// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL12n1082\ngeometric_solution  7.18575260\noriented_manifold\nCS_known 0.0000000000000000\n\n2 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n8\n   1    1    2    3 \n 0132 2310 0132 0132\n   1    0    0    1 \n  0  1 -1  0 -1  0  2 -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 -9  8  1  3  0 -7  4  3 -3  0  0  9  0 -9  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.521684081251   0.712854186683\n\n   0    4    4    0 \n 0132 0132 3201 3201\n   1    0    1    0 \n  0  0  0  0  1  0  0 -1  1  0  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  0  0  0 -3  0  0  3 -9  0  0  9 -3  0  3  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.668555432716   0.913546256000\n\n   5    5    3    0 \n 0132 3201 0213 0132\n   1    0    1    0 \n  0 -1  0  1  1  0  1 -2  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  8  0 -8 -4  0 -3  7 -8 -1  0  9 -4  4  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.068645091381   0.701254709135\n\n   6    2    0    7 \n 0132 0213 0132 0132\n   1    0    0    0 \n  0  0  0  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  0 -1  1  0  0 -4  4  0  3  0 -3  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.436367157221   0.522133338972\n\n   1    1    5    7 \n 2310 0132 0213 0321\n   1    0    0    1 \n  0  0  0  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  0  0  0 -3  0  0  3  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  0.521684081251   0.712854186683\n\n   2    4    2    7 \n 0132 0213 2310 0213\n   1    0    0    1 \n  0  0  0  0 -1  0  1  0 -1  0  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  0  1 -1  4  0 -4  0  4  0  0 -4  8  0 -8  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.345898561988   0.429227362159\n\n   3    7    6    6 \n 0132 3012 2031 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  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  0.391359558901   0.998222165631\n\n   6    4    3    5 \n 1230 0321 0132 0213\n   1    0    0    0 \n  0  0  0  0  0  0  1 -1  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 -1  1  0  0 -4  4  0  0  0  0  0 -3  3  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.954815979743   0.884514204582\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_0' : 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' : 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' : 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' : 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' : d['1'],
          's_0_1' : d['1'],
          'c_1100_6' : d['c_0101_6'],
          'c_1100_5' : d['c_0011_2'],
          'c_1100_4' : d['c_1001_7'],
          'c_1100_7' : d['c_1001_7'],
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0011_0']),
          'c_1100_0' : d['c_1001_7'],
          'c_1100_3' : d['c_1001_7'],
          'c_1100_2' : d['c_1001_7'],
          'c_0101_7' : d['c_0101_6'],
          'c_0101_6' : d['c_0101_6'],
          'c_0101_5' : d['c_0101_0'],
          'c_0101_4' : negation(d['c_0011_2']),
          'c_0101_3' : d['c_0011_7'],
          'c_0101_2' : d['c_0011_3'],
          'c_0101_1' : d['c_0011_7'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : negation(d['c_0011_2']),
          'c_0011_4' : d['c_0011_0'],
          'c_0011_7' : d['c_0011_7'],
          'c_0011_6' : negation(d['c_0011_3']),
          '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' : negation(d['c_1001_0']),
          'c_1001_4' : negation(d['c_1001_0']),
          'c_1001_7' : d['c_1001_7'],
          'c_1001_6' : negation(d['c_0011_7']),
          'c_1001_1' : d['c_0011_2'],
          'c_1001_0' : d['c_1001_0'],
          'c_1001_3' : negation(d['c_0101_0']),
          'c_1001_2' : negation(d['c_0101_0']),
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0011_7'],
          'c_0110_3' : d['c_0101_6'],
          'c_0110_2' : d['c_0101_0'],
          'c_0110_5' : d['c_0011_3'],
          'c_0110_4' : negation(d['c_0011_7']),
          'c_0110_7' : negation(d['c_0011_3']),
          'c_0110_6' : d['c_0011_7'],
          'c_1010_7' : d['c_0011_2'],
          'c_1010_6' : negation(d['c_0101_6']),
          'c_1010_5' : d['c_1001_7'],
          'c_1010_4' : d['c_0011_2'],
          'c_1010_3' : d['c_1001_7'],
          'c_1010_2' : d['c_1001_0'],
          'c_1010_1' : negation(d['c_1001_0']),
          'c_1010_0' : negation(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_3, c_0011_7, c_0101_0, c_0101_6, c_1001_0, c_1001_7> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          c_0011_0 * c_1001_7 - c_0011_7 * c_1001_0 - c_0101_0^2,
          c_0011_0^2 + c_0011_2 * c_0101_0 + c_0011_7 * c_1001_0,
          c_0011_2 * c_1001_7 + c_0011_3 * c_1001_0 + c_0101_0^2,
          - c_0011_3 * c_1001_7 + c_0011_7 * c_1001_7 - c_0101_0 * c_0101_6,
          c_0011_0 * c_1001_7 + c_0011_2^2 + c_0011_7 * c_1001_0,
          - c_0011_2^2 - c_0011_3 * c_1001_0 - c_0101_0 * c_1001_7,
          - c_0011_3 * c_0101_6 - c_0011_7^2 + c_0101_6^2,
          - c_0011_2 * c_0101_6 - c_0011_3 * c_1001_7 + c_0011_7 * c_1001_7,
          - 1 + c_0011_0,
          - 1 + c_0011_7,
          - 1 + c_0011_0 * c_0011_2 * c_0011_3 * c_0011_7 * c_0101_0 * c_0101_6 * c_1001_0 * c_1001_7 * 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);