// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL14n15036\ngeometric_solution  6.59380483\noriented_manifold\nCS_known 0.0000000000000006\n\n2 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n8\n   1    1    2    1 \n 0132 1230 0132 2031\n   1    1    0    1 \n  0  0  0  0  0  0  0  0  2 -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  1  0 -1  0  0  0  0  1 -1  0  0  1  0 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.171968019581   1.077808857529\n\n   0    0    0    3 \n 0132 1302 3012 0132\n   1    1    1    0 \n  0  0  0  0  0  0  0  0 -1  0  0  1 -2  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 -1  1 -1  1  0  0 -1  0  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.855640083077   0.904775187333\n\n   4    5    6    0 \n 0132 0132 0132 0132\n   1    1    1    1 \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  0  0  0  0  0 -1  0  1  1 -1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.405925078682   0.239333693274\n\n   4    7    1    7 \n 2103 0132 0132 2310\n   1    1    1    1 \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  1  0 -1  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  0.860504622090   0.523045912094\n\n   2    5    3    5 \n 0132 0213 2103 1230\n   1    1    1    1 \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 -1  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  0.171968019581   1.077808857529\n\n   4    2    4    6 \n 3012 0132 0213 1230\n   1    1    1    1 \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 -1  1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.724118441459   0.291724048168\n\n   5    7    7    2 \n 3012 0213 2031 0132\n   1    1    1    1 \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  0.766066196015   1.448421167212\n\n   3    3    6    6 \n 3201 0132 0213 1302\n   1    1    1    1 \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  0.579960586221   0.260850905436\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' : negation(d['1']),
          's_3_3' : d['1'],
          's_3_2' : negation(d['1']),
          's_3_5' : d['1'],
          's_3_4' : d['1'],
          's_3_7' : negation(d['1']),
          's_3_0' : d['1'],
          's_2_0' : negation(d['1']),
          's_2_1' : d['1'],
          's_2_2' : negation(d['1']),
          's_2_3' : negation(d['1']),
          's_2_4' : d['1'],
          's_2_5' : d['1'],
          's_2_6' : negation(d['1']),
          's_2_7' : d['1'],
          's_1_7' : negation(d['1']),
          's_1_6' : d['1'],
          's_1_5' : d['1'],
          's_1_4' : d['1'],
          's_1_3' : negation(d['1']),
          's_1_2' : d['1'],
          's_1_1' : d['1'],
          's_1_0' : d['1'],
          's_0_6' : d['1'],
          's_0_7' : 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' : negation(d['1']),
          's_0_1' : negation(d['1']),
          'c_1100_6' : negation(d['c_1001_3']),
          'c_1100_5' : negation(d['c_0011_2']),
          'c_1100_4' : d['c_0011_6'],
          'c_1100_7' : d['c_0101_6'],
          's_3_6' : negation(d['1']),
          'c_1100_1' : negation(d['c_0011_3']),
          'c_1100_0' : negation(d['c_1001_3']),
          'c_1100_3' : negation(d['c_0011_3']),
          'c_1100_2' : negation(d['c_1001_3']),
          'c_0101_7' : d['c_0011_6'],
          'c_0101_6' : d['c_0101_6'],
          'c_0101_5' : negation(d['c_0011_2']),
          'c_0101_4' : d['c_0101_0'],
          'c_0101_3' : d['c_0101_0'],
          'c_0101_2' : negation(d['c_0011_2']),
          'c_0101_1' : negation(d['c_0011_0']),
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : negation(d['c_0011_2']),
          'c_0011_4' : negation(d['c_0011_2']),
          'c_0011_7' : negation(d['c_0011_3']),
          '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' : d['c_0011_2'],
          'c_1001_5' : d['c_0011_3'],
          'c_1001_4' : d['c_0011_3'],
          'c_1001_7' : negation(d['c_0110_7']),
          'c_1001_6' : negation(d['c_0110_7']),
          'c_1001_1' : negation(d['c_0011_0']),
          'c_1001_0' : d['c_0011_3'],
          'c_1001_3' : d['c_1001_3'],
          'c_1001_2' : d['c_0101_6'],
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : negation(d['c_0011_0']),
          'c_0110_3' : negation(d['c_0011_6']),
          'c_0110_2' : d['c_0101_0'],
          'c_0110_5' : d['c_0011_6'],
          'c_0110_4' : negation(d['c_0011_2']),
          'c_0110_7' : d['c_0110_7'],
          'c_0110_6' : negation(d['c_0011_2']),
          'c_1010_7' : d['c_1001_3'],
          'c_1010_6' : d['c_0101_6'],
          'c_1010_5' : d['c_0101_6'],
          'c_1010_4' : negation(d['c_0011_2']),
          'c_1010_3' : negation(d['c_0110_7']),
          'c_1010_2' : d['c_0011_3'],
          'c_1010_1' : d['c_1001_3'],
          'c_1010_0' : negation(d['c_0011_0'])})}";
print "PY=EVAL=SECTION=ENDS=HERE";

cputime := Cputime();


// Computation



// Setting up the Polynomial ring and ideal

R<t, c_0011_0, c_0011_2, c_0011_3, c_0011_6, c_0101_0, c_0101_6, c_0110_7, c_1001_3> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          c_0011_0 * c_0011_3 + c_0011_0 * c_0101_0 + c_0011_0 * c_1001_3,
          - c_0011_0 * c_0011_3 - c_0011_0 * c_0101_0 - c_0011_0 * c_1001_3,
          - c_0011_2 * c_0011_3 - c_0011_2 * c_1001_3 - c_0101_0 * c_0101_6,
          c_0011_3^2 - c_0011_6 * c_1001_3 - c_0101_0 * c_0110_7,
          - c_0011_2 * c_0011_3 - c_0011_2 * c_0011_6 + c_0011_2 * c_0101_0,
          c_0011_2 * c_0101_6 + c_0011_2^2 + c_0011_3 * c_0011_6,
          - c_0011_2 * c_0110_7 - c_0011_6 * c_1001_3 + c_0101_6^2,
          c_0011_3 * c_0101_6 - c_0011_6 * c_1001_3 + c_0110_7^2,
          - 1 + c_0011_0,
          - 1 + c_0101_0,
          - 1 + c_0011_0 * c_0011_2 * c_0011_3 * c_0011_6 * c_0101_0 * c_0101_6 * c_0110_7 * c_1001_3 * 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);