// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n10^2_56\ngeometric_solution 13.84505059\noriented_manifold\nCS_known 0.0000000000000006\n\n2 0\n torus 0.000000000000 0.000000000000\n torus 0.000000000000 0.000000000000\n\n15\n 1 1 2 3 \n 0132 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 -1 1 0 0 0 0 0 1 0 -1 -1 1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.492385626683 1.000686230421\n\n 0 4 5 0 \n 0132 0132 0132 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 0 0 0 0 0 1 -1 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 0.341493399377 0.591955682466\n\n 4 6 6 0 \n 0321 0132 1302 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 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.612097161239 1.169301939723\n\n 7 8 0 9 \n 0132 0132 0132 0132\n 0 0 1 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 0 -1 0 1 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.195471196468 0.604133236704\n\n 2 1 10 10 \n 0321 0132 0132 3120\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 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 0.797538576286 0.919619196485\n\n 11 8 9 1 \n 0132 1023 2103 0132\n 0 0 0 1 \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 1 0 0 -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 0.679925289661 1.097271232394\n\n 2 2 9 12 \n 2031 0132 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 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.648609774830 0.671268056626\n\n 3 9 11 13 \n 0132 2103 0132 0132\n 0 0 0 1 \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 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.835258229521 0.401127278779\n\n 5 3 11 10 \n 1023 0132 3012 0321\n 0 0 0 1 \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 -1 1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.788878699927 0.930667850596\n\n 5 7 3 6 \n 2103 2103 0132 1302\n 0 0 0 1 \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 -1 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 -0.132266926468 0.799796350974\n\n 4 8 14 4 \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 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 0.228333918399 1.037137103536\n\n 5 8 13 7 \n 0132 1230 2103 0132\n 0 0 1 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 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 0.767526485680 0.264329672374\n\n 14 13 6 14 \n 0213 2310 0132 3012\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 -6 -1 0 7 1 0 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.102784715200 0.665456951153\n\n 11 14 7 12 \n 2103 3120 0132 3201\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 -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 0.054279701881 0.934419393744\n\n 12 13 12 10 \n 0213 3120 1230 0132\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 6 0 -7 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 0.719021472361 0.533292114966\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' : negation(d['c_1001_13']), 'c_1001_11' : d['c_0011_13'], 'c_1001_10' : negation(d['c_0011_13']), 'c_1001_13' : d['c_1001_13'], 'c_1001_12' : d['c_0011_14'], 'c_1001_5' : d['c_0011_9'], 'c_1001_4' : d['c_1001_3'], 'c_1001_7' : d['c_0011_9'], 'c_1001_6' : negation(d['c_0110_9']), 'c_1001_1' : negation(d['c_0011_10']), 'c_1001_0' : negation(d['c_0110_9']), 'c_1001_3' : d['c_1001_3'], 'c_1001_2' : d['c_0011_14'], 'c_1001_9' : negation(d['c_0011_11']), 'c_1001_8' : negation(d['c_0011_11']), 'c_1010_13' : negation(d['c_0011_14']), 'c_1010_12' : negation(d['c_0011_12']), 'c_1010_11' : d['c_0011_9'], 'c_1010_10' : d['c_1001_3'], 'c_1010_14' : negation(d['c_0011_13']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_0_14' : d['1'], 's_3_14' : d['1'], 's_2_8' : d['1'], 'c_0101_12' : d['c_0011_14'], 'c_0101_11' : d['c_0101_1'], 'c_0101_10' : d['c_0101_10'], 'c_0101_14' : d['c_0011_12'], 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : negation(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_14' : d['1'], 's_0_9' : 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' : 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_0011_11' : d['c_0011_11'], 'c_1100_8' : negation(d['c_0011_13']), 'c_0011_13' : d['c_0011_13'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0110_9']), 'c_1100_4' : negation(d['c_0101_10']), 'c_1100_7' : negation(d['c_0011_12']), 'c_1100_6' : d['c_1001_13'], 'c_1100_1' : negation(d['c_0110_9']), 'c_1100_0' : d['c_0101_6'], 'c_1100_3' : d['c_0101_6'], 'c_1100_2' : d['c_0101_6'], 'c_1100_14' : negation(d['c_0101_10']), 's_3_11' : d['1'], 'c_1100_9' : d['c_0101_6'], 'c_1100_11' : negation(d['c_0011_12']), 'c_1100_10' : negation(d['c_0101_10']), 'c_1100_13' : negation(d['c_0011_12']), 's_0_11' : d['1'], 's_3_13' : d['1'], 'c_1010_7' : d['c_1001_13'], 'c_1010_6' : d['c_0011_14'], 'c_1010_5' : negation(d['c_0011_10']), 's_0_13' : d['1'], 'c_1010_3' : negation(d['c_0011_11']), 'c_1010_2' : negation(d['c_0110_9']), 'c_1010_1' : d['c_1001_3'], 'c_1010_0' : d['c_1001_3'], 'c_1010_9' : negation(d['c_1001_13']), 'c_1010_8' : d['c_1001_3'], '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_1001_13'], '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' : 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_11']), 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : d['c_0011_0'], 'c_0011_7' : negation(d['c_0011_11']), 'c_0011_6' : negation(d['c_0011_2']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_11'], 'c_0011_2' : d['c_0011_2'], 'c_0110_11' : d['c_0101_5'], 'c_0110_10' : negation(d['c_0011_2']), 'c_0110_13' : d['c_0011_12'], 'c_0110_12' : negation(d['c_0101_10']), 'c_0110_14' : d['c_0101_10'], 'c_1010_4' : negation(d['c_0011_10']), 's_0_8' : d['1'], 'c_0101_7' : d['c_0101_5'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : negation(d['c_0011_2']), 'c_0101_3' : d['c_0101_1'], 'c_0101_2' : d['c_0011_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : negation(d['c_0011_0']), 'c_0101_9' : d['c_0101_5'], 'c_0101_8' : d['c_0011_9'], 'c_0011_10' : d['c_0011_10'], '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_0110_9'], 'c_0110_8' : negation(d['c_0011_10']), 'c_0110_1' : negation(d['c_0011_0']), 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0101_5'], 'c_0110_2' : negation(d['c_0011_0']), 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : negation(d['c_0011_2']), 'c_0110_7' : d['c_0101_1'], 'c_0110_6' : d['c_0011_14'], 's_2_9' : d['1'], 'c_0101_13' : d['c_0101_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);