// Preambel print "==TRIANGULATION" cat "=BEGINS=="; print "% Triangulation\nK12a835\ngeometric_solution 10.85275762\noriented_manifold\nCS_known -0.0000000000000004\n\n1 0\n torus 0.000000000000 0.000000000000\n\n12\n 0 0 1 2 \n 1230 3012 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 -1 0 0 1 -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 1.325736728188 0.548566313474\n\n 2 3 4 0 \n 1302 0132 0132 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 -1 1 0 0 0 0 0 0 0 0 -4 4 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.904056218695 0.815871460063\n\n 5 1 0 6 \n 0132 2031 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 0 0 0 0 0 -1 1 -4 4 0 0 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.881168950301 0.649846505901\n\n 7 1 5 7 \n 0132 0132 2031 2103\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 0 0 0 -1 0 1 0 0 -4 0 4 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n -0.014165274689 0.863489643313\n\n 8 9 10 1 \n 0132 0132 0132 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 -1 0 1 0 0 0 0 0 0 0 0 5 0 -5 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.634572385106 0.499715328930\n\n 2 8 8 3 \n 0132 0213 0132 1302\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 1 0 -1 0 0 0 0 0 0 0 0 4 0 -4 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.236495269431 0.960728869500\n\n 10 7 2 11 \n 0132 2103 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 -1 1 -5 0 0 5 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.825044151289 0.836502940303\n\n 3 6 11 3 \n 0132 2103 2103 2103\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 4 -4 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 -0.014165274689 0.863489643313\n\n 4 9 5 5 \n 0132 1302 0213 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 1 -1 0 0 0 0 0 -5 1 0 4 0 0 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.758414517977 0.981407144379\n\n 10 4 11 8 \n 1302 0132 0213 2031\n 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 1 0 -1 5 0 -4 -1 0 0 0 0 5 0 -5 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 1.009122285434 0.998154507921\n\n 6 9 11 4 \n 0132 2031 0132 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 0 0 0 0 0 -5 0 5 5 -5 0 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n 0.245796902862 0.789469214070\n\n 7 9 6 10 \n 2103 0213 0132 0132\n 0 0 0 0 \n 0 0 0 0 0 0 0 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 0 0 0 1 0 -1 0 -4 4 0 0 0 5 -5 0\n 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n -0.146765083751 0.649830285686\n\n"; print "==TRIANGULATION" cat "=ENDS=="; print "PY=EVAL=SECTION" cat "=BEGINS=HERE"; print "{'variable_dict' : (lambda d, negation = (lambda x:-x): { 'c_1001_11' : d['c_1001_1'], 'c_1001_10' : negation(d['c_0110_9']), 'c_1001_5' : d['c_0110_9'], 'c_1001_4' : negation(d['c_0011_4']), 'c_1001_7' : negation(d['c_0011_10']), 'c_1001_6' : d['c_0011_1'], 'c_1001_1' : d['c_1001_1'], 'c_1001_0' : negation(d['c_0011_0']), 'c_1001_3' : negation(d['c_0011_0']), 'c_1001_2' : negation(d['c_0101_0']), 'c_1001_9' : d['c_1001_1'], 'c_1001_8' : d['c_0110_9'], 'c_1010_11' : negation(d['c_0110_9']), 