// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_419\ngeometric_solution 13.98207661\noriented_manifold\nCS_known 0.0000000000000002\n\n1 0\n torus 0.000000000000 0.000000000000\n\n15\n 1 2 3 2 \n 0132 0132 0132 0213\n 0 0 0 0 \n 0 0 0 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 0 1 -1 0 0 0 0 -7 0 0 7 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.462027389364 1.432009751707\n\n 0 4 6 5 \n 0132 0132 0132 0132\n 0 0 0 0 \n 0 0 -1 1 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 6 -6 0 0 0 0 0 1 0 -1 7 -7 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.353783630829 0.984554683523\n\n 7 0 8 0 \n 0132 0132 0132 0213\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 -1 1 7 0 0 -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 0.462027389364 1.432009751707\n\n 4 9 9 0 \n 2310 0132 0321 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 0 -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 0.642067861300 1.019522945044\n\n 7 1 3 10 \n 1023 0132 3201 0132\n 0 0 0 0 \n 0 0 0 0 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 0 0 0 0 0 0 0 0 7 0 -7 1 -1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.094639962993 0.869442653709\n\n 7 11 1 12 \n 2310 0132 0132 0132\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 -6 6 0 -1 0 0 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 0.419425265786 0.763797275989\n\n 8 8 13 1 \n 2310 3120 0132 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 7 -6 0 0 0 0 -6 6 0 0 0 1 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.263287206280 1.381600285751\n\n 2 4 5 14 \n 0132 1023 3201 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 1 -1 -7 0 0 7 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 0.228544535222 0.425184687731\n\n 12 6 6 2 \n 0321 3120 3201 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 -6 0 6 0 6 -6 0 0 -1 1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.300507131840 0.563558475921\n\n 11 3 3 14 \n 3012 0132 0321 0321\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 0 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 0.642067861300 1.019522945044\n\n 14 13 4 11 \n 3012 1023 0132 1230\n 0 0 0 0 \n 0 0 0 0 0 0 0 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 0 0 0 0 -1 1 0 0 -7 0 7 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n -0.117878050260 0.542381850296\n\n 10 5 13 9 \n 3012 0132 3012 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 6 -6 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 0.167547082906 0.792343723503\n\n 8 14 5 13 \n 0321 2031 0132 0132\n 0 0 0 0 \n 0 -1 0 1 0 0 0 0 1 0 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 7 0 -7 1 0 -1 0 -6 0 0 6 6 -6 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.196092644376 1.096304564611\n\n 10 11 12 6 \n 1023 1230 0132 0132\n 0 0 0 0 \n 0 0 -1 1 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 0 7 -7 0 0 0 0 -1 0 0 1 0 6 -6 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.245616015965 0.655814516449\n\n 12 9 7 10 \n 1302 0321 0132 1230\n 0 0 0 0 \n 0 0 0 0 -1 0 1 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 -1 1 0 6 0 -7 1 -7 0 0 7 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n -0.385914047672 1.253269832100\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_14' : d['c_0101_10'], 'c_1001_11' : negation(d['c_0011_10']), 'c_1001_10' : negation(d['c_0011_8']), 'c_1001_13' : d['c_0011_14'], 'c_1001_12' : negation(d['c_0011_10']), 'c_1001_5' : negation(d['c_0101_3']), 'c_1001_4' : negation(d['c_0101_3']), 'c_1001_7' : negation(d['c_0101_0']), 'c_1001_6' : d['c_0101_11'], 'c_1001_1' : negation(d['c_0011_8']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0101_10'], 'c_1001_2' : negation(d['c_0011_6']), 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : negation(d['c_0101_11']), 'c_1010_13' : d['c_0101_11'], 'c_1010_12' : d['c_0011_14'], 'c_1010_11' : negation(d['c_0101_3']), 'c_1010_10' : d['c_0101_11'], 'c_1010_14' : d['c_0101_10'], 's_0_10' : d['1'], 's_3_10' : d['1'], 's_3_13' : d['1'], 's_3_12' : d['1'], 's_0_14' : d['1'], 's_3_14' : d['1'], 'c_0101_13' : negation(d['c_0011_8']), 'c_0101_12' : d['c_0101_1'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : d['c_0101_10'], 'c_0101_14' : negation(d['c_0011_12']), '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_2_12' : d['1'], 's_2_13' : d['1'], 's_2_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : 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_0011_14' : d['c_0011_14'], 'c_1100_9' : d['c_0101_10'], 'c_0011_10' : d['c_0011_10'], 'c_0011_13' : d['c_0011_10'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_1100_1'], 'c_1100_4' : negation(d['c_0011_3']), 'c_1100_7' : d['c_0011_11'], 'c_1100_6' : d['c_1100_1'], 'c_1100_1' : d['c_1100_1'], 'c_1100_0' : d['c_1001_0'], 'c_1100_3' : d['c_1001_0'], 'c_1100_2' : negation(d['c_0011_6']), 'c_1100_14' : d['c_0011_11'], 's_3_11' : d['1'], 'c_1100_11' : negation(d['c_0011_14']), 'c_1100_10' : negation(d['c_0011_3']), 'c_1100_13' : d['c_1100_1'], 's_0_11' : d['1'], 's_0_12' : d['1'], 'c_1010_7' : d['c_0101_10'], 'c_1010_6' : negation(d['c_0011_8']), 'c_1010_5' : negation(d['c_0011_10']), 'c_1010_4' : negation(d['c_0011_8']), 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : negation(d['c_0101_3']), 'c_1010_0' : negation(d['c_0011_6']), 'c_1010_9' : d['c_0101_10'], 'c_1010_8' : negation(d['c_0011_6']), 'c_1100_8' : negation(d['c_0011_6']), 's_3_1' : d['1'], 's_3_0' : 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_6' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], 'c_1100_12' : d['c_1100_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_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_3']), 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : d['c_0011_0'], '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_0110_11' : negation(d['c_0011_3']), 'c_0110_10' : d['c_0011_11'], 'c_0110_13' : d['c_0101_11'], 'c_0110_12' : negation(d['c_0011_8']), 'c_0110_14' : d['c_0011_10'], 's_0_13' : d['1'], 's_2_14' : d['1'], 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : negation(d['c_0101_1']), 'c_0101_6' : d['c_0101_11'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : negation(d['c_0101_0']), 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : negation(d['c_0011_12']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0101_3']), 'c_0101_8' : negation(d['c_0101_1']), 's_2_8' : d['1'], 's_1_14' : d['1'], 's_1_13' : d['1'], 's_1_12' : d['1'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : negation(d['c_0011_14']), 'c_0110_8' : negation(d['c_0011_12']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0101_1']), 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : negation(d['c_0011_12']), 'c_0110_6' : d['c_0101_1'], 's_2_9' : d['1']})}"; print "PY=EVAL=SECTION=ENDS=HERE"; cputime := Cputime(); // Computation // Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 16); I := ideal; // 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);