// Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 19); MyIdeal := ideal; print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_322\ngeometric_solution 17.27731814\noriented_manifold\nCS_unknown\n\n1 0\n torus 0.000000000000 0.000000000000\n\n18\n 1 2 1 3 \n 0132 0132 3012 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 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 0.717031285359 0.981851602655\n\n 0 0 5 4 \n 0132 1230 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 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.271015867904 0.940377329645\n\n 6 0 7 6 \n 0132 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 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 0.514918436142 0.664236164609\n\n 8 9 0 4 \n 0132 0132 0132 2103\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 1 0 0 -1 -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 0.509902650446 0.597324811588\n\n 10 10 1 3 \n 0132 1302 0132 2103\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 -1 0 0 1 0 1 0 -1 17 -16 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.712553481635 0.884888728517\n\n 11 10 12 1 \n 0132 1230 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 0.987618489005 0.778463419128\n\n 2 2 13 11 \n 0132 1302 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 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 0.271015867904 0.940377329645\n\n 13 9 14 2 \n 2031 0321 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 -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 0.820944113684 1.000556906657\n\n 3 15 12 16 \n 0132 0132 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 -1 0 1 -1 0 0 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 0.311134861904 0.785378991008\n\n 17 3 12 7 \n 0132 0132 2310 0321\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 0.434981048034 0.734910160900\n\n 4 14 5 4 \n 0132 1230 3012 2031\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 0 -1 1 0 0 -1 -17 1 0 16 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.332057223265 1.022220396897\n\n 5 6 16 17 \n 0132 1302 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 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 0.375476632933 0.492263562363\n\n 15 9 8 5 \n 2310 3201 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 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 0.283585111505 0.704516004627\n\n 16 16 7 6 \n 3201 2103 1302 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 -1 0 1 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 0.712553481635 0.884888728517\n\n 17 15 10 7 \n 3012 1302 3012 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 0 1 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.564007938405 1.100548499541\n\n 17 8 12 14 \n 1023 0132 3201 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 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 -0.969053631291 2.112353765593\n\n 11 13 8 13 \n 2103 2103 0132 2310\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 -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 0.447958418889 0.685556081598\n\n 9 15 11 14 \n 0132 1023 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 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 0.283585111505 0.704516004627\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_15' : d['c_0011_13'], 'c_1001_14' : negation(d['c_0011_10']), 'c_1001_17' : d['c_0101_15'], 'c_1001_16' : d['c_0011_13'], 'c_1001_11' : d['c_0011_16'], 'c_1001_10' : d['c_0011_11'], 'c_1001_13' : d['c_0011_16'], 'c_1001_12' : negation(d['c_0011_14']), 'c_1001_5' : d['c_1001_5'], 'c_1001_4' : d['c_0101_0'], 'c_1001_7' : d['c_0011_12'], 'c_1001_6' : d['c_0101_6'], 'c_1001_1' : d['c_0101_10'], 'c_1001_0' : d['c_0011_0'], 'c_1001_3' : d['c_1001_2'], 'c_1001_2' : d['c_1001_2'], 'c_1001_9' : negation(d['c_1001_5']), 'c_1001_8' : d['c_0011_14'], 'c_1010_13' : d['c_0101_6'], 'c_1010_12' : d['c_1001_5'], 'c_1010_11' : negation(d['c_0101_7']), 'c_1010_10' : negation(d['c_0011_10']), 'c_1010_17' : negation(d['c_0011_10']), 'c_1010_16' : negation(d['c_0101_6']), 'c_1010_15' : d['c_0011_14'], 'c_1010_14' : d['c_0011_12'], '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_0_17' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_1'], 'c_0101_10' : d['c_0101_10'], 'c_0101_17' : negation(d['c_0011_7']), 'c_0101_16' : d['c_0101_1'], 'c_0101_15' : d['c_0101_15'], 'c_0101_14' : negation(d['c_0011_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_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_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' : negation(d['1']), 's_0_3' : 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_15'], 'c_0011_16' : d['c_0011_16'], 'c_0011_11' : d['c_0011_11'], 'c_1100_8' : d['c_0011_13'], 'c_0011_13' : d['c_0011_13'], 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0101_8']), 'c_1100_4' : negation(d['c_0101_8']), 'c_1100_7' : negation(d['c_0011_11']), 'c_1100_6' : d['c_0101_7'], 'c_1100_1' : negation(d['c_0101_8']), 'c_1100_0' : negation(d['c_0101_10']), 'c_1100_3' : negation(d['c_0101_10']), 'c_1100_2' : negation(d['c_0011_11']), 'c_1100_15' : negation(d['c_0011_12']), 's_0_10' : d['1'], 'c_1100_17' : d['c_0101_7'], 'c_1100_16' : d['c_0011_13'], 'c_1100_11' : negation(d['c_0011_7']), 'c_1100_10' : negation(d['c_1001_5']), 'c_1100_13' : d['c_0101_7'], 's_3_10' : d['1'], 's_3_13' : d['1'], 'c_1010_7' : d['c_1001_2'], 'c_1010_6' : d['c_0011_11'], 'c_1010_5' : d['c_0101_10'], 's_3_12' : d['1'], 'c_1010_3' : negation(d['c_1001_5']), 'c_1010_2' : d['c_0011_0'], 'c_1010_1' : d['c_0101_0'], 'c_1100_14' : negation(d['c_0011_11']), 's_3_15' : d['1'], 'c_1010_9' : d['c_1001_2'], 'c_1010_8' : d['c_0011_13'], 's_3_17' : d['1'], 's_3_16' : d['1'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : d['1'], 's_3_2' : negation(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_8']), 's_1_7' : d['1'], 's_1_6' : negation(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_15']), 'c_0011_8' : negation(d['c_0011_15']), 'c_0011_5' : negation(d['c_0011_11']), 'c_0011_4' : negation(d['c_0011_10']), 'c_0101_13' : negation(d['c_0011_7']), 'c_0011_6' : d['c_0011_0'], 'c_0011_1' : negation(d['c_0011_0']), 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : d['c_0011_15'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : negation(d['c_0101_15']), 'c_0110_10' : d['c_0101_0'], 'c_0110_13' : d['c_0101_6'], 'c_0110_12' : negation(d['c_0101_15']), 'c_0110_15' : negation(d['c_0011_10']), 'c_0110_14' : d['c_0101_7'], 'c_0110_17' : d['c_0011_14'], 'c_0110_16' : d['c_0011_7'], 'c_1010_4' : d['c_1001_5'], 'c_0101_12' : negation(d['c_0011_13']), 'c_0011_7' : d['c_0011_7'], 'c_0110_0' : d['c_0101_1'], 'c_1010_0' : d['c_1001_2'], 's_2_14' : d['1'], 's_2_15' : d['1'], 's_3_14' : d['1'], 'c_0101_7' : d['c_0101_7'], 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : negation(d['c_0101_15']), 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_1'], 'c_0101_2' : d['c_0011_16'], 'c_0101_1' : d['c_0101_1'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0011_14'], 'c_0101_8' : d['c_0101_8'], '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_0011_7']), 'c_0110_8' : d['c_0101_1'], 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : d['c_0011_12'], 'c_0110_3' : d['c_0101_8'], 'c_0110_2' : d['c_0101_6'], 'c_0110_5' : d['c_0101_1'], 'c_0110_4' : d['c_0101_10'], 'c_0110_7' : d['c_0011_16'], 'c_0110_6' : d['c_0011_16']})}"; 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);