// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_108\ngeometric_solution 16.23534160\noriented_manifold\nCS_known -0.0000000000000005\n\n1 0\n torus 0.000000000000 0.000000000000\n\n17\n 1 2 3 3 \n 0132 0132 0132 1302\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 -1 0 0 0 0 0 0 0 0 0 7 -6 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.013452973896 1.221322377259\n\n 0 4 5 2 \n 0132 0132 0132 1023\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 -7 7 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.346657164284 0.930479590838\n\n 6 0 3 1 \n 0132 0132 3201 1023\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 1 0 0 0 1 -1 -6 6 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.221537922976 0.522331431593\n\n 2 6 0 0 \n 2310 2310 2031 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 -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 0.013452973896 1.221322377259\n\n 6 1 7 8 \n 1023 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 -1 0 -1 0 1 0 1 0 0 -1 0 -7 7 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.630524525136 1.320794870260\n\n 9 10 6 1 \n 0132 0132 1023 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 0 0 0 0 0 0 0 0 0 0 0 0 -6 6 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.630524525136 1.320794870260\n\n 2 4 5 3 \n 0132 1023 1023 3201\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 1 0 -1 0 0 0 0 0 -1 0 1 6 0 -6 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.346657164284 0.930479590838\n\n 11 10 12 4 \n 0132 0321 0132 0132\n 0 0 0 0 \n 0 0 0 0 0 0 0 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 0 0 -1 1 0 0 1 -1 7 0 0 -7 6 1 -7 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.173150334729 1.054005309284\n\n 9 10 4 13 \n 2103 0213 0132 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 0 0 0 0 0 0 0 1 -1 0 0 0 -1 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.375421041268 0.708187895821\n\n 5 14 8 11 \n 0132 0132 2103 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 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 0.091309099408 0.766352941871\n\n 15 5 8 7 \n 0132 0132 0213 0321\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 1 -1 -6 6 0 0 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.329489321953 0.502449262730\n\n 7 16 9 14 \n 0132 0132 0132 0132\n 0 0 0 0 \n 0 0 0 0 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 1 -1 0 0 0 0 0 -6 0 0 6 -7 7 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.270475834916 0.922214550585\n\n 16 16 13 7 \n 3120 1230 0132 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 -1 0 1 1 0 0 -1 -7 0 0 7 0 -1 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.301271886414 0.712815875648\n\n 14 15 8 12 \n 3120 0321 0132 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 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 0.077533228004 1.028334427891\n\n 15 9 11 13 \n 1023 0132 0132 3120\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 6 0 -6 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.118676695387 1.576535831057\n\n 10 14 16 13 \n 0132 1023 1302 0321\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 0 0 1 0 0 -1 6 -6 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.320674350288 0.875056235599\n\n 15 11 12 12 \n 2031 0132 3012 3120\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 -1 1 0 0 0 1 -1 0 -7 0 7 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.301271886414 0.712815875648\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' : d['c_0101_14'], 'c_1001_14' : negation(d['c_0011_12']), 'c_1001_16' : negation(d['c_0011_12']), 'c_1001_11' : negation(d['c_0011_12']), 'c_1001_10' : d['c_1001_1'], 'c_1001_13' : d['c_0101_16'], 