// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL14a21812\nflat_solution  0.00000000\noriented_manifold\nCS_unknown\n\n2 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n8\n   0    1    1    0 \n 3012 0132 1023 1230\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  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  1.445041867913   0.000000000000\n\n   2    0    0    2 \n 0132 0132 1023 1023\n   0    0    0    0 \n  0 -1  0  1  0  0  1 -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  0 -7  0  0 -7  7  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  1.246979603717   0.000000000000\n\n   1    3    4    1 \n 0132 0132 0132 1023\n   0    0    0    0 \n  0  0 -1  1  0  0  1 -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  7 -7  0  0 -7  7  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  1.246979603717   0.000000000000\n\n   3    2    5    3 \n 3012 0132 0132 1230\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  1.445041867913   0.000000000000\n\n   6    6    5    2 \n 0132 1302 1023 0132\n   0    0    0    1 \n  0  0 -1  1  0  0  1 -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  7 -7 -1  0 -6  7  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 -0.801937735805   0.000000000000\n\n   7    7    4    3 \n 0132 1302 1023 0132\n   0    0    0    1 \n  0  1 -1  0 -1  0  1  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 -6  6  0  7  0 -7  0  0  0  0  0 -7  8 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -1.246979603717   0.000000000000\n\n   4    7    7    4 \n 0132 3120 3120 2031\n   0    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  0  0  0  0\n  0  0  0  0  1  0 -1  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  0.554958132087   0.000000000000\n\n   5    6    6    5 \n 0132 3120 3120 2031\n   0    0    1    0 \n  0  0  0  0  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  0  0  0 -7  0  1  6  7  1  0 -8  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.445041867913   0.000000000000\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' : negation(d['1']),
          's_3_4' : negation(d['1']),
          's_3_7' : d['1'],
          's_3_0' : negation(d['1']),
          's_2_0' : 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' : negation(d['1']),
          's_2_7' : negation(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' : negation(d['1']),
          's_1_1' : d['1'],
          's_1_0' : d['1'],
          's_0_6' : negation(d['1']),
          's_0_7' : negation(d['1']),
          's_0_4' : negation(d['1']),
          's_0_5' : negation(d['1']),
          's_0_2' : d['1'],
          's_0_3' : d['1'],
          's_0_0' : negation(d['1']),
          's_0_1' : d['1'],
          'c_1100_6' : negation(d['c_0101_3']),
          'c_1100_5' : negation(d['c_0011_0']),
          'c_1100_4' : d['c_0011_0'],
          'c_1100_7' : negation(d['c_0101_2']),
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0011_0']),
          'c_1100_0' : d['c_0011_0'],
          'c_1100_3' : negation(d['c_0011_0']),
          'c_1100_2' : d['c_0011_0'],
          'c_0101_7' : d['c_0101_3'],
          'c_0101_6' : d['c_0101_2'],
          'c_0101_5' : d['c_0101_4'],
          'c_0101_4' : d['c_0101_4'],
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : d['c_0101_2'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : d['c_0011_4'],
          'c_0011_4' : d['c_0011_4'],
          'c_0011_7' : negation(d['c_0011_4']),
          'c_0011_6' : negation(d['c_0011_4']),
          'c_0011_1' : negation(d['c_0011_0']),
          'c_0011_0' : d['c_0011_0'],
          'c_0011_3' : negation(d['c_0011_0']),
          'c_0011_2' : d['c_0011_0'],
          'c_1001_5' : d['c_0101_4'],
          'c_1001_4' : d['c_0101_4'],
          'c_1001_7' : negation(d['c_1001_6']),
          'c_1001_6' : d['c_1001_6'],
          'c_1001_1' : d['c_0101_0'],
          'c_1001_0' : d['c_0101_1'],
          'c_1001_3' : d['c_0101_2'],
          'c_1001_2' : d['c_0101_3'],
          'c_0110_1' : d['c_0101_2'],
          'c_0110_0' : d['c_0011_0'],
          'c_0110_3' : negation(d['c_0011_0']),
          'c_0110_2' : d['c_0101_1'],
          'c_0110_5' : d['c_0101_3'],
          'c_0110_4' : d['c_0101_2'],
          'c_0110_7' : d['c_0101_4'],
          'c_0110_6' : d['c_0101_4'],
          'c_1010_7' : d['c_0011_4'],
          'c_1010_6' : d['c_0011_4'],
          'c_1010_5' : d['c_0101_2'],
          'c_1010_4' : d['c_0101_3'],
          'c_1010_3' : d['c_0101_3'],
          'c_1010_2' : d['c_0101_2'],
          'c_1010_1' : d['c_0101_1'],
          '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_4, c_0101_0, c_0101_1, c_0101_2, c_0101_3, c_0101_4, c_1001_6> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          c_0011_0 * c_0101_1 - c_0011_0^2 + c_0101_0^2,
          c_0011_0^2 + c_0101_0 * c_0101_2 - c_0101_1^2,
          - c_0011_0^2 + c_0101_1 * c_0101_3 + c_0101_2^2,
          - c_0011_0 * c_0101_2 - c_0011_0^2 + c_0101_3^2,
          - c_0011_0 * c_0011_4 + c_0101_2 * c_0101_4 + c_0101_3 * c_0101_4,
          c_0011_0 * c_0011_4 + c_0101_2 * c_0101_4 + c_0101_3 * c_0101_4,
          - c_0011_4 * c_0101_2 - c_0011_4 * c_0101_3 - c_0101_4 * c_1001_6,
          - c_0011_4 * c_0101_2 - c_0011_4 * c_0101_3 + c_0101_4 * c_1001_6,
          - 1 + c_0011_0,
          - 1 + c_0011_4,
          - 1 + c_0011_0 * c_0011_4 * c_0101_0 * c_0101_1 * c_0101_2 * c_0101_3 * c_0101_4 * c_1001_6 * 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);