// Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 19); MyIdeal := ideal; print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\n11_340\ngeometric_solution 17.08797076\noriented_manifold\nCS_unknown\n\n1 0\n torus 0.000000000000 0.000000000000\n\n18\n 1 2 3 2 \n 0132 0132 0132 0213\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 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 0.272635548687 0.764307557347\n\n 0 4 6 5 \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 0.224277004802 0.710599545446\n\n 7 0 8 0 \n 0132 0132 0132 0213\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 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 0.272635548687 0.764307557347\n\n 7 6 6 0 \n 2031 3012 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 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.460472674911 0.863877776187\n\n 7 1 5 9 \n 1023 0132 2103 0132\n 0 0 0 0 \n 0 0 -1 1 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 -13 13 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 0.412111270178 1.317966628224\n\n 4 10 1 11 \n 2103 0132 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 0 0 0 0 13 0 0 -13 -1 1 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.892937525631 1.000914188270\n\n 3 12 3 1 \n 1230 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 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 0.520089226019 0.832753973894\n\n 2 4 3 11 \n 0132 1023 1302 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 1 -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 0.403233240438 1.419691405016\n\n 9 13 13 2 \n 0321 0132 0321 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 -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 0.486828433075 0.915743148132\n\n 8 12 4 14 \n 0321 0213 0132 0132\n 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 13 -13 0 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 0.519691282162 0.457129991720\n\n 15 5 16 15 \n 0132 0132 0132 2031\n 0 0 0 0 \n 0 0 -1 1 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 -14 14 0 0 0 0 0 -1 0 1 -14 0 14 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.288538212666 0.487024083205\n\n 13 16 5 7 \n 0132 0132 0132 1023\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 -1 0 0 1 0 0 0 0 0 -13 13 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.460613729129 0.531417933480\n\n 17 6 9 17 \n 0132 0132 0213 2031\n 0 0 0 0 \n 0 0 -1 1 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 -13 13 0 0 1 -1 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 0.482549727196 0.664582360439\n\n 11 8 8 14 \n 0132 0132 0321 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 -1 0 1 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 0.486828433075 0.915743148132\n\n 16 15 9 13 \n 0213 2310 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 0 0 -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 -0.115365489878 1.036569352653\n\n 10 10 17 14 \n 0132 1302 1023 3201\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 14 -14 0 0 0 -1 1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.099575184795 1.519828400088\n\n 14 11 17 10 \n 0213 0132 2031 0132\n 0 0 0 0 \n 0 0 -1 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 0 -14 14 -1 0 1 0 1 13 0 -14 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 1.380585196170 1.584031959535\n\n 12 12 15 16 \n 0132 1302 1023 1302\n 0 0 0 0 \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 1 0 -1 0 0 0 0 -1 -13 0 14 0 1 -1 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.284606980918 0.985261320165\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_0101_15'], 'c_1001_14' : d['c_1001_14'], 'c_1001_17' : d['c_0101_15'], 'c_1001_16' : negation(d['c_0011_9']), 'c_1001_11' : d['c_1001_10'], 'c_1001_10' : d['c_1001_10'], 'c_1001_13' : d['c_1001_13'], 'c_1001_12' : d['c_1001_1'], 'c_1001_5' : negation(d['c_0011_10']), 'c_1001_4' : negation(d['c_0011_10']), 'c_1001_7' : d['c_0101_0'], 'c_1001_6' : negation(d['c_0011_12']), 