// Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 19); MyIdeal := ideal; print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_71\ngeometric_solution 16.81275955\noriented_manifold\nCS_unknown\n\n1 0\n torus 0.000000000000 0.000000000000\n\n18\n 1 2 3 4 \n 0132 0132 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 1 -1 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 0.232597637777 0.543326107590\n\n 0 5 6 5 \n 0132 0132 0132 1230\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 -1 0 0 1 -1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.049319445621 0.654102387602\n\n 3 0 8 7 \n 0321 0132 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 -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 0.752773401899 0.699073080265\n\n 2 9 6 0 \n 0321 0132 3201 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 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 -0.312013371187 1.031557174190\n\n 8 10 0 11 \n 0132 0132 0132 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 0 0 0 0 0 0 0 -8 8 0 0 0 1 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.515014872366 0.915141996467\n\n 1 1 12 10 \n 3012 0132 0132 2310\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 1 0 -1 -1 0 9 -8 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 0.713915240916 0.491199342911\n\n 3 11 13 1 \n 2310 2310 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 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 0.132323524867 1.408521108920\n\n 14 13 2 15 \n 0132 3012 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 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.865175353612 1.368475226841\n\n 4 16 15 2 \n 0132 0132 1302 0132\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 1 -1 0 0 0 0 0 0 0 0 8 0 -8 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.947867561837 1.239476637172\n\n 14 3 17 14 \n 3012 0132 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 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 0.834889791156 1.034754125385\n\n 5 4 13 16 \n 3201 0132 3120 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 0 0 0 1 0 -1 0 1 -1 0 0 8 -8 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.556204620329 0.701269939610\n\n 16 12 4 6 \n 0132 3201 0132 3201\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 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 0.796563496092 0.694476982718\n\n 17 17 11 5 \n 2310 3012 2310 0132\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 0 0 9 -9 -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 0.641242246860 0.561606279380\n\n 7 17 10 6 \n 1230 3120 3120 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 0.941585572035 0.985942925356\n\n 7 9 15 9 \n 0132 1302 2031 1230\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 0 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.150376680479 0.942418349401\n\n 8 16 7 14 \n 2031 0321 0132 1302\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 -1 0 0 1 8 -9 0 1 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.047942248035 0.667649752077\n\n 11 8 10 15 \n 0132 0132 0132 0321\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 0.176076454016 0.855526610977\n\n 12 13 12 9 \n 1230 3120 3201 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 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 0.117467355262 0.772930787810\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 's_3_0' : d['1'], 'c_1001_15' : negation(d['c_0101_13']), 'c_1001_14' : negation(d['c_0110_15']), 'c_1001_17' : negation(d['c_0101_12']), 'c_1001_16' : d['c_1001_16'], 'c_1001_11' : negation(d['c_0101_12']), 'c_1001_10' : negation(d['c_0101_12']), 'c_1001_13' : d['c_0101_12'], 'c_1001_12' : negation(d['c_0011_17']), 'c_1001_5' : negation(d['c_0101_17']), 'c_1001_4' : d['c_1001_16'], 'c_1001_7' : negation(d['c_0011_13']), 'c_1001_6' : negation(d['c_0011_17']), 'c_1001_1' : negation(d['c_0101_16']), 'c_1001_0' : negation(d['c_0011_13']), 'c_1001_3' : d['c_0011_14'], 'c_1001_2' : d['c_1001_16'], 'c_1001_9' : negation(d['c_0011_13']), 'c_1001_8' : d['c_0110_15'], 'c_1010_13' : negation(d['c_0011_17']), 'c_1010_12' : negation(d['c_0101_17']), 'c_1010_11' : d['c_0011_17'], 'c_1010_10' : d['c_1001_16'], 'c_1010_17' : negation(d['c_0011_13']), 'c_1010_16' : d['c_0110_15'], 'c_1010_15' : d['c_0110_15'], 'c_1010_14' : d['c_0011_12'], 's_0_10' : d['1'], 's_0_11' : d['1'], 's_0_12' : d['1'], 's_3_12' : d['1'], 's_0_14' : d['1'], 's_0_15' : d['1'], 's_3_17' : d['1'], 