// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\nK11n62\ngeometric_solution 9.61445626\noriented_manifold\nCS_known -0.0000000000000007\n\n1 0\n torus 0.000000000000 0.000000000000\n\n11\n 1 2 3 1 \n 0132 0132 0132 1302\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 -1 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 0.575529132130 0.471680960321\n\n 0 3 0 2 \n 0132 1230 2031 3120\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 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 0.586816950432 0.310311457856\n\n 1 0 5 4 \n 3120 0132 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 1 0 0 0 0 0 -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 0.255101301888 1.014528716824\n\n 6 7 1 0 \n 0132 0132 3012 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 -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 0.255101301888 1.014528716824\n\n 6 8 2 9 \n 2103 0132 0132 0132\n 0 0 0 0 \n 0 0 0 0 0 0 0 0 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 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 -0.161126684779 0.721684223413\n\n 10 10 9 2 \n 0132 1230 0132 0132\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 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 -0.143595260606 0.972174721962\n\n 3 10 4 7 \n 0132 2310 2103 1023\n 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 -1 0 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 0.432553819040 1.168418294011\n\n 9 3 8 6 \n 1302 0132 0132 1023\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 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 0.134046797200 0.493274805321\n\n 10 4 9 7 \n 1302 0132 1302 0132\n 0 0 0 0 \n 0 0 0 0 0 0 -1 1 -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 0 0 0 1 0 0 -1 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 -0.511375281700 1.216889241064\n\n 8 7 4 5 \n 2031 2031 0132 0132\n 0 0 0 0 \n 0 0 0 0 0 0 0 0 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 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 0.157433740462 1.306017678278\n\n 5 8 5 6 \n 0132 2031 3012 3201\n 0 0 0 0 \n 0 1 -1 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 1 0 0 0 -1 1 -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 1.148688851642 1.006659567968\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_10' : d['c_0011_10'], 'c_1001_5' : negation(d['c_0011_3']), 'c_1001_4' : d['c_1001_0'], 'c_1001_7' : d['c_1001_0'], 'c_1001_6' : d['c_0011_4'], 'c_1001_1' : negation(d['c_0101_1']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0011_0'], 'c_1001_2' : d['c_0101_10'], 'c_1001_9' : d['c_0101_5'], 'c_1001_8' : d['c_0101_5'], 'c_1010_10' : negation(d['c_0011_4']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_10' : d['c_0101_10'], '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_10' : d['1'], 's_0_8' : 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' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_1100_9' : d['c_1100_2'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : d['c_1100_2'], 'c_1100_4' : d['c_1100_2'], 'c_1100_7' : d['c_0101_9'], 'c_1100_6' : negation(d['c_0101_9']), 'c_1100_1' : negation(d['c_0101_10']), 'c_1100_0' : d['c_0101_1'], 'c_1100_3' : d['c_0101_1'], 'c_1100_2' : d['c_1100_2'], 'c_1100_10' : d['c_0011_3'], 'c_1010_7' : d['c_0011_0'], 'c_1010_6' : negation(d['c_0101_5']), 'c_1010_5' : d['c_0101_10'], 'c_1010_4' : d['c_0101_5'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_0011_0'], 'c_1010_0' : d['c_0101_10'], 'c_1010_9' : negation(d['c_0011_3']), 'c_1010_8' : d['c_1001_0'], 'c_1100_8' : d['c_0101_9'], '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' : negation(d['1']), 's_3_6' : negation(d['1']), 's_3_9' : d['1'], 's_3_8' : d['1'], 's_1_7' : negation(d['1']), 's_1_6' : d['1'], 's_1_5' : d['1'], 's_1_4' : d['1'], 's_1_3' : negation(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_4']), 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : negation(d['c_0011_3']), 'c_0011_6' : negation(d['c_0011_3']), '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_10' : d['c_0101_5'], 'c_0101_7' : negation(d['c_0011_10']), 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : d['c_0101_5'], 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0011_0'], 'c_0101_2' : d['c_0101_10'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_9'], 'c_0101_8' : negation(d['c_0011_10']), 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_5'], 'c_0110_8' : negation(d['c_0011_10']), '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_0'], 'c_0110_5' : d['c_0101_10'], 'c_0110_4' : d['c_0101_9'], 'c_0110_7' : negation(d['c_0101_5']), 'c_0110_6' : d['c_0011_0']})}"; print "PY=EVAL=SECTION=ENDS=HERE"; cputime := Cputime(); // Computation // Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 12); 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);