// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\n8_4\ngeometric_solution  5.50048642\noriented_manifold\nCS_known -0.0000000000000001\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n6\n   1    2    3    3 \n 0132 0132 0132 1302\n   0    0    0    0 \n  0  1  0 -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 -7 -1  8  8  0 -8  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  1.327004938689   1.351922223780\n\n   0    3    5    4 \n 0132 3120 0132 0132\n   0    0    0    0 \n  0 -1  1  0  1  0  0 -1  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  7 -7  0 -8  0  1  7  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  0.461192749201   1.075526068049\n\n   5    0    3    5 \n 1023 0132 3201 3120\n   0    0    0    0 \n  0 -1  1  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  7 -7  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  0.372343707258   0.743244198804\n\n   2    1    0    0 \n 2310 3120 2031 0132\n   0    0    0    0 \n  0  0  0  0  0  0  1 -1  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 -8  8 -1  0  0  1  7 -7  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.303215286974   0.975199063032\n\n   4    5    1    4 \n 3012 3201 0132 1230\n   0    0    0    0 \n  0  0  0  0  0  0  1 -1  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 -7  7 -7  7  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.091865755064   0.648044450689\n\n   2    2    4    1 \n 3120 1023 2310 0132\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 -7  7  1  0  0 -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  0.461192749201   1.075526068049\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_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_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_5' : d['c_0011_4'],
          'c_1100_4' : d['c_0011_4'],
          'c_1100_1' : d['c_0011_4'],
          'c_1100_0' : d['c_0101_3'],
          'c_1100_3' : d['c_0101_3'],
          'c_1100_2' : negation(d['c_0011_3']),
          'c_0101_5' : d['c_0011_3'],
          'c_0101_4' : d['c_0101_0'],
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : negation(d['c_0101_0']),
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : negation(d['c_0011_0']),
          'c_0011_4' : 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_3'],
          'c_0011_2' : negation(d['c_0011_0']),
          'c_1001_5' : negation(d['c_0101_0']),
          'c_1001_4' : negation(d['c_0011_3']),
          'c_1001_1' : d['c_0101_1'],
          'c_1001_0' : d['c_0011_0'],
          'c_1001_3' : negation(d['c_0101_1']),
          'c_1001_2' : negation(d['c_0101_3']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0101_0'],
          'c_0110_2' : d['c_0101_1'],
          'c_0110_5' : d['c_0101_1'],
          'c_0110_4' : d['c_0011_4'],
          'c_1010_5' : d['c_0101_1'],
          'c_1010_4' : d['c_0101_0'],
          'c_1010_3' : d['c_0011_0'],
          'c_1010_2' : d['c_0011_0'],
          'c_1010_1' : negation(d['c_0011_3']),
          'c_1010_0' : negation(d['c_0101_3'])})}";
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_0101_0, c_0101_1, c_0101_3> := PolynomialRing(RationalField(), 7);
I := ideal<R |
          c_0011_0 * c_0101_1 + c_0011_0 * c_0101_3 + c_0101_0 * c_0101_3,
          - c_0011_0 * c_0011_4 + c_0011_3 * c_0101_1 + c_0101_0 * c_0101_1,
          c_0011_0 * c_0011_3 + c_0011_0 * c_0101_0 - c_0101_1 * c_0101_3,
          - c_0011_0 * c_0101_3 + c_0011_3 * c_0101_3 - c_0101_0 * c_0101_1,
          - c_0011_3 * c_0011_4 + c_0011_4^2 - c_0101_0^2,
          - c_0011_0 * c_0011_4 - c_0011_3 * c_0101_1 - c_0101_0 * c_0101_1,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0101_0 * c_0101_1 * c_0101_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);