// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\nL14n363\ngeometric_solution 11.12854463\noriented_manifold\nCS_known -0.0000000000000003\n\n2 0\n torus 0.000000000000 0.000000000000\n torus 0.000000000000 0.000000000000\n\n12\n 1 2 3 4 \n 0132 0132 0132 0132\n 1 0 1 1 \n 0 1 0 -1 1 0 -1 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 -5 -1 6 1 0 -1 0 0 1 0 -1 -6 6 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.355657349585 0.740845956219\n\n 0 4 6 5 \n 0132 2103 0132 0132\n 1 0 1 1 \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 0 1 -1 -1 0 0 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 0.736684648461 0.548494537300\n\n 7 0 8 5 \n 0132 0132 0132 3120\n 1 0 1 1 \n 0 -1 1 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 5 -5 0 0 0 0 0 0 -6 0 6 0 -1 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.670016580283 1.342740932460\n\n 8 6 9 0 \n 2103 0132 0132 0132\n 1 0 1 1 \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 -1 0 1 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 -0.320206315757 0.748708435528\n\n 10 1 0 9 \n 0132 2103 0132 0132\n 1 0 1 1 \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 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n -0.288685300830 1.481691912438\n\n 2 11 1 9 \n 3120 0132 0132 3120\n 1 0 1 1 \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 -1 1 -6 0 0 6 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.469426740394 0.980204738560\n\n 7 3 11 1 \n 2103 0132 2103 0132\n 1 0 1 1 \n 0 0 0 0 0 0 1 -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 1 0 -1 0 0 0 0 0 0 0 0 5 0 -5 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.177279508029 0.772034007311\n\n 2 8 6 10 \n 0132 3120 2103 2103\n 1 0 1 1 \n 0 -1 0 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 5 0 -5 0 0 0 0 0 0 0 0 0 5 -5 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.526288515583 0.462785142598\n\n 11 7 3 2 \n 2103 3120 2103 0132\n 1 0 1 1 \n 0 1 0 -1 -1 0 1 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 -5 0 5 0 0 0 0 1 0 0 -1 5 -5 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.204932961969 0.553957708209\n\n 5 10 4 3 \n 3120 3120 0132 0132\n 1 0 1 1 \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 -1 0 0 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 0.146938316986 0.978954833470\n\n 4 9 11 7 \n 0132 3120 0132 2103\n 1 0 1 1 \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 1 -6 0 5 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.498874737859 0.607402609718\n\n 6 5 8 10 \n 2103 0132 2103 0132\n 1 0 1 1 \n 0 0 0 0 -1 0 1 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 5 0 -5 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.507592365152 1.014834206805\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_0011_8'], 'c_1001_10' : d['c_1001_10'], 'c_1001_5' : d['c_1001_10'], 'c_1001_4' : negation(d['c_0011_0']), 'c_1001_7' : negation(d['c_0011_3']), 'c_1001_6' : d['c_0011_11'], 'c_1001_1' : negation(d['c_0011_10']), 'c_1001_0' : d['c_0011_11'], 'c_1001_3' : negation(d['c_0011_10']), 'c_1001_2' : negation(d['c_0011_0']), 'c_1001_9' : negation(d['c_1001_10']), 'c_1001_8' : d['c_0011_3'], 'c_1010_11' : d['c_1001_10'], 'c_1010_10' : d['c_0011_8'], 's_0_10' : d['1'], 's_0_11' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_11'], '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_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_11' : d['c_0011_11'], 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : negation(d['c_0101_10']), 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : negation(d['c_0101_1']), 'c_1100_6' : negation(d['c_0101_10']), 'c_1100_1' : negation(d['c_0101_10']), 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : negation(d['c_0101_0']), 's_3_11' : d['1'], 'c_1100_9' : d['c_1100_0'], 'c_1100_11' : negation(d['c_0101_2']), 'c_1100_10' : negation(d['c_0101_2']), 's_3_10' : d['1'], 'c_1010_7' : negation(d['c_0011_8']), 'c_1010_6' : negation(d['c_0011_10']), 'c_1010_5' : d['c_0011_8'], 'c_1010_4' : negation(d['c_1001_10']), 'c_1010_3' : d['c_0011_11'], 'c_1010_2' : d['c_0011_11'], 'c_1010_1' : d['c_1001_10'], 'c_1010_0' : negation(d['c_0011_0']), 'c_1010_9' : negation(d['c_0011_10']), 'c_1010_8' : negation(d['c_0011_0']), 'c_1100_8' : negation(d['c_0101_0']), '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'], '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_8']), 'c_0011_8' : d['c_0011_8'], 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : d['c_0011_0'], '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_11' : d['c_0101_10'], 'c_0110_10' : d['c_0101_1'], 'c_0101_7' : d['c_0101_11'], 'c_0101_6' : d['c_0101_11'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_11'], 'c_0101_2' : d['c_0101_2'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_10'], 'c_0101_8' : d['c_0101_11'], 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0101_11'], 'c_0110_8' : d['c_0101_2'], '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_11'], 'c_0110_5' : d['c_0101_11'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0101_2'], 'c_0110_6' : d['c_0101_1']})}"; print "PY=EVAL=SECTION=ENDS=HERE"; cputime := Cputime(); // Computation // Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 13); 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);