// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK12n582\ngeometric_solution  5.85424272\noriented_manifold\nCS_known 0.0000000000000001\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n7\n   1    2    2    1 \n 0132 0132 3201 3201\n   0    0    0    0 \n  0  0 -1  1  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 -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  0.006968172435   0.595046953652\n\n   0    0    4    3 \n 0132 2310 0132 0132\n   0    0    0    0 \n  0 -1  1  0  0  0  0  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 -1  1  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  0.068511737678   2.247132954061\n\n   0    0    6    5 \n 2310 0132 0132 0132\n   0    0    0    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  0  0  0  0  0 -1  1  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 -0.067666618322   1.254227508717\n\n   6    5    1    6 \n 1230 0132 0132 3120\n   0    0    0    0 \n  0  0  0  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  0  0  0 -1  0  0  1  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 -0.478727453162   0.464354214666\n\n   5    5    6    1 \n 3201 3012 3120 0132\n   0    0    0    0 \n  0  1  0 -1  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  0.216048724412   0.481115422447\n\n   4    3    2    4 \n 1230 0132 0132 2310\n   0    0    0    0 \n  0  0  0  0  0  0  0  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  0  0  0  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  0.253949238490   1.104061389536\n\n   3    3    4    2 \n 3120 3012 3120 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 -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  0.730264791283   0.743351439498\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' : 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_2_5' : d['1'],
          's_2_6' : d['1'],
          's_1_6' : d['1'],
          's_1_5' : 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_6' : d['1'],
          's_0_4' : d['1'],
          's_0_5' : d['1'],
          's_0_2' : d['1'],
          's_0_3' : d['1'],
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_6' : d['c_0011_4'],
          'c_1100_5' : d['c_0011_4'],
          'c_1100_4' : negation(d['c_0101_6']),
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0101_6']),
          'c_1100_0' : d['c_0011_0'],
          'c_1100_3' : negation(d['c_0101_6']),
          'c_1100_2' : d['c_0011_4'],
          'c_0101_6' : d['c_0101_6'],
          'c_0101_5' : negation(d['c_0101_0']),
          'c_0101_4' : negation(d['c_0011_4']),
          'c_0101_3' : d['c_0101_0'],
          'c_0101_2' : d['c_0011_6'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : negation(d['c_0011_3']),
          'c_0011_4' : d['c_0011_4'],
          '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' : d['c_0011_3'],
          'c_1001_6' : negation(d['c_0011_3']),
          'c_1001_1' : d['c_0101_0'],
          'c_1001_0' : negation(d['c_0011_6']),
          'c_1001_3' : negation(d['c_0101_1']),
          'c_1001_2' : negation(d['c_0101_0']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0011_6'],
          'c_0110_2' : negation(d['c_0101_0']),
          'c_0110_5' : d['c_0011_4'],
          'c_0110_4' : d['c_0101_1'],
          'c_0110_6' : d['c_0011_6'],
          'c_1010_6' : negation(d['c_0101_0']),
          'c_1010_5' : negation(d['c_0101_1']),
          'c_1010_4' : d['c_0101_0'],
          'c_1010_3' : negation(d['c_0011_6']),
          'c_1010_2' : negation(d['c_0011_6']),
          'c_1010_1' : negation(d['c_0101_1']),
          'c_1010_0' : negation(d['c_0101_0'])})}";
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_0011_6, c_0101_0, c_0101_1, c_0101_6> := PolynomialRing(RationalField(), 8);
I := ideal<R |
          c_0011_0^2 - c_0011_6 * c_0101_1 + c_0101_0^2,
          c_0011_0 * c_0101_6 + c_0101_0^2 + c_0101_1^2,
          - c_0011_0 * c_0011_4 + c_0011_6^2 + c_0101_0^2,
          - c_0011_3 * c_0101_6 + c_0011_6 * c_0101_0 - c_0011_6 * c_0101_1,
          c_0011_3 * c_0101_1 + c_0011_4 * c_0101_0 - c_0011_4 * c_0101_6,
          - c_0011_3 * c_0011_4 - c_0011_4 * c_0011_6 - c_0101_0 * c_0101_1,
          - c_0011_3 * c_0011_6 + c_0011_4 * c_0011_6 + c_0101_0 * c_0101_6,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0011_6 * c_0101_0 * c_0101_1 * c_0101_6 * 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);