'c_1010_10' : negation(d['c_0011_4']), 's_0_10' : d['1'], 's_3_10' : d['1'], 's_2_8' : d['1'], 's_2_9' : d['1'], 'c_0101_11' : d['c_0101_10'], 'c_0101_10' : d['c_0101_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_10' : d['1'], 's_2_11' : d['1'], 's_0_8' : d['1'], 's_0_9' : d['1'], 's_0_6' : d['1'], 's_0_7' : negation(d['1']), 's_0_4' : d['1'], 's_0_5' : d['1'], 's_0_2' : d['1'], 's_0_3' : negation(d['1']), 's_0_0' : d['1'], 's_0_1' : d['1'], 'c_0011_11' : negation(d['c_0011_10']), 'c_0011_10' : d['c_0011_10'], 'c_1100_5' : d['c_0101_3'], 'c_1100_4' : d['c_1100_0'], 'c_1100_7' : negation(d['c_0101_10']), 'c_1100_6' : d['c_1100_0'], 'c_1100_1' : d['c_1100_0'], 'c_1100_0' : d['c_1100_0'], 'c_1100_3' : negation(d['c_0101_3']), 'c_1100_2' : d['c_1100_0'], 's_3_11' : d['1'], 'c_1100_11' : d['c_1100_0'], 'c_1100_10' : d['c_1100_0'], 's_0_11' : d['1'], 'c_1010_7' : negation(d['c_1001_1']), 'c_1010_6' : d['c_1001_1'], 'c_1010_5' : d['c_0101_3'], 'c_1010_4' : d['c_1001_1'], 'c_1010_3' : d['c_1001_1'], 'c_1010_2' : d['c_0011_1'], 'c_1010_1' : negation(d['c_0011_0']), 'c_1010_0' : negation(d['c_0101_0']), 'c_1010_9' : negation(d['c_0011_4']), 'c_1010_8' : d['c_0110_9'], 'c_1100_8' : d['c_0101_3'], 's_3_1' : d['1'], 's_3_0' : d['1'], 's_3_3' : negation(d['1']), 's_3_2' : d['1'], 's_3_5' : d['1'], 's_3_4' : d['1'], 's_3_7' : negation(d['1']), 's_3_6' : d['1'], 's_3_9' : d['1'], 's_3_8' : d['1'], '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' : d['1'], 's_1_1' : d['1'], 'c_0110_0' : d['c_0011_0'], 's_1_9' : d['1'], 's_1_8' : d['1'], 'c_0011_9' : negation(d['c_0011_4']), 'c_0011_8' : negation(d['c_0011_4']), 'c_0011_5' : negation(d['c_0011_2']), 'c_0011_4' : d['c_0011_4'], 'c_0011_7' : d['c_0011_1'], 'c_0011_6' : negation(d['c_0011_10']), 'c_0011_1' : d['c_0011_1'], 'c_0011_0' : d['c_0011_0'], 'c_0011_3' : negation(d['c_0011_1']), 'c_0011_2' : d['c_0011_2'], 'c_0110_11' : d['c_0101_10'], 'c_0110_10' : d['c_0101_4'], 'c_0101_7' : d['c_0101_10'], 'c_0101_6' : d['c_0101_4'], 'c_0101_5' : d['c_0101_4'], 'c_0101_4' : d['c_0101_4'], 'c_0101_3' : d['c_0101_3'], 'c_0101_2' : d['c_0011_0'], 'c_0101_1' : negation(d['c_0011_2']), 'c_0101_0' : d['c_0101_0'], 'c_0101_9' : negation(d['c_0011_10']), 'c_0101_8' : negation(d['c_0011_2']), 's_1_11' : d['1'], 's_1_10' : d['1'], 'c_0110_9' : d['c_0110_9'], 'c_0110_8' : d['c_0101_4'], 'c_0110_1' : d['c_0101_0'], 'c_1100_9' : negation(d['c_0110_9']), 'c_0110_3' : d['c_0101_10'], 'c_0110_2' : d['c_0101_4'], 'c_0110_5' : d['c_0011_0'], 'c_0110_4' : negation(d['c_0011_2']), 'c_0110_7' : d['c_0101_3'], 'c_0110_6' : d['c_0101_10'], 's_1_0' : d['1']})}"; print "PY=EVAL=SECTION=ENDS=HERE"; cputime := Cputime(); // Computation // Setting up the Polynomial ring and ideal R := PolynomialRing(RationalField(), 13); I := ideal; // Value indicating failure P := -1; // Computing the primary decomposition P,Q:=PrimaryDecomposition(I); if Type(P) eq RngIntElt then // Some error occured print "PRIMARY=DECOMPOSITION" cat "=FAILED"; else // Success print "PRIMARY=DECOMPOSITION" cat "=BEGINS=HERE"; P; print "PRIMARY=DECOMPOSITION" cat "=ENDS=HERE"; end if; print "CPUTIME :", Cputime(cputime);