// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n10_111\ngeometric_solution 14.26502301\noriented_manifold\nCS_known 0.0000000000000001\n\n1 0\n torus 0.000000000000 0.000000000000\n\n16\n 1 2 2 3 \n 0132 0132 1302 0132\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 1 0 -1 0 0 0 0 9 -9 0 0 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.762103696101 0.551135258866\n\n 0 4 6 5 \n 0132 0132 0132 0132\n 0 0 0 0 \n 0 0 0 0 0 0 -1 1 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 10 -10 1 -1 0 0 -9 9 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 1.127320840780 0.878859054858\n\n 0 0 8 7 \n 2031 0132 0132 0132\n 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 -1 0 1 0 0 0 0 -1 0 0 1 0 9 -9 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.138429854723 0.623067028120\n\n 6 5 0 9 \n 0132 0321 0132 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 -10 0 0 10 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 0.824919425672 0.640456417409\n\n 10 1 7 11 \n 0132 0132 1302 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 1 0 -1 0 0 -9 0 9 -1 1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.653901543924 0.331999633643\n\n 10 7 1 3 \n 1302 1302 0132 0321\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 -10 0 10 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 0.368126045272 0.503471842452\n\n 3 12 8 1 \n 0132 0132 0213 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 10 0 0 -10 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 0.529652255790 0.352062458254\n\n 4 11 2 5 \n 2031 0321 0132 2031\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 -1 1 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 0.459077230473 0.785477546005\n\n 13 6 9 2 \n 0132 0213 3012 0132\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 0 0 0 0 0 0 -9 0 0 9 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.169219096124 0.557248490333\n\n 12 8 3 13 \n 3120 1230 0132 1302\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 1 -1 10 0 -10 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 -0.285766382684 0.977171729388\n\n 4 5 15 14 \n 0132 2031 0132 0132\n 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 -1 1 0 -1 0 0 1 1 0 0 -1 0 10 -10 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 1.043060818796 0.671632817476\n\n 15 14 4 7 \n 0132 0132 0132 0321\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 0 0 0 0 10 -1 -9 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 1.043060818796 0.671632817476\n\n 15 6 13 9 \n 1302 0132 2310 3120\n 0 0 0 0 \n 0 0 0 0 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 0 0 0 1 0 9 -10 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 0.476337313417 1.528306988254\n\n 8 12 9 14 \n 0132 3201 2031 2103\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 1 -1 0 0 0 0 9 -9 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.476337313417 1.528306988254\n\n 15 11 10 13 \n 2103 0132 0132 2103\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 -1 1 -1 1 0 0 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.802760377819 0.720685004099\n\n 11 12 14 10 \n 0132 2031 2103 0132\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 -10 0 0 10 0 -1 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.802760377819 0.720685004099\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_15' : negation(d['c_0011_11']), 'c_1001_14' : d['c_0011_5'], 'c_1001_11' : d['c_1001_1'], 'c_1001_10' : d['c_0011_12'], 'c_1001_13' : negation(d['c_0011_11']), 'c_1001_12' : d['c_1001_1'], 'c_1001_5' : d['c_0110_7'], 'c_1001_4' : d['c_0110_7'], 'c_1001_7' : d['c_0101_7'], 'c_1001_6' : negation(d['c_0011_9']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_0101_7'], 'c_1001_3' : d['c_1001_2'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : d['c_1001_9'], 'c_1001_8' : negation(d['c_0011_9']), 'c_1010_13' : negation(d['c_1001_1']), 'c_1010_12' : negation(d['c_0011_9']), 'c_1010_11' : d['c_0011_5'], 'c_1010_10' : d['c_0011_5'], 'c_1010_15' : d['c_0011_12'], 'c_1010_14' : d['c_1001_1'], 's_0_10' : negation(d['1']), 's_3_10' : d['1'], 's_0_12' : d['1'], 's_0_13' : d['1'], 's_0_14' : d['1'], 's_0_15' : d['1'], 's_2_8' : d['1'], 'c_0101_12' : d['c_0011_11'], 'c_0101_11' : d['c_0101_10'], 'c_0101_10' : d['c_0101_10'], 'c_0101_15' : negation(d['c_0011_7']), 'c_0101_14' : negation(d['c_0011_7']), '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' : negation(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' : negation(d['1']), 's_0_5' : negation(d['1']), 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_15' : negation(d['c_0011_11']), 'c_0011_14' : negation(d['c_0011_11']), 'c_0011_11' : d['c_0011_11'], 'c_1100_8' : negation(d['c_1001_9']), 'c_0011_13' : d['c_0011_13'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_1001_2'], 'c_1100_4' : d['c_0101_7'], 'c_1100_7' : negation(d['c_1001_9']), 'c_1100_6' : d['c_1001_2'], 'c_1100_1' : d['c_1001_2'], 'c_1100_0' : d['c_0101_13'], 'c_1100_3' : d['c_0101_13'], 'c_1100_2' : negation(d['c_1001_9']), 'c_1100_14' : negation(d['c_0101_8']), 'c_1100_15' : negation(d['c_0101_8']), 's_3_11' : d['1'], 'c_1100_9' : d['c_0101_13'], 'c_1100_11' : d['c_0101_7'], 'c_1100_10' : negation(d['c_0101_8']), 'c_1100_13' : negation(d['c_0101_8']), 's_0_11' : d['1'], 's_3_13' : d['1'], 'c_1010_7' : d['c_0011_5'], 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : d['c_1001_9'], 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : d['c_1001_9'], 'c_1010_2' : d['c_0101_7'], 'c_1010_1' : d['c_0110_7'], 'c_1010_0' : d['c_1001_2'], 's_3_15' : d['1'], 'c_1010_9' : d['c_0101_8'], 's_3_14' : d['1'], 's_3_1' : negation(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_0011_13'], 's_1_7' : 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' : negation(d['1']), 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_9'], 'c_0011_8' : negation(d['c_0011_13']), 'c_0011_5' : d['c_0011_5'], 'c_0011_4' : d['c_0011_0'], 'c_0101_13' : d['c_0101_13'], 'c_0011_6' : negation(d['c_0011_12']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_12'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0011_7']), 'c_0110_10' : negation(d['c_0011_7']), 'c_0110_13' : d['c_0101_8'], 'c_0110_12' : d['c_0011_11'], 'c_0110_15' : d['c_0101_10'], 'c_0110_14' : d['c_0101_8'], 'c_0011_7' : d['c_0011_7'], 's_3_12' : d['1'], 's_2_14' : d['1'], 's_2_15' : d['1'], 'c_1010_8' : d['c_1001_2'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : negation(d['c_0011_13']), 'c_0101_5' : d['c_0011_0'], 'c_0101_4' : negation(d['c_0011_7']), 'c_0101_3' : d['c_0101_1'], 'c_0101_2' : d['c_0101_13'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0011_0'], 'c_0101_9' : negation(d['c_0011_13']), 'c_0101_8' : d['c_0101_8'], 'c_0011_10' : negation(d['c_0011_0']), 's_1_15' : 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' : negation(d['1']), 'c_0110_9' : d['c_0011_11'], 'c_0110_8' : d['c_0101_13'], 'c_0110_1' : d['c_0011_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : negation(d['c_0011_13']), 'c_0110_2' : d['c_0101_7'], 'c_0110_5' : negation(d['c_0011_12']), 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0110_7'], '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(), 17); 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);