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : negation(d['c_0101_6']), 'c_1001_3' : d['c_0011_12'], 'c_1001_2' : d['c_1001_13'], 'c_1001_9' : d['c_1001_1'], 'c_1001_8' : d['c_0101_10'], 'c_1010_13' : d['c_0101_10'], 'c_1010_12' : negation(d['c_0011_12']), 'c_1010_11' : negation(d['c_0011_9']), 'c_1010_10' : negation(d['c_0011_10']), 'c_1010_17' : negation(d['c_1001_14']), 'c_1010_16' : d['c_1001_10'], 'c_1010_15' : negation(d['c_1001_14']), 'c_1010_14' : negation(d['c_0101_10']), 's_0_10' : d['1'], 's_0_11' : d['1'], 's_3_13' : d['1'], 's_3_12' : 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' : d['c_0101_11'], 'c_0101_10' : d['c_0101_10'], 'c_0101_17' : d['c_0101_15'], 'c_0101_16' : d['c_0011_14'], 'c_0101_15' : d['c_0101_15'], 'c_0101_14' : negation(d['c_0011_11']), 's_2_0' : d['1'], 's_2_1' : d['1'], 's_2_2' : d['1'], 's_2_3' : d['1'], 's_2_4' : negation(d['1']), 's_2_5' : negation(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_2_15' : d['1'], 's_0_6' : d['1'], 's_0_7' : d['1'], 's_0_4' : d['1'], 's_0_5' : negation(d['1']), 's_0_2' : d['1'], 's_0_3' : d['1'], 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_15' : negation(d['c_0011_10']), 'c_0011_14' : d['c_0011_14'], 'c_0011_17' : negation(d['c_0011_12']), 'c_0011_16' : negation(d['c_0011_11']), 'c_1100_9' : negation(d['c_0101_11']), 'c_1100_8' : d['c_1001_13'], 'c_0011_13' : negation(d['c_0011_11']), 'c_0011_12' : d['c_0011_12'], 'c_1100_5' : negation(d['c_0101_3']), 'c_1100_4' : negation(d['c_0101_11']), 'c_1100_7' : d['c_0101_3'], 'c_1100_6' : negation(d['c_0101_3']), 'c_1100_1' : negation(d['c_0101_3']), 'c_1100_0' : negation(d['c_0101_6']), 'c_1100_3' : negation(d['c_0101_6']), 'c_1100_2' : d['c_1001_13'], 'c_1100_14' : negation(d['c_0101_11']), 'c_1100_15' : negation(d['c_0011_14']), 's_3_11' : d['1'], 'c_1100_17' : d['c_0011_14'], 'c_1100_16' : d['c_1001_14'], 'c_1100_11' : negation(d['c_0101_3']), 'c_1100_10' : d['c_1001_14'], 'c_1100_13' : d['c_0101_10'], 's_3_10' : d['1'], 's_0_12' : d['1'], 'c_1010_7' : d['c_0101_13'], 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : d['c_1001_10'], 's_0_13' : d['1'], 'c_1010_3' : negation(d['c_0101_6']), 'c_1010_2' : negation(d['c_0101_6']), 'c_1010_1' : negation(d['c_0011_10']), 'c_1010_0' : d['c_1001_13'], 's_3_15' : d['1'], 'c_1010_9' : d['c_1001_14'], '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' : d['c_1001_14'], 's_1_7' : d['1'], 's_1_6' : d['1'], 's_1_5' : d['1'], 's_1_4' : negation(d['1']), 's_1_3' : d['1'], 's_1_2' : d['1'], 's_1_1' : negation(d['1']), 's_1_0' : d['1'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : d['c_0011_9'], 'c_0011_8' : d['c_0011_11'], 'c_0011_5' : negation(d['c_0011_10']), 'c_0011_4' : d['c_0011_0'], 'c_0101_13' : d['c_0101_13'], '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' : d['c_0011_3'], 'c_0011_2' : negation(d['c_0011_0']), 'c_0110_11' : d['c_0101_13'], 'c_0110_10' : d['c_0101_15'], 'c_0110_13' : d['c_0101_11'], 'c_0110_12' : d['c_0101_15'], 'c_0110_15' : d['c_0101_10'], 'c_0110_14' : negation(d['c_0101_10']), 'c_0110_17' : d['c_0011_9'], 'c_0110_16' : d['c_0101_10'], 'c_1010_4' : d['c_1001_1'], 'c_0101_12' : d['c_0011_9'], 'c_0011_7' : d['c_0011_0'], 's_2_14' : d['1'], 's_0_9' : d['1'], 'c_1010_8' : d['c_1001_13'], 'c_0011_11' : d['c_0011_11'], 'c_0101_7' : negation(d['c_0011_3']), 'c_0101_6' : d['c_0101_6'], 'c_0101_5' : d['c_0101_0'], 'c_0101_4' : d['c_0101_0'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : negation(d['c_0011_9']), 'c_0101_1' : d['c_0011_3'], 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : d['c_0101_13'], 'c_0101_8' : negation(d['c_0101_13']), '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_11']), 'c_0110_8' : negation(d['c_0011_9']), 'c_0110_1' : d['c_0101_0'], 'c_0110_0' : d['c_0011_3'], 'c_0110_3' : d['c_0101_0'], 'c_0110_2' : negation(d['c_0011_3']), 'c_0110_5' : d['c_0101_11'], 'c_0110_4' : d['c_0101_13'], 'c_0110_7' : negation(d['c_0011_9']), 'c_0110_6' : d['c_0011_3']})}"; 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);