// Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 19); MyIdeal := ideal; print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_78\ngeometric_solution 17.23527563\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 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 0 0 6 -6 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 0.174442117425 0.791011853222\n\n 0 5 7 6 \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 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 0.397968767662 1.064203846088\n\n 8 0 10 9 \n 0132 0132 0132 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 1 0 -1 7 0 -7 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 0.549971257653 0.769690636469\n\n 9 10 8 0 \n 0132 0132 0132 0132\n 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 0 0 0 6 0 0 -6 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 0.549971257653 0.769690636469\n\n 11 5 0 12 \n 0132 1302 0132 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 -1 1 -6 0 6 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 0.827291739887 0.980129494006\n\n 8 1 13 4 \n 1023 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 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 0.223689558005 1.400248197026\n\n 8 14 1 12 \n 2103 0132 0132 2103\n 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 0 0 0 -7 0 0 7 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 0.035245671891 0.760267980687\n\n 11 15 14 1 \n 3120 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 -1 0 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.753171749105 0.703951812415\n\n 2 5 6 3 \n 0132 1023 2103 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 -7 0 7 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 0.174442117425 0.791011853222\n\n 3 10 2 10 \n 0132 0213 0132 3120\n 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 0 1 -1 -6 0 0 6 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 0.637450583974 0.472225117543\n\n 9 3 9 2 \n 3120 0132 0213 0132\n 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 0 0 0 -6 0 -1 7 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 0.637450583974 0.472225117543\n\n 4 15 16 7 \n 0132 1230 0132 3120\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 -1 0 1 6 0 -6 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 0.419624960069 0.455121915012\n\n 14 17 4 6 \n 2103 0132 0132 2103\n 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 1 -1 0 7 0 0 -7 -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 0.538983283178 0.561492626218\n\n 14 15 17 5 \n 0321 0321 2031 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 0 0 0 0 0 0 0 0 -7 7 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.361556148558 0.619618057995\n\n 13 6 12 7 \n 0321 0132 2103 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 1 -1 7 0 -7 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 0.272852748840 1.170346805475\n\n 16 7 11 13 \n 2103 0132 3012 0321\n 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 1 -1 0 6 0 1 -7 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 0.311097107161 0.547102036115\n\n 17 17 15 11 \n 2103 1023 2103 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 -6 6 -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 0.584308635858 0.870128184304\n\n 16 12 16 13 \n 1023 0132 2103 1302\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 1 -1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.468104185700 0.792077184443\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_0110_6' : d['c_0110_6'], 'c_1001_15' : negation(d['c_0011_11']), 'c_1001_14' : d['c_0011_12'], 'c_1001_17' : negation(d['c_0011_12']), 'c_1001_16' : d['c_0011_15'], 'c_1001_11' : d['c_0110_17'], 'c_1001_10' : d['c_1001_0'], 'c_1001_13' : negation(d['c_0110_17']), 'c_1001_12' : d['c_1001_12'], 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : d['c_0110_5'], 