// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK14n6006\ngeometric_solution  4.99327197\noriented_manifold\nCS_known -0.0000000000000007\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n8\n   1    2    3    3 \n 0132 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 -1  0  1  0  0  0  0  0  0  0  0 14 -13 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.252457647121   0.945969528968\n\n   0    4    2    4 \n 0132 0132 3201 0213\n   0    0    0    0 \n  0  0  0  0  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  0 -1  1  0  0 -1  1 -14 14  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.197695796997   0.707207235014\n\n   1    0    4    5 \n 2310 0132 1302 0132\n   0    0    0    0 \n  0  0  0  0  0  0 -1  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  1  0 -1  0  0 -14 14  1 13  0 -14  1  0 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.323264616759   0.179144753701\n\n   0    6    6    0 \n 3201 0132 3201 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  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 -0.332411823479   0.377430235730\n\n   2    1    5    1 \n 2031 0132 0213 0213\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  1 -1  0  0  0  0  1  0  0 -1 14 -14  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.197695796997   0.707207235014\n\n   7    4    2    7 \n 0132 0213 0132 3201\n   0    0    0    0 \n  0  0  0  0  0  0 -1  1  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  1  0  0  0 -14 14  0  0  0  0 -14  0 14  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.129272721997   0.734848917019\n\n   3    3    7    7 \n 2310 0132 3120 0213\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  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  3.738480836474   1.525675378430\n\n   5    5    6    6 \n 0132 2310 3120 0213\n   0    0    0    0 \n  0  0  0  0  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  0  0  0  0  0  0  0 14 -14  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  3.223053271484   1.532722505548\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_7' : d['1'],
          's_3_0' : d['1'],
          's_2_0' : d['1'],
          's_2_1' : d['1'],
          's_2_2' : negation(d['1']),
          's_2_3' : d['1'],
          's_2_4' : d['1'],
          's_2_5' : d['1'],
          's_2_6' : d['1'],
          's_2_7' : d['1'],
          's_1_7' : d['1'],
          's_1_6' : d['1'],
          's_1_5' : d['1'],
          's_1_4' : negation(d['1']),
          's_1_3' : d['1'],
          's_1_2' : negation(d['1']),
          's_1_1' : negation(d['1']),
          's_1_0' : negation(d['1']),
          's_0_6' : d['1'],
          's_0_7' : d['1'],
          's_0_4' : negation(d['1']),
          's_0_5' : 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' : negation(d['c_0101_7']),
          'c_1100_5' : d['c_0011_5'],
          'c_1100_4' : d['c_1001_0'],
          'c_1100_7' : negation(d['c_0101_6']),
          's_3_6' : d['1'],
          'c_1100_1' : d['c_0011_0'],
          'c_1100_0' : d['c_0011_3'],
          'c_1100_3' : d['c_0011_3'],
          'c_1100_2' : d['c_0011_5'],
          'c_0101_7' : d['c_0101_7'],
          'c_0101_6' : d['c_0101_6'],
          'c_0101_5' : negation(d['c_0101_1']),
          'c_0101_4' : d['c_0011_5'],
          'c_0101_3' : negation(d['c_0101_1']),
          'c_0101_2' : negation(d['c_0011_0']),
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_5'],
          'c_0011_4' : d['c_0011_0'],
          'c_0011_7' : negation(d['c_0011_5']),
          'c_0011_6' : negation(d['c_0011_3']),
          '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' : d['c_1001_0'],
          'c_1001_4' : d['c_1001_0'],
          'c_1001_7' : negation(d['c_1001_0']),
          'c_1001_6' : d['c_1001_0'],
          'c_1001_1' : d['c_0011_0'],
          'c_1001_0' : d['c_1001_0'],
          'c_1001_3' : negation(d['c_0101_6']),
          '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_0101_0'],
          'c_0110_2' : negation(d['c_0101_1']),
          'c_0110_5' : d['c_0101_7'],
          'c_0110_4' : negation(d['c_0101_0']),
          'c_0110_7' : negation(d['c_0101_1']),
          'c_0110_6' : d['c_0101_1'],
          'c_1010_7' : negation(d['c_0101_7']),
          'c_1010_6' : negation(d['c_0101_6']),
          'c_1010_5' : d['c_1001_0'],
          'c_1010_4' : d['c_0011_0'],
          'c_1010_3' : d['c_1001_0'],
          'c_1010_2' : d['c_1001_0'],
          'c_1010_1' : d['c_1001_0'],
          '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_5, c_0101_0, c_0101_1, c_0101_6, c_0101_7, c_1001_0> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          c_0011_0 * c_0011_3 - c_0101_0^2 - c_0101_1 * c_1001_0,
          - c_0011_0 * c_0101_0 - c_0011_0^2 + c_0101_1 * c_1001_0,
          c_0011_0 * c_0011_5 - c_0011_0 * c_1001_0 + c_0101_0 * c_0101_1,
          c_0011_3^2 - c_0101_0 * c_0101_6 + c_0101_1 * c_1001_0,
          c_0011_0 * c_0011_5 + c_0011_0 * c_1001_0 + c_0101_0 * c_1001_0,
          c_0011_5^2 + c_0101_1 * c_1001_0 + c_0101_7 * c_1001_0,
          c_0011_3 * c_0101_7 + c_0101_1 * c_1001_0 + c_0101_6^2,
          c_0011_5 * c_0101_6 + c_0101_1 * c_1001_0 + c_0101_7^2,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_5 * c_0101_0 * c_0101_1 * c_0101_6 * c_0101_7 * c_1001_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);