'c_1001_12' : d['c_0101_12'], 'c_1001_5' : d['c_0101_6'], 'c_1001_4' : d['c_0101_6'], 'c_1001_7' : d['c_0101_16'], 'c_1001_6' : d['c_0101_11'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : d['c_0101_0'], 'c_1001_3' : negation(d['c_0101_1']), 'c_1001_2' : negation(d['c_0101_3']), 'c_1001_9' : negation(d['c_0011_13']), 'c_1001_8' : d['c_1001_1'], 'c_1010_13' : d['c_0101_12'], 'c_1010_12' : d['c_0101_16'], 'c_1010_11' : negation(d['c_0011_12']), 'c_1010_10' : d['c_0101_6'], 'c_1010_16' : negation(d['c_0011_12']), 'c_1010_15' : d['c_0101_12'], 'c_1010_14' : negation(d['c_0011_13']), 's_0_10' : d['1'], 's_0_11' : d['1'], 's_0_12' : d['1'], 's_0_13' : d['1'], 's_0_14' : d['1'], 's_0_15' : d['1'], 's_0_16' : d['1'], 's_3_16' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : negation(d['c_0011_13']), 'c_0101_16' : d['c_0101_16'], 'c_0101_15' : d['c_0011_11'], 'c_0101_14' : d['c_0101_14'], '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_2_16' : d['1'], 's_0_8' : d['1'], 's_2_15' : 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_15' : negation(d['c_0011_10']), 'c_0011_14' : negation(d['c_0011_10']), 'c_0011_16' : negation(d['c_0011_11']), 'c_1100_9' : negation(d['c_0101_13']), 'c_0011_10' : d['c_0011_10'], 'c_0011_13' : d['c_0011_13'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_0011_3'], 'c_1100_4' : d['c_1100_12'], 'c_1100_7' : d['c_1100_12'], 'c_1100_6' : negation(d['c_0011_3']), 'c_1100_1' : d['c_0011_3'], 'c_1100_0' : d['c_0101_3'], 'c_1100_3' : d['c_0101_3'], 'c_1100_2' : negation(d['c_0011_3']), 'c_1100_14' : negation(d['c_0101_13']), 'c_1100_15' : d['c_0101_16'], 's_3_11' : d['1'], 'c_1100_16' : negation(d['c_0101_12']), 'c_1100_11' : negation(d['c_0101_13']), 'c_1100_10' : d['c_0101_16'], 'c_1100_13' : d['c_1100_12'], 's_3_10' : d['1'], 's_3_13' : d['1'], 'c_1010_7' : d['c_0101_6'], 'c_1010_6' : d['c_0101_1'], 'c_1010_5' : d['c_1001_1'], 's_3_12' : d['1'], 'c_1010_3' : d['c_0101_0'], 'c_1010_2' : d['c_0101_0'], 'c_1010_1' : d['c_0101_6'], 'c_1010_0' : negation(d['c_0101_3']), 's_3_15' : d['1'], 'c_1010_9' : negation(d['c_0011_12']), 's_3_14' : d['1'], 'c_1100_8' : d['c_1100_12'], '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_12'], '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' : d['c_0011_10'], 'c_0011_8' : negation(d['c_0011_13']), 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : d['c_0011_0'], 'c_0101_13' : d['c_0101_13'], '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_0110_11' : d['c_0101_14'], 'c_0110_10' : d['c_0011_11'], 'c_0110_13' : d['c_0101_12'], 'c_0110_12' : d['c_0101_14'], 'c_0110_15' : negation(d['c_0011_13']), 'c_0110_14' : d['c_0101_12'], 'c_0110_16' : d['c_0101_14'], 'c_1010_4' : d['c_1001_1'], 'c_0101_12' : d['c_0101_12'], 'c_0011_7' : negation(d['c_0011_11']), 's_2_14' : d['1'], 's_0_9' : d['1'], 'c_1010_8' : d['c_0101_16'], 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : d['c_0101_14'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_11'], 'c_0101_4' : d['c_0101_11'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : negation(d['c_0101_0']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_1'], 'c_0101_8' : d['c_0101_1'], 's_1_16' : d['1'], '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' : d['1'], 'c_0110_9' : d['c_0101_11'], 'c_0110_8' : d['c_0101_13'], 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_6'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_1'], 'c_0110_7' : d['c_0101_11'], 'c_0110_6' : negation(d['c_0101_0'])})}"; print "PY=EVAL=SECTION=ENDS=HERE"; cputime := Cputime(); // Computation // Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 18); 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);