'c_1001_7' : d['c_1001_5'], 'c_1001_6' : d['c_1001_5'], 'c_1001_1' : negation(d['c_0011_11']), 'c_1001_0' : d['c_1001_0'], 'c_1001_3' : d['c_0110_5'], 'c_1001_2' : d['c_0110_5'], 'c_1001_9' : d['c_1001_0'], 'c_1001_8' : negation(d['c_0011_14']), 'c_1010_13' : d['c_1001_5'], 'c_1010_12' : negation(d['c_0011_12']), 'c_1010_11' : d['c_0011_15'], 'c_1010_10' : d['c_0110_5'], 'c_1010_17' : d['c_1001_12'], 'c_1010_16' : d['c_0110_17'], 'c_1010_15' : d['c_1001_5'], 'c_1010_14' : d['c_1001_5'], 's_3_11' : 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' : negation(d['1']), 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_11'], 'c_0101_10' : d['c_0011_10'], 'c_0101_17' : d['c_0011_15'], 'c_0101_16' : d['c_0011_15'], 'c_0101_15' : d['c_0011_15'], 'c_0101_14' : d['c_0101_11'], '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' : negation(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_2_15' : 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' : negation(d['1']), 's_0_3' : d['1'], 's_0_0' : negation(d['1']), 's_0_1' : negation(d['1']), 'c_0011_15' : d['c_0011_15'], 'c_0011_14' : d['c_0011_14'], 'c_0011_17' : negation(d['c_0011_12']), 'c_0011_16' : negation(d['c_0011_12']), 'c_0011_11' : d['c_0011_11'], 'c_0011_10' : d['c_0011_10'], 'c_0011_13' : d['c_0011_13'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_1001_12']), 'c_1100_4' : negation(d['c_0110_6']), 'c_1100_7' : negation(d['c_0110_12']), 'c_1100_6' : negation(d['c_0110_12']), 'c_1100_1' : negation(d['c_0110_12']), 'c_1100_0' : negation(d['c_0110_6']), 'c_1100_3' : negation(d['c_0110_6']), 'c_1100_2' : negation(d['c_0011_10']), 'c_1100_14' : negation(d['c_0110_12']), 'c_1100_15' : negation(d['c_0110_17']), 's_0_10' : d['1'], 'c_1100_17' : negation(d['c_0101_11']), 'c_1100_16' : d['c_0011_13'], 'c_1100_11' : d['c_0011_13'], 'c_1100_10' : negation(d['c_0011_10']), 'c_1100_13' : negation(d['c_1001_12']), 's_3_10' : d['1'], 's_3_13' : d['1'], 'c_1010_7' : negation(d['c_0011_11']), 'c_1010_6' : d['c_0011_12'], 'c_1010_5' : negation(d['c_0011_11']), 's_3_12' : d['1'], 'c_1010_3' : d['c_1001_0'], 'c_1010_2' : d['c_1001_0'], 'c_1010_1' : d['c_1001_5'], 'c_1010_0' : d['c_0110_5'], 's_3_15' : d['1'], 'c_1010_9' : negation(d['c_0011_10']), 's_3_14' : d['1'], 's_3_17' : d['1'], 's_0_17' : d['1'], 's_3_1' : negation(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' : negation(d['c_0110_6']), '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' : d['c_0011_10'], 'c_0011_8' : d['c_0011_0'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_11']), 'c_0011_7' : negation(d['c_0011_15']), 'c_0011_6' : negation(d['c_0011_14']), 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_10']), 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_1'], 'c_0110_10' : d['c_0101_2'], 'c_0110_13' : negation(d['c_0011_14']), 'c_0110_12' : d['c_0110_12'], 'c_0110_15' : negation(d['c_0011_13']), 'c_0110_14' : negation(d['c_0011_13']), 'c_0110_17' : d['c_0110_17'], 'c_0110_16' : d['c_0101_11'], 'c_1010_4' : d['c_1001_12'], 'c_0101_12' : d['c_0101_11'], 'c_0110_0' : d['c_0101_1'], 's_0_8' : negation(d['1']), 's_0_9' : d['1'], 'c_1010_8' : d['c_0110_5'], 'c_0101_7' : negation(d['c_0011_13']), 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : negation(d['c_0011_14']), 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_2'], '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_0'], 'c_0101_8' : d['c_0101_0'], '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' : d['c_0101_2'], 'c_0110_8' : d['c_0101_2'], 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : negation(d['c_0011_10']), 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : d['c_0101_0'], 'c_0110_5' : d['c_0110_5'], 'c_0110_4' : d['c_0101_11'], 'c_0110_7' : d['c_0101_1'], 'c_1100_8' : negation(d['c_0110_6']), 'c_0101_13' : negation(d['c_0101_11'])})}"; 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);