// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\n10_161\ngeometric_solution  5.63877295\noriented_manifold\nCS_known 0.0000000000000002\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n7\n   0    1    2    0 \n 3012 0132 0132 1230\n   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  0 -1  1 -1  0  0  1 -1 -8  0  9 -9  9  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.359228803262   0.594338367165\n\n   3    0    2    4 \n 0132 0132 1302 0132\n   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  0  0  0  0  0  0  0  0 -9  0  9 -9  8  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.540002612013   0.580668832822\n\n   1    5    6    0 \n 2031 0132 0132 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 -1  0  1  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  1.342331118200   0.703502081734\n\n   1    3    6    3 \n 0132 1302 1023 2031\n   0    0    0    0 \n  0  0  0  0  0  0  0  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  0  0  0  0  9  0  0 -9  0  9 -9  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.759815142066   1.019874351229\n\n   6    5    1    6 \n 1023 0213 0132 1230\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  0  0  0  0  0  0  9  0 -9  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.548064703195   0.792918996048\n\n   5    2    4    5 \n 3201 0132 0213 2310\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  1  0 -1  1  0  0 -1  1  0  0 -1  1 -1  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.375083882825   0.459715029893\n\n   4    4    3    2 \n 3012 1023 1023 0132\n   0    0    0    0 \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  0  0  0  0  0 -9  9  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.493460392091   0.173964841139\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' : negation(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' : 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_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_0'],
          'c_1100_5' : negation(d['c_0011_2']),
          'c_1100_4' : d['c_0101_2'],
          's_3_6' : d['1'],
          'c_1100_1' : d['c_0101_2'],
          'c_1100_0' : d['c_0011_0'],
          'c_1100_3' : negation(d['c_0011_0']),
          'c_1100_2' : d['c_0011_0'],
          'c_0101_6' : negation(d['c_0011_2']),
          'c_0101_5' : d['c_0011_4'],
          'c_0101_4' : d['c_0101_3'],
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : d['c_0101_2'],
          'c_0101_1' : negation(d['c_0011_2']),
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : negation(d['c_0011_2']),
          'c_0011_4' : d['c_0011_4'],
          'c_0011_6' : d['c_0011_4'],
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          'c_0011_3' : d['c_0011_0'],
          'c_0011_2' : d['c_0011_2'],
          'c_1001_5' : d['c_1001_0'],
          'c_1001_4' : d['c_1001_0'],
          'c_1001_6' : d['c_0101_3'],
          'c_1001_1' : d['c_0101_0'],
          'c_1001_0' : d['c_1001_0'],
          'c_1001_3' : negation(d['c_0011_2']),
          'c_1001_2' : d['c_0011_4'],
          'c_0110_1' : d['c_0101_3'],
          'c_0110_0' : d['c_0011_0'],
          'c_0110_3' : negation(d['c_0011_2']),
          'c_0110_2' : d['c_0101_0'],
          'c_0110_5' : negation(d['c_0011_4']),
          'c_0110_4' : d['c_0011_4'],
          'c_0110_6' : d['c_0101_2'],
          'c_1010_6' : d['c_0011_4'],
          'c_1010_5' : d['c_0011_4'],
          'c_1010_4' : negation(d['c_0011_2']),
          'c_1010_3' : d['c_0011_0'],
          'c_1010_2' : d['c_1001_0'],
          'c_1010_1' : d['c_1001_0'],
          'c_1010_0' : 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_2, c_0011_4, c_0101_0, c_0101_2, c_0101_3, c_1001_0> := PolynomialRing(RationalField(), 8);
I := ideal<R |
          c_0011_0 * c_1001_0 + c_0011_0^2 - c_0101_0^2,
          - c_0011_0 * c_0101_2 + c_0011_2 * c_1001_0 + c_0101_0 * c_0101_3,
          c_0011_0 * c_0011_2 + c_0011_4 * c_0101_0 - c_0101_2 * c_1001_0,
          - c_0011_0 * c_0101_3 + c_0011_0^2 - c_0011_2^2,
          c_0011_2 * c_0101_3 + c_0011_4 * c_0101_2 + c_0011_4 * c_1001_0,
          c_0011_2^2 - c_0011_4 * c_1001_0 - c_0011_4^2,
          c_0011_0 * c_0011_4 + c_0011_2 * c_0011_4 + c_0101_2 * c_0101_3,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_2 * c_0011_4 * c_0101_0 * c_0101_2 * c_0101_3 * 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);