// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nK12a1157\ngeometric_solution  6.28957675\noriented_manifold\nCS_known -0.0000000000000004\n\n1 0\n    torus   0.000000000000   0.000000000000\n\n8\n   1    2    3    4 \n 0132 0132 0132 0132\n   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 -1  0  1 14  0 -14  0 -15 15  0  0  1  0 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.445725557089   0.633077419799\n\n   0    5    4    5 \n 0132 0132 1230 1230\n   0    0    0    0 \n  0  0  0  0  1  0 -1  0  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 -14  0 14  0 -1  1  0  0 15  0 -15  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.782865570445   0.894168081760\n\n   6    0    3    5 \n 0132 0132 0213 3012\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  1  0 -1  0  0  0  0  0  0  0  0 15 -15  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.772343597327   0.300527638631\n\n   6    2    5    0 \n 1230 0213 2031 0132\n   0    0    0    0 \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 -14  0  0 14 -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 -1.078536885384   1.177528617168\n\n   4    4    0    1 \n 1302 2031 0132 3012\n   0    0    0    0 \n  0  1  0 -1  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 -14 -1 15  0  0  0  0 14  0  0 -14  0  0  0  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.613487583890   1.201762094929\n\n   1    1    2    3 \n 3012 0132 1230 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 -1  1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.256452762004   1.056082514101\n\n   2    3    7    7 \n 0132 3012 0132 3201\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 -15 14  0  1  0  1 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.699024941492   0.528844444090\n\n   7    6    7    6 \n 2310 2310 3201 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 -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 -1.012589614226   0.339880843558\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' : d['1'],
          's_3_3' : negation(d['1']),
          's_3_2' : 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' : 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' : negation(d['1']),
          's_1_5' : d['1'],
          's_1_4' : d['1'],
          's_1_3' : d['1'],
          's_1_2' : negation(d['1']),
          's_1_1' : d['1'],
          's_1_0' : negation(d['1']),
          's_0_6' : negation(d['1']),
          's_0_7' : d['1'],
          's_0_4' : d['1'],
          's_0_5' : d['1'],
          's_0_2' : negation(d['1']),
          's_0_3' : negation(d['1']),
          's_0_0' : d['1'],
          's_0_1' : d['1'],
          'c_1100_6' : negation(d['c_0011_7']),
          'c_1100_5' : d['c_0101_3'],
          'c_1100_4' : negation(d['c_1001_1']),
          'c_1100_7' : negation(d['c_0011_7']),
          's_3_6' : d['1'],
          'c_1100_1' : d['c_0110_4'],
          'c_1100_0' : negation(d['c_1001_1']),
          'c_1100_3' : negation(d['c_1001_1']),
          'c_1100_2' : negation(d['c_0101_5']),
          'c_0101_7' : negation(d['c_0101_3']),
          'c_0101_6' : d['c_0101_3'],
          'c_0101_5' : d['c_0101_5'],
          'c_0101_4' : negation(d['c_0011_4']),
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : d['c_0011_3'],
          'c_0101_1' : negation(d['c_0011_4']),
          'c_0101_0' : d['c_0011_0'],
          'c_0011_5' : d['c_0011_0'],
          'c_0011_4' : d['c_0011_4'],
          'c_0011_7' : d['c_0011_7'],
          'c_0011_6' : d['c_0011_0'],
          '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' : d['c_0101_5'],
          'c_1001_4' : negation(d['c_0110_4']),
          'c_1001_7' : d['c_0101_3'],
          'c_1001_6' : negation(d['c_0011_3']),
          'c_1001_1' : d['c_1001_1'],
          'c_1001_0' : negation(d['c_0101_5']),
          'c_1001_3' : negation(d['c_0110_4']),
          'c_1001_2' : negation(d['c_0110_4']),
          'c_0110_1' : d['c_0011_0'],
          'c_0110_0' : negation(d['c_0011_4']),
          'c_0110_3' : d['c_0011_0'],
          'c_0110_2' : d['c_0101_3'],
          'c_0110_5' : d['c_0110_4'],
          'c_0110_4' : d['c_0110_4'],
          'c_0110_7' : d['c_0101_3'],
          'c_0110_6' : d['c_0011_3'],
          'c_1010_7' : negation(d['c_0011_3']),
          'c_1010_6' : negation(d['c_0101_3']),
          'c_1010_5' : d['c_1001_1'],
          'c_1010_4' : d['c_0011_4'],
          'c_1010_3' : negation(d['c_0101_5']),
          'c_1010_2' : negation(d['c_0101_5']),
          'c_1010_1' : d['c_0101_5'],
          'c_1010_0' : negation(d['c_0110_4'])})}";
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_0011_7, c_0101_3, c_0101_5, c_0110_4, c_1001_1> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          - c_0011_0 * c_0110_4 + c_0011_0 * c_1001_1 + c_0011_4 * c_0101_5,
          - c_0011_0 * c_0110_4 + c_0011_0 * c_1001_1 + c_0011_4 * c_0101_5,
          c_0011_0 * c_0101_5 - c_0011_3 * c_0101_5 + c_0101_3 * c_0110_4,
          - c_0011_0 * c_0110_4 + c_0011_3 * c_1001_1 - c_0101_3 * c_0101_5,
          - c_0011_4 * c_1001_1 + c_0011_4^2 - c_0110_4^2,
          c_0011_0 * c_0101_3 + c_0101_5 * c_0110_4 - c_0101_5 * c_1001_1,
          - c_0011_0 * c_0011_7 + c_0011_3^2 - c_0101_3^2,
          - c_0011_3 * c_0101_3 - c_0011_7^2 + c_0101_3^2,
          - 1 + c_0011_0,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0011_7 * c_0101_3 * c_0101_5 * c_0110_4 * c_1001_1 * 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);