// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL11n210\ngeometric_solution  7.39753978\noriented_manifold\nCS_known -0.0000000000000001\n\n2 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n8\n   1    2    3    4 \n 0132 0132 0132 0132\n   1    0    1    0 \n  0  0  0  0  1  0  0 -1  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 -1  1  0 -3  0  1  2  1  3  0 -4  0 -2  2  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.025386582545   0.673869459198\n\n   0    5    2    6 \n 0132 0132 3120 0132\n   1    0    0    1 \n  0  0 -1  1 -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  0 -3  3  3  0 -3  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  0.318914292276   0.447599827562\n\n   4    0    1    5 \n 0213 0132 3120 2310\n   1    0    0    1 \n  0  0  0  0  1  0 -1  0  1 -1  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 -1  0 -3  0  3  0 -2  2  0  0  0 -3  3  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.147283692575   0.689499158795\n\n   7    4    6    0 \n 0132 0321 0213 0132\n   1    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  1 -1  0  0  1 -1 -1  3  0 -2  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.967591309734   0.838314632758\n\n   2    5    0    3 \n 0213 2310 0132 0321\n   1    0    0    1 \n  0  0  0  0 -1  0  1  0 -1  0  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  0  0  0  2  0 -2  0  3  0  0 -3  0 -4  4  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.564493186909   0.790623468771\n\n   2    1    6    4 \n 3201 0132 0132 3201\n   1    0    1    0 \n  0  0 -1  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  0 -4  4  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  0.534527068654   0.970385841205\n\n   7    3    1    5 \n 2103 0213 0132 0132\n   1    0    0    0 \n  0  0 -1  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 -3  4  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  0.046046730465   1.191089415307\n\n   3    7    6    7 \n 0132 2310 2103 3201\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 -1  1  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  0.724983630995   0.903376684085\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' : 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' : 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_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' : d['1'],
          's_0_1' : d['1'],
          'c_1100_6' : negation(d['c_0011_4']),
          'c_1100_5' : negation(d['c_0011_4']),
          'c_1100_4' : d['c_1001_3'],
          'c_1100_7' : d['c_0011_3'],
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0011_4']),
          'c_1100_0' : d['c_1001_3'],
          'c_1100_3' : d['c_1001_3'],
          'c_1100_2' : d['c_0011_0'],
          'c_0101_7' : d['c_0101_0'],
          'c_0101_6' : d['c_0101_0'],
          'c_0101_5' : negation(d['c_0011_3']),
          'c_0101_4' : negation(d['c_0011_0']),
          'c_0101_3' : d['c_0011_6'],
          'c_0101_2' : d['c_0011_4'],
          'c_0101_1' : negation(d['c_0011_0']),
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_0'],
          'c_0011_4' : d['c_0011_4'],
          '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' : negation(d['c_0011_0']),
          'c_1001_5' : d['c_1001_3'],
          'c_1001_4' : negation(d['c_1001_1']),
          'c_1001_7' : d['c_0011_6'],
          'c_1001_6' : d['c_1001_3'],
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : negation(d['c_0110_5']),
          'c_1001_3' : d['c_1001_3'],
          'c_1001_2' : negation(d['c_1001_1']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : negation(d['c_0011_0']),
          'c_0110_3' : d['c_0101_0'],
          'c_0110_2' : d['c_0011_3'],
          'c_0110_5' : d['c_0110_5'],
          'c_0110_4' : negation(d['c_0011_3']),
          'c_0110_7' : d['c_0011_6'],
          'c_0110_6' : negation(d['c_0011_3']),
          'c_1010_7' : negation(d['c_0011_6']),
          'c_1010_6' : d['c_1001_3'],
          'c_1010_5' : d['c_1001_1'],
          'c_1010_4' : negation(d['c_0110_5']),
          'c_1010_3' : negation(d['c_0110_5']),
          'c_1010_2' : negation(d['c_0110_5']),
          'c_1010_1' : d['c_1001_3'],
          'c_1010_0' : negation(d['c_1001_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_4, c_0011_6, c_0101_0, c_0110_5, c_1001_1, c_1001_3> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          c_0011_0 * c_0110_5 + c_0011_0 * c_1001_3 + c_0101_0 * c_1001_1,
          c_0011_0 * c_0011_4 + c_0011_0 * c_1001_3 + c_0101_0 * c_1001_1,
          - c_0011_0^2 - c_0011_3 * c_1001_1 + c_0011_4 * c_0110_5,
          c_0011_3 * c_1001_3 + c_0011_6 * c_0110_5 + c_0101_0 * c_1001_3,
          - c_0011_0 * c_0110_5 + c_0011_3 * c_1001_1 + c_0011_4 * c_1001_3,
          - c_0011_0 * c_0011_4 + c_0011_3 * c_1001_1 + c_0110_5 * c_1001_3,
          - c_0011_3 * c_1001_3 - c_0011_4 * c_0011_6 - c_0101_0 * c_1001_3,
          - c_0011_3^2 + c_0011_6 * c_0101_0 + c_0011_6^2,
          - 1 + c_0011_0,
          - 1 + c_0101_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0011_6 * c_0101_0 * c_0110_5 * c_1001_1 * 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);