// Preambel

print "==TRIANGULATION" cat "=BEGINS==";
print "% Triangulation\nL12n1660\ngeometric_solution  6.92737711\noriented_manifold\nCS_known 0.0000000000000002\n\n3 0\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n    torus   0.000000000000   0.000000000000\n\n8\n   1    2    3    4 \n 0132 0132 0132 0132\n   1    1    1    2 \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  1 -1  0  0  0  3 -3  0  0  0  0 -3  1  2  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.906226979623   0.965785051063\n\n   0    3    6    5 \n 0132 3120 0132 0132\n   0    1    2    1 \n  0 -1  0  1  0  0 -1  1 -1  0  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 -2  1  1  0  0  2 -2  3  0  0 -3  0  3 -3  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  1.027460617127   0.907232200914\n\n   5    0    4    6 \n 0132 0132 1302 1230\n   1    1    2    1 \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 -1  3 -2  0  0  0  0  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  0.483333451442   0.550622349810\n\n   6    1    5    0 \n 1230 3120 1230 0132\n   1    1    2    0 \n  0  1 -1  0 -1  0  0  1 -1  0  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 -3  2  1  3  0  0 -3  2  0  0 -2 -1  2 -1  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.027460617127   0.907232200914\n\n   2    7    0    7 \n 2031 0132 0132 2310\n   1    1    1    1 \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 -3  0  3  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  0.876625538290   0.639803909167\n\n   2    6    1    3 \n 0132 0213 0132 3012\n   0    1    1    2 \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  2 -2  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  0.549797992433   0.512878400111\n\n   2    3    5    1 \n 3012 3012 0213 0132\n   0    1    1    2 \n  0  0  0  0 -1  0  0  1  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  1  0 -1  2  0  0 -2  0 -3  0  3 -1 -2  3  0\n  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n  0.453113489811   0.482892525532\n\n   4    4    7    7 \n 3201 0132 2031 1302\n   1    1    1    1 \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  0.560142084391   0.177422800517\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' : negation(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' : negation(d['1']),
          's_3_0' : d['1'],
          's_2_0' : d['1'],
          's_2_1' : negation(d['1']),
          's_2_2' : d['1'],
          's_2_3' : d['1'],
          's_2_4' : d['1'],
          's_2_5' : negation(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' : negation(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_0101_3']),
          'c_1100_5' : negation(d['c_0101_3']),
          'c_1100_4' : negation(d['c_0011_4']),
          'c_1100_7' : d['c_0101_7'],
          's_3_6' : negation(d['1']),
          'c_1100_1' : negation(d['c_0101_3']),
          'c_1100_0' : negation(d['c_0011_4']),
          'c_1100_3' : negation(d['c_0011_4']),
          'c_1100_2' : d['c_0101_1'],
          'c_0101_7' : d['c_0101_7'],
          'c_0101_6' : d['c_0011_0'],
          'c_0101_5' : d['c_0011_6'],
          'c_0101_4' : d['c_0101_1'],
          'c_0101_3' : d['c_0101_3'],
          'c_0101_2' : negation(d['c_0011_4']),
          'c_0101_1' : d['c_0101_1'],
          'c_0101_0' : d['c_0011_6'],
          'c_0011_5' : d['c_0011_0'],
          'c_0011_4' : d['c_0011_4'],
          'c_0011_7' : negation(d['c_0011_4']),
          'c_0011_6' : d['c_0011_6'],
          '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' : negation(d['c_0011_3']),
          'c_1001_4' : negation(d['c_0101_7']),
          'c_1001_7' : negation(d['c_0110_7']),
          'c_1001_6' : negation(d['c_0011_3']),
          'c_1001_1' : negation(d['c_0101_3']),
          'c_1001_0' : d['c_0011_0'],
          'c_1001_3' : d['c_0101_3'],
          'c_1001_2' : negation(d['c_0101_7']),
          'c_0110_1' : d['c_0011_6'],
          'c_0110_0' : d['c_0101_1'],
          'c_0110_3' : d['c_0011_6'],
          'c_0110_2' : d['c_0011_6'],
          'c_0110_5' : negation(d['c_0011_4']),
          'c_0110_4' : negation(d['c_0101_7']),
          'c_0110_7' : d['c_0110_7'],
          'c_0110_6' : d['c_0101_1'],
          'c_1010_7' : negation(d['c_0101_7']),
          'c_1010_6' : negation(d['c_0101_3']),
          'c_1010_5' : negation(d['c_0101_3']),
          'c_1010_4' : negation(d['c_0110_7']),
          'c_1010_3' : d['c_0011_0'],
          'c_1010_2' : d['c_0011_0'],
          'c_1010_1' : negation(d['c_0011_3']),
          'c_1010_0' : negation(d['c_0101_7'])})}";
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_6, c_0101_1, c_0101_3, c_0101_7, c_0110_7> := PolynomialRing(RationalField(), 9);
I := ideal<R |
          - c_0011_0 * c_0011_4 + c_0011_0 * c_0101_1 + c_0011_6 * c_0101_7,
          c_0011_0 * c_0101_3 - c_0011_3 * c_0101_1 + c_0011_6 * c_0101_3,
          c_0011_0 * c_0011_4 - c_0011_0 * c_0101_1 - c_0011_6 * c_0101_7,
          - c_0011_0 * c_0101_3 - c_0011_3 * c_0011_4 + c_0011_6 * c_0101_3,
          - c_0011_4^2 + c_0101_1 * c_0110_7 + c_0101_7^2,
          c_0011_0 * c_0101_3 + c_0011_3 * c_0011_4 - c_0011_6 * c_0101_3,
          - c_0011_0 * c_0101_3 + c_0011_3 * c_0101_1 - c_0011_6 * c_0101_3,
          - c_0011_4 * c_0101_7 - c_0101_7^2 + c_0110_7^2,
          - 1 + c_0011_0,
          - 1 + c_0101_1,
          - 1 - c_0101_3,
          - 1 + c_0011_0 * c_0011_3 * c_0011_4 * c_0011_6 * c_0101_1 * c_0101_3 * c_0101_7 * c_0110_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);