// Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 19); MyIdeal := ideal; print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_354\ngeometric_solution 16.80895098\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 -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 -1 0 1 1 0 -1 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 0.468098588589 1.082786476530\n\n 0 5 2 6 \n 0132 0132 1023 0132\n 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 0 0 0 -1 0 1 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 0.127123449039 0.616021204791\n\n 7 0 1 8 \n 0132 0132 1023 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 -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 -0.172993850324 1.502663350557\n\n 8 4 9 0 \n 0132 1023 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 -1 1 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 1.235472114268 1.002353618012\n\n 3 9 0 10 \n 1023 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 -1 1 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 0.024889222057 0.724166334788\n\n 7 1 11 11 \n 1023 0132 0132 3120\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 -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 0.721566874285 0.645730575142\n\n 7 12 1 13 \n 2103 0132 0132 0132\n 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 0 0 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 0.466564805526 0.593991605514\n\n 2 5 6 12 \n 0132 1023 2103 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 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 0.212516917912 0.895285032358\n\n 3 10 2 13 \n 0132 1023 0132 1023\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 0.468098588589 1.082786476530\n\n 14 4 15 3 \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 -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 0.429523928602 0.687252901516\n\n 8 14 4 15 \n 1023 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 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.429523928602 0.687252901516\n\n 5 12 16 5 \n 3120 0321 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 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 0.563067902515 1.305843762668\n\n 7 6 17 11 \n 3120 0132 0132 0321\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 -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 1.105933456014 0.510904038208\n\n 17 14 6 8 \n 0132 1230 0132 1023\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 -1 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.468098588589 1.082786476530\n\n 9 10 13 16 \n 0132 0132 3012 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 -1 1 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 0.715097811235 0.861478807402\n\n 17 16 10 9 \n 2103 3201 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 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 0.715097811235 0.861478807402\n\n 17 14 15 11 \n 1302 2310 2310 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 -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 0.952595240547 1.379268939239\n\n 13 16 15 12 \n 0132 2031 2103 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 1.235472114268 1.002353618012\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_0011_13']), 'c_1001_14' : negation(d['c_0011_13']), 'c_1001_17' : d['c_0011_15'], 'c_1001_16' : negation(d['c_1001_10']), 'c_1001_11' : negation(d['c_0101_9']), 'c_1001_10' : d['c_1001_10'], 'c_1001_13' : d['c_0011_16'], 'c_1001_12' : d['c_0011_16'], 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : d['c_0101_1'], 'c_1001_7' : negation(d['c_0011_12']), 'c_1001_6' : d['c_1001_5'], 'c_1001_1' : negation(d['c_0011_11']), 'c_1001_0' : d['c_0101_10'], 'c_1001_3' : d['c_0101_1'], 'c_1001_2' : d['c_0101_1'], 'c_1001_9' : d['c_1001_10'], 'c_1001_8' : d['c_0101_10'], 'c_1010_13' : d['c_0101_14'], 'c_1010_12' : d['c_1001_5'], 'c_1010_11' : d['c_1001_5'], 'c_1010_10' : negation(d['c_0011_13']), 'c_1010_17' : d['c_0011_16'], 'c_1010_16' : negation(d['c_0101_9']), 'c_1010_15' : d['c_1001_10'], 'c_1010_14' : d['c_1001_10'], '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' : 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_15'], 'c_0101_16' : d['c_0011_13'], 'c_0101_15' : d['c_0101_15'], 'c_0101_14' : d['c_0101_14'], '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' : negation(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' : negation(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' : negation(d['c_0011_10']), 'c_0011_17' : negation(d['c_0011_13']), 'c_0011_16' : d['c_0011_16'], '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' : d['c_0011_15'], 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : negation(d['c_0101_12']), 'c_1100_6' : d['c_1100_1'], 'c_1100_1' : d['c_1100_1'], 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : d['c_1100_0'], 'c_1100_2' : negation(d['c_1100_1']), 'c_1100_15' : d['c_1100_0'], 's_0_10' : d['1'], 'c_1100_17' : negation(d['c_0101_9']), 'c_1100_16' : d['c_0011_15'], 'c_1100_11' : d['c_0011_15'], 'c_1100_10' : d['c_1100_0'], 'c_1100_13' : d['c_1100_1'], 's_3_10' : d['1'], 'c_1100_9' : d['c_1100_0'], 's_3_13' : d['1'], 'c_1010_7' : negation(d['c_0011_12']), 'c_1010_6' : d['c_0011_16'], 'c_1010_5' : negation(d['c_0011_11']), 's_3_12' : d['1'], 'c_1010_3' : d['c_0101_10'], 'c_1010_2' : d['c_0101_10'], 'c_1010_1' : d['c_1001_5'], 'c_1100_14' : negation(d['c_0011_16']), 's_3_15' : d['1'], 'c_1010_9' : d['c_0101_1'], 's_3_14' : d['1'], 'c_1100_8' : negation(d['c_1100_1']), 's_3_17' : d['1'], 's_0_17' : d['1'], 's_3_1' : negation(d['1']), 'c_0101_13' : d['c_0101_12'], '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_0101_9']), '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_10'], 'c_0011_5' : d['c_0011_0'], 'c_0011_4' : negation(d['c_0011_10']), 'c_0011_7' : d['c_0011_0'], 'c_0011_6' : negation(d['c_0011_12']), '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' : negation(d['c_0011_12']), 'c_0110_10' : d['c_0101_15'], 'c_0110_13' : d['c_0101_15'], 'c_0110_12' : negation(d['c_0011_11']), 'c_0110_15' : d['c_0101_9'], 'c_0110_14' : d['c_0101_9'], 'c_0110_17' : d['c_0101_12'], 'c_0110_16' : negation(d['c_0011_15']), 'c_1010_4' : d['c_1001_10'], 'c_0101_12' : d['c_0101_12'], 'c_1010_0' : d['c_0101_1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 'c_1010_8' : d['c_0101_15'], 'c_0101_7' : d['c_0101_0'], 'c_0101_6' : d['c_0101_0'], 'c_0101_5' : negation(d['c_0011_12']), 'c_0101_4' : d['c_0101_1'], 'c_0101_3' : d['c_0101_14'], 'c_0101_2' : negation(d['c_0011_11']), 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_9'], '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_14'], 'c_0110_8' : d['c_0101_14'], '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' : negation(d['c_0011_12']), 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : negation(d['c_0011_11']), 'c_0110_6' : d['c_0101_12']})}"; 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);