// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nv2984\ngeometric_solution  6.16423507\noriented_manifold\nCS_known 0.0000000000000000\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n7\n   1    2    1    3 \n 0132 0132 2031 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  1 -1  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  0.409580395075   0.941176527096\n\n   0    3    4    0 \n 0132 3120 0132 1302\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  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  0.611244961654   0.893321851536\n\n   5    0    6    4 \n 0132 0132 0132 1302\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 -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  0.840303039855   1.431634640447\n\n   6    1    0    5 \n 0213 3120 0132 0213\n   0    0    0    0 \n  0 -1  0  1  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  1 -1  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  0.136964601058   0.643797066178\n\n   5    6    2    1 \n 2310 2103 2031 0132\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 -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  0.989082839761   1.151117846192\n\n   2    6    4    3 \n 0132 1230 3201 0213\n   0    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  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  0.566373837738   0.144040508091\n\n   3    4    5    2 \n 0213 2103 3012 0132\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  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  0.394383044358   0.794431027020\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_0101_4'],
          'c_1100_5' : d['c_0011_0'],
          'c_1100_4' : d['c_0101_0'],
          's_3_6' : d['1'],
          'c_1100_1' : d['c_0101_0'],
          'c_1100_0' : d['c_0011_3'],
          'c_1100_3' : d['c_0011_3'],
          'c_1100_2' : d['c_0101_4'],
          'c_0101_6' : d['c_0011_3'],
          'c_0101_5' : negation(d['c_0011_6']),
          'c_0101_4' : d['c_0101_4'],
          'c_0101_3' : d['c_0011_6'],
          'c_0101_2' : d['c_0101_2'],
          'c_0101_1' : d['c_0011_6'],
          '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_0101_4']),
          'c_1001_4' : d['c_0011_6'],
          'c_1001_6' : negation(d['c_0011_0']),
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : negation(d['c_0101_0']),
          'c_1001_3' : negation(d['c_1001_1']),
          'c_1001_2' : negation(d['c_1001_1']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0011_6'],
          'c_0110_3' : negation(d['c_0101_2']),
          'c_0110_2' : negation(d['c_0011_6']),
          'c_0110_5' : d['c_0101_2'],
          'c_0110_4' : d['c_0011_6'],
          'c_0110_6' : d['c_0101_2'],
          'c_1010_6' : negation(d['c_1001_1']),
          'c_1010_5' : d['c_0011_3'],
          'c_1010_4' : d['c_1001_1'],
          'c_1010_3' : d['c_0011_0'],
          'c_1010_2' : negation(d['c_0101_0']),
          'c_1010_1' : negation(d['c_0011_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_6, c_0101_0, c_0101_2, c_0101_4, c_1001_1> := PolynomialRing(RationalField(), 8);
I := ideal<R |
          c_0011_0 * c_0011_3 - c_0011_6 * c_0101_0 + c_0101_0 * c_1001_1,
          - c_0011_0 * c_0101_0 + c_0011_3 * c_0011_6 + c_0101_0 * c_1001_1,
          - c_0011_0 * c_0101_4 + c_0011_6 * c_1001_1 + c_0101_0 * c_0101_2,
          - c_0011_0 * c_0011_6 + c_0011_3^2 + c_0101_2 * c_1001_1,
          - c_0011_0 * c_0101_0 + c_0011_6^2 - c_0101_4 * c_1001_1,
          c_0011_0^2 + c_0011_3 * c_0011_6 - c_0101_2 * c_0101_4,
          - c_0011_0 * c_0101_2 + c_0011_3 * c_1001_1 + c_0011_6 * c_0101_4,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_6 * c_0101_0 * c_0101_2 * c_0101_4 * c_1001_1 * 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);