R := PolynomialRing(RationalField(), 16, "grevlex"); MyIdeal := ideal; print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\nm146\ngeometric_solution 3.75884495\noriented_manifold\nCS_unknown\n\n1 0\n torus 0.000000000000 0.000000000000\n\n4\n 1 2 3 3 \n 0132 0132 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 1 0 -1 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 0.301695873632 1.081512576550\n\n 0 2 1 1 \n 0132 1230 1230 3012\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 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 0.421350946931 0.652575763252\n\n 3 0 1 3 \n 2103 0132 3012 1230\n 0 0 0 0 \n 0 0 0 0 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 -1 0 1 -1 0 0 1 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 0.421350946931 0.652575763252\n\n 2 0 2 0 \n 3012 2310 2103 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 0 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 -0.239310146598 0.857873626595\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1020_2' : d['c_0102_2'], 'c_1020_3' : d['c_0102_2'], 'c_1020_0' : d['c_0012_0'], 'c_1020_1' : d['c_0102_2'], 'c_0201_0' : d['c_0201_0'], 'c_0201_1' : d['c_0102_2'], 'c_0201_2' : d['c_0102_1'], 'c_0201_3' : d['c_0102_1'], 'c_2100_0' : d['c_0012_3'], 'c_2100_1' : d['c_0201_0'], 'c_2100_2' : d['c_0201_0'], 'c_2100_3' : d['c_0012_3'], 'c_2010_2' : d['c_0102_1'], 'c_2010_3' : d['c_0102_1'], 'c_2010_0' : d['c_0012_1'], 'c_2010_1' : d['c_0102_1'], 'c_0102_0' : d['c_0102_0'], 'c_0102_1' : d['c_0102_1'], 'c_0102_2' : d['c_0102_2'], 'c_0102_3' : d['c_0102_2'], 'c_1101_0' : d['c_1101_0'], 'c_1101_1' : d['c_1101_1'], 'c_1101_2' : d['c_1011_1'], 'c_1101_3' : negation(d['c_0111_2']), 'c_1200_2' : d['c_0102_0'], 'c_1200_3' : d['c_0021_3'], 'c_1200_0' : d['c_0021_3'], 'c_1200_1' : d['c_0102_0'], 'c_1110_2' : d['c_0111_3'], 'c_1110_3' : d['c_1101_0'], 'c_1110_0' : negation(d['c_1011_3']), 'c_1110_1' : d['c_1101_1'], 'c_0120_0' : d['c_0102_1'], 'c_0120_1' : d['c_0102_0'], 'c_0120_2' : d['c_0012_3'], 'c_0120_3' : d['c_0102_0'], 'c_2001_0' : d['c_0102_1'], 'c_2001_1' : d['c_0102_0'], 'c_2001_2' : d['c_0012_1'], 'c_2001_3' : d['c_0012_0'], 'c_0012_2' : d['c_0012_1'], 'c_0012_3' : d['c_0012_3'], 'c_0012_0' : d['c_0012_0'], 'c_0012_1' : d['c_0012_1'], 'c_0111_0' : d['c_0111_0'], 'c_0111_1' : negation(d['c_0111_0']), 'c_0111_2' : d['c_0111_2'], 'c_0111_3' : d['c_0111_3'], 'c_0210_2' : d['c_0021_3'], 'c_0210_3' : d['c_0201_0'], 'c_0210_0' : d['c_0102_2'], 'c_0210_1' : d['c_0201_0'], 'c_1002_2' : d['c_0012_0'], 'c_1002_3' : d['c_0012_1'], 'c_1002_0' : d['c_0102_2'], 'c_1002_1' : d['c_0201_0'], 'c_1011_2' : negation(d['c_1011_0']), 'c_1011_3' : d['c_1011_3'], 'c_1011_0' : d['c_1011_0'], 'c_1011_1' : d['c_1011_1'], 'c_0021_0' : d['c_0012_1'], 'c_0021_1' : d['c_0012_0'], 'c_0021_2' : d['c_0012_0'], 'c_0021_3' : d['c_0021_3']})}"; print "PY=EVAL=SECTION=ENDS=HERE"; // Initialize Q to -1 so that we can check whether an error happend // by checking that Q is still of type integer. Q := -1; // Remember start time to calculate computation time primTime := Cputime(); Groebner(MyIdeal); print "Status: Computed Groebner Basis"; for i := 1 to #Names(R) do MyIdeal := Saturation(MyIdeal, R.i); Groebner(MyIdeal); print "Status: Saturated ", i, "/", #Names(R); end for; print "Dimension: ", Dimension(MyIdeal); // MyIdeal := Radical(MyIdeal); // P is radical // Q is primary Qgrevlex, P := PrimaryDecomposition(MyIdeal); function ToLex(compQ) if Dimension(compQ) le 0 then return ChangeOrder(compQ, "lex"); else return compQ; end if; end function; Q := [ToLex(compQ): compQ in Qgrevlex]; for compQ in Q do if not IsRadical(compQ) then print "Failure: Not Radical!!!"; print "IDEAL=DECOMPOSITION" cat "=FAILED"; Q := -1; end if; if not IsPrime(compQ) then print "Failure: Not prime!!!"; print "IDEAL=DECOMPOSITION" cat "=FAILED"; Q := -1; end if; D := Dimension(compQ); end for; print "DECOMPOSITION=TYPE: Radicals of Primary Decomposition computed in several steps"; print "IDEAL=DECOMPOSITION" cat "=TIME: ", Cputime(primTime); if Type(Q) eq RngIntElt then // Some error occured print "IDEAL=DECOMPOSITION" cat "=FAILED"; exit; else // Success print "IDEAL=DECOMPOSITION" cat "=BEGINS=HERE"; Q; print "IDEAL=DECOMPOSITION" cat "=ENDS=HERE"; print "FREE=VARIABLES=IN=COMPONENTS" cat "=BEGINS=HERE"; N := Names(R); isFirstComp := true; freeVarStr := "["; for Comp in Q do if isFirstComp then isFirstComp := false; else freeVarStr := freeVarStr cat ","; end if; freeVarStr := freeVarStr cat "\n [ "; 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 "\n]"; print freeVarStr; print "FREE=VARIABLES=IN=COMPONENTS" cat "=ENDS=HERE"; end if; print "CPUTIME: ", Cputime(primTime);