 0132 0213 3201\n   0    0    0    0 \n  0  0  0  0 -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 -1  0 19  0 -1 -18 -19  0  0 19  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.906128790143   0.934273688260\n\n   3    5    4    2 \n 0213 2310 0132 0132\n   0    0    0    0 \n  0  1 -1  0  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 -19 19  0  0  0  0  0  0 18  0 -18  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.641393497043   0.508112818567\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_5' : d['1'],
          's_3_4' : d['1'],
          's_3_0' : negation(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' : negation(d['1']),
          's_2_5' : d['1'],
          's_2_6' : d['1'],
          's_1_6' : d['1'],
          's_1_5' : negation(d['1']),
          's_1_4' : 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_6' : d['1'],
          's_0_4' : negation(d['1']),
          's_0_5' : negation(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_1100_0'],
          'c_1100_5' : negation(d['c_0011_6']),
          'c_1100_4' : d['c_1100_0'],
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0011_0']),
          'c_1100_0' : d['c_1100_0'],
          'c_1100_3' : d['c_1100_0'],
          'c_1100_2' : d['c_1100_0'],
          'c_0101_6' : d['c_0011_3'],
          'c_0101_5' : d['c_0011_3'],
          'c_0101_4' : d['c_0101_1'],
          'c_0101_3' : d['c_0011_6'],
          'c_0101_2' : negation(d['c_0101_0']),
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_0'],
          'c_0011_4' : negation(d['c_0011_0']),
          'c_0011_6' : d['c_0011_6'],
          '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' : negation(d['c_0011_6']),
          'c_1001_4' : negation(d['c_0101_1']),
          'c_1001_6' : negation(d['c_1001_1']),
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : negation(d['c_0011_6']),
          'c_1001_3' : negation(d['c_0011_6']),
          'c_1001_2' : negation(d['c_0101_1']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0101_0'],
          'c_0110_2' : d['c_0011_6'],
          'c_0110_5' : d['c_0101_1'],
          'c_0110_4' : d['c_0011_3'],
          'c_0110_6' : negation(d['c_0101_0']),
          'c_1010_6' : negation(d['c_0101_1']),
          'c_1010_5' : d['c_1001_1'],
          'c_1010_4' : negation(d['c_1001_1']),
          'c_1010_3' : negation(d['c_0011_6']),
          'c_1010_2' : negation(d['c_0011_6']),
          'c_1010_1' : negation(d['c_0011_6']),
          'c_1010_0' : negation(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_3, c_0011_6, c_0101_0, c_0101_1, c_1001_1, c_1100_0> := PolynomialRing(RationalField(), 8);
I := ideal<R |
          - c_0011_0 * c_1100_0 - c_0011_6 * c_0101_1 - c_0101_0 * c_0101_1,
          c_0011_0^2 - c_0011_6 * c_0101_1 - c_0101_0 * c_1001_1,
          - c_0011_0 * c_1100_0 - c_0011_6 * c_0101_0 - c_0011_6 * c_0101_1,
          c_0011_3 * c_1100_0 - c_0011_6 * c_0101_0 + c_0011_6^2,
          c_0011_0 * c_1100_0 + c_0011_3 * c_0101_1 + c_0101_1 * c_1001_1,
          - c_0011_0 * c_0011_6 + c_0011_3 * c_1001_1 + c_0011_6 * c_0101_1,
          c_0011_3 * c_0101_1 + c_0011_6 * c_1100_0 + c_0101_0 * c_1001_1,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_6 * c_0101_0 * c_0101_1 * c_1001_1 * 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);