// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK12n749\ngeometric_solution  5.98614936\noriented_manifold\nCS_known 0.0000000000000002\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n8\n   1    0    0    2 \n 0132 1230 3012 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 -1  0  1  0 -1  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  0.420769652217   0.695227054783\n\n   0    3    5    4 \n 0132 0132 0132 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  4 -4 -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  1.859178510584   0.612652554603\n\n   5    6    0    6 \n 0132 0132 0132 1023\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  0  0  0  4 -5  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.222023070973   1.665408373341\n\n   7    1    7    4 \n 0132 0132 1023 2031\n   0    0    0    0 \n  0  0 -1  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  0  5 -5 -5  0  5  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  0.489937349152   0.675116000427\n\n   5    3    1    5 \n 2103 1302 0132 2031\n   0    0    0    0 \n  0  0 -1  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  0  0  4 -4  0  0 -1  1 -5  5  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.228419672017   0.550189108778\n\n   2    4    4    1 \n 0132 1302 2103 0132\n   0    0    0    0 \n  0  0 -1  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  0 -1  5 -4  0  0  0  0 -4  4  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n -0.064416388051   0.855109747776\n\n   7    2    7    2 \n 3201 0132 2310 1023\n   0    0    0    0 \n  0  0  0  0  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  0  0  0  0  0  0  0  0 -5  5  0  0  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.554361283144   0.296862314590\n\n   3    6    3    6 \n 0132 3201 1023 2310\n   0    0    0    0 \n  0  0  1 -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  0 -5  5  5  0 -5  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  0.612405083223   0.189746298105\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_7' : 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_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' : 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' : negation(d['c_0011_0']),
          'c_1100_5' : negation(d['c_0011_4']),
          'c_1100_4' : negation(d['c_0011_4']),
          'c_1100_7' : negation(d['c_0011_2']),
          's_3_6' : d['1'],
          'c_1100_1' : negation(d['c_0011_4']),
          'c_1100_0' : d['c_0011_0'],
          'c_1100_3' : d['c_0011_2'],
          'c_1100_2' : d['c_0011_0'],
          'c_0101_7' : d['c_0101_7'],
          'c_0101_6' : negation(d['c_0101_3']),
          'c_0101_5' : d['c_0101_0'],
          'c_0101_4' : d['c_0101_0'],
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : d['c_0101_1'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0101_0'],
          'c_0011_5' : negation(d['c_0011_2']),
          'c_0011_4' : d['c_0011_4'],
          'c_0011_7' : negation(d['c_0011_0']),
          'c_0011_6' : negation(d['c_0011_2']),
          '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_0011_4'],
          'c_1001_4' : d['c_0101_7'],
          'c_1001_7' : d['c_0101_3'],
          'c_1001_6' : d['c_0110_6'],
          'c_1001_1' : d['c_0011_4'],
          'c_1001_0' : negation(d['c_0011_0']),
          'c_1001_3' : d['c_0101_7'],
          'c_1001_2' : d['c_0101_0'],
          'c_0110_1' : d['c_0101_0'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0101_7'],
          'c_0110_2' : d['c_0101_0'],
          'c_0110_5' : d['c_0101_1'],
          'c_0110_4' : d['c_0011_4'],
          'c_0110_7' : d['c_0101_3'],
          'c_0110_6' : d['c_0110_6'],
          'c_1010_7' : negation(d['c_0110_6']),
          'c_1010_6' : d['c_0101_0'],
          'c_1010_5' : d['c_0011_4'],
          'c_1010_4' : negation(d['c_0011_2']),
          'c_1010_3' : d['c_0011_4'],
          'c_1010_2' : d['c_0110_6'],
          'c_1010_1' : d['c_0101_7'],
          '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_1, c_0101_3, c_0101_7, c_0110_6> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          - c_0011_0 * c_0101_1 + c_0011_0^2 - c_0101_0^2,
          c_0011_0 * c_0011_4 + c_0011_4 * c_0101_0 - c_0101_1 * c_0101_7,
          c_0011_0 * c_0011_2 + c_0101_0^2 - c_0101_1 * c_0110_6,
          c_0011_0 * c_0011_2 - c_0011_4 * c_0101_3 + c_0101_7^2,
          c_0011_2 * c_0101_0 + c_0011_4 * c_0101_7 - c_0011_4^2,
          c_0011_2 * c_0011_4 - c_0011_4 * c_0101_0 + c_0011_4 * c_0101_1,
          c_0011_0 * c_0011_2 + c_0101_0 * c_0101_3 + c_0110_6^2,
          c_0011_0 * c_0011_2 + c_0101_3^2 + c_0101_7 * c_0110_6,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_2 * c_0011_4 * c_0101_0 * c_0101_1 * c_0101_3 * c_0101_7 * c_0110_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);