's_3_16' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : negation(d['c_0011_15']), 'c_0101_10' : d['c_0101_10'], 'c_0101_17' : d['c_0101_17'], 'c_0101_16' : d['c_0101_16'], 'c_0101_15' : d['c_0101_14'], 'c_0101_14' : d['c_0101_14'], 's_2_0' : negation(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_2_17' : d['1'], 's_2_14' : 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' : negation(d['1']), 's_0_3' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_15' : d['c_0011_15'], 'c_0011_14' : d['c_0011_14'], 'c_0011_17' : d['c_0011_17'], 'c_0011_16' : negation(d['c_0011_10']), 'c_1100_9' : negation(d['c_0011_12']), 'c_1100_8' : d['c_0101_14'], 'c_0011_13' : d['c_0011_13'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : d['c_0011_10'], 'c_1100_4' : negation(d['c_0011_6']), 'c_1100_7' : d['c_0101_14'], 'c_1100_6' : negation(d['c_0101_10']), 'c_1100_1' : negation(d['c_0101_10']), 'c_1100_0' : negation(d['c_0011_6']), 'c_1100_3' : negation(d['c_0011_6']), 'c_1100_2' : d['c_0101_14'], 'c_1100_15' : d['c_0101_14'], 's_3_11' : d['1'], 'c_1100_17' : negation(d['c_0011_12']), 'c_1100_16' : negation(d['c_0101_13']), 'c_1100_11' : negation(d['c_0011_6']), 'c_1100_10' : negation(d['c_0101_13']), 'c_1100_13' : negation(d['c_0101_10']), 's_3_10' : d['1'], 's_3_13' : d['1'], 'c_1010_7' : negation(d['c_0101_13']), 'c_1010_6' : negation(d['c_0101_16']), 'c_1010_5' : negation(d['c_0101_16']), 's_0_13' : d['1'], 'c_1010_3' : negation(d['c_0011_13']), 'c_1010_2' : negation(d['c_0011_13']), 'c_1010_1' : negation(d['c_0101_17']), 'c_1100_14' : negation(d['c_0110_15']), 's_3_15' : d['1'], 'c_1010_9' : d['c_0011_14'], 's_3_14' : d['1'], 's_0_16' : d['1'], 's_0_17' : d['1'], 's_3_1' : d['1'], 'c_0101_13' : d['c_0101_13'], 's_3_3' : negation(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_10'], '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' : negation(d['1']), 's_1_1' : d['1'], 's_1_0' : negation(d['1']), 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_3']), 'c_0011_8' : d['c_0011_10'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : negation(d['c_0011_14']), 'c_0011_6' : d['c_0011_6'], '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_16'], 'c_0110_10' : d['c_0101_16'], 'c_0110_13' : negation(d['c_0011_14']), 'c_0110_12' : negation(d['c_0101_17']), 'c_0110_15' : d['c_0110_15'], 'c_0110_14' : negation(d['c_0011_3']), 'c_0110_17' : d['c_0011_12'], 'c_0110_16' : negation(d['c_0011_15']), 'c_1010_4' : negation(d['c_0101_12']), 'c_0101_12' : d['c_0101_12'], 'c_1010_0' : d['c_1001_16'], 's_0_8' : d['1'], 's_2_15' : d['1'], 'c_1010_8' : d['c_1001_16'], 'c_0011_11' : d['c_0011_10'], 'c_0101_7' : negation(d['c_0011_3']), 'c_0101_6' : negation(d['c_0011_14']), 'c_0101_5' : negation(d['c_0101_17']), 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : negation(d['c_0101_1']), 'c_0101_2' : d['c_0101_1'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0011_0'], 'c_0101_9' : d['c_0011_12'], 'c_0101_8' : negation(d['c_0011_15']), 'c_0011_10' : d['c_0011_10'], 's_1_17' : d['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' : negation(d['c_0110_15']), 'c_0110_8' : d['c_0101_1'], 'c_0110_1' : d['c_0011_0'], 'c_0110_0' : d['c_0101_1'], 'c_0110_3' : d['c_0011_0'], 'c_0110_2' : negation(d['c_0011_3']), 'c_0110_5' : negation(d['c_0101_10']), 'c_0110_4' : negation(d['c_0011_15']), 'c_0110_7' : d['c_0101_14'], 'c_0110_6' : d['c_0101_1']})}"; print "PY=EVAL=SECTION=ENDS=HERE"; // Value indicating failure P := -1; // Computing the primary decomposition primTime := Cputime(); P, Q := PrimaryDecomposition(MyIdeal); print "PRIMARY_DECOMPOSITION_TIME: ", Cputime(primTime); if Type(P) eq RngIntElt then // Some error occured print "PRIMARY=DECOMPOSITION" cat "=FAILED"; exit; else // Success print "PRIMARY=DECOMPOSITION" cat "=BEGINS=HERE"; P; print "PRIMARY=DECOMPOSITION" cat "=ENDS=HERE"; print "FREE=VARIABLES=IN=COMPONENTS" cat "=BEGINS=HERE"; N := Names(R); isFirstComp := true; freeVarStr := "["; for Comp in P do if isFirstComp then isFirstComp := false; else freeVarStr := freeVarStr cat ","; end if; freeVarStr := freeVarStr cat " [ "; D, Vars := Dimension(Comp); isFirstVar := true; for Var in Vars do if isFirstVar then isFirstVar := false; else freeVarStr := freeVarStr cat ", "; end if; freeVarStr := freeVarStr cat "\"" cat N[Var] cat "\""; end for; freeVarStr := freeVarStr cat " ]"; end for; freeVarStr := freeVarStr cat " ]"; print freeVarStr; print "FREE=VARIABLES=IN=COMPONENTS" cat "=ENDS=HERE"; end if; print "CPUTIME: ", Cputime(primTime);