// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nv0793\ngeometric_solution  4.73281167\noriented_manifold\nCS_known 0.0000000000000001\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n7\n   1    0    1    0 \n 0132 1302 1023 2031\n   0    0    0    0 \n  0 -1  0  1  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 -1  0  1  0  0 -1  1  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  0.420806345623   0.108340259301\n\n   0    2    0    2 \n 0132 0132 1023 2310\n   0    0    0    0 \n  0 -1  1  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 -1  1  0  0  0  0  0 -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 -0.180379534904   1.409986098889\n\n   1    1    3    4 \n 3201 0132 0132 0132\n   0    0    0    0 \n  0  1 -1  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  1 -1  0 -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 -0.906693983817   1.250293295367\n\n   4    4    5    2 \n 1230 1023 0132 0132\n   0    0    0    0 \n  0  0 -1  1  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  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  0.563900253803   1.280759834661\n\n   3    3    2    5 \n 1023 3012 0132 3201\n   0    0    0    0 \n  0  0  0  0  0  0  1 -1  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  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.563900253803   1.280759834661\n\n   6    4    6    3 \n 0132 2310 1023 0132\n   0    0    0    0 \n  0  0 -1  1  1  0  0 -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  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  0.541952226190   0.395587569979\n\n   5    6    5    6 \n 0132 1302 1023 2031\n   0    0    0    0 \n  0  0  0  0 -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  0  0 -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  0.564432171482   0.088549967268\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' : negation(d['1']),
          's_3_5' : d['1'],
          's_3_4' : 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' : d['1'],
          's_2_4' : negation(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' : negation(d['1']),
          's_1_3' : d['1'],
          's_1_2' : d['1'],
          's_1_1' : d['1'],
          's_1_0' : negation(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' : negation(d['1']),
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_6' : d['c_0011_5'],
          'c_1100_5' : negation(d['c_0011_5']),
          'c_1100_4' : negation(d['c_0011_5']),
          's_3_6' : d['1'],
          'c_1100_1' : d['c_0011_0'],
          'c_1100_0' : negation(d['c_0011_0']),
          'c_1100_3' : negation(d['c_0011_5']),
          'c_1100_2' : negation(d['c_0011_5']),
          'c_0101_6' : d['c_0101_3'],
          'c_0101_5' : d['c_0101_5'],
          'c_0101_4' : d['c_0101_4'],
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : d['c_0011_3'],
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : negation(d['c_0011_3']),
          'c_0011_5' : d['c_0011_5'],
          'c_0011_4' : d['c_0011_3'],
          'c_0011_6' : negation(d['c_0011_5']),
          '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_0'],
          'c_1001_5' : d['c_0101_3'],
          'c_1001_4' : negation(d['c_0011_3']),
          'c_1001_6' : d['c_0101_5'],
          'c_1001_1' : negation(d['c_0011_3']),
          'c_1001_0' : d['c_0101_1'],
          'c_1001_3' : d['c_0101_4'],
          'c_1001_2' : negation(d['c_0101_4']),
          'c_0110_1' : negation(d['c_0011_3']),
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0011_3'],
          'c_0110_2' : d['c_0101_4'],
          'c_0110_5' : d['c_0101_3'],
          'c_0110_4' : negation(d['c_0101_4']),
          'c_0110_6' : d['c_0101_5'],
          'c_1010_6' : negation(d['c_0011_5']),
          'c_1010_5' : d['c_0101_4'],
          'c_1010_4' : negation(d['c_0101_3']),
          'c_1010_3' : negation(d['c_0101_4']),
          'c_1010_2' : negation(d['c_0011_3']),
          'c_1010_1' : negation(d['c_0101_4']),
          'c_1010_0' : d['c_0011_0']})}";
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_5, c_0101_1, c_0101_3, c_0101_4, c_0101_5> := PolynomialRing(RationalField(), 8);
I := ideal<R |
          c_0011_0 * c_0011_3 + c_0011_0^2 - c_0101_1^2,
          - c_0011_0^2 + c_0011_3^2 + c_0101_1 * c_0101_4,
          - c_0011_0 * c_0011_5 - c_0011_3^2 + c_0101_4^2,
          c_0011_3 * c_0011_5 + c_0011_3 * c_0101_4 - c_0101_3 * c_0101_4,
          c_0011_3 * c_0011_5 + c_0011_3 * c_0101_4 - c_0101_3 * c_0101_4,
          - c_0011_5^2 + c_0101_3^2 - c_0101_4 * c_0101_5,
          c_0011_5 * c_0101_3 - c_0011_5^2 + c_0101_5^2,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_5 * c_0101_1 * c_0101_3 * c_0101_4 * c_0101_5 * 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);