______________________________________________________________________________ [2] x^2-2 0 1 2 2 [2] 0.051 10.0e-4 [[A-e1,A],[e1^2-2,e1]] _______________________________________________________________________________ [3] x^3-2 0 1 using a factor (-12*c3)+A^3-6 over the cyclotomic_3 6 3 [3] 0.064 10.0e-4 [[A-e1,A],[e1^3-12*c3-6,e1],[c3^2+c3+1,c3]] _______________________________________________________________________________ [4] x^4-2 0 1 8 8 [2,2,2] 0.075 0.004 [[A-e3,A],[e3^2+3*e2+4*e1,e3],[e2^2-2,e2],[e1^2+2,e1]] _______________________________________________________________________________ [5] x^5-2 0 1 using a factor (-30*c5^3)+10*c5^2-20*c5+A^5-10 over the cyclotomic_5 20 5 [5] 0.069 0.002 [[A-e1,A],[e1^5-30*c5^3+10*c5^2-20*c5-10,e1],[c5^4+c5^3+c5^2+c5+1,c5]] _______________________________________________________________________________ [6] x^6-2 0 1 using a factor (-720*c3)+A^6-74 over the cyclotomic_3 12 6 [2,3] 0.068 0.003 [[A-e2,A],[e2^3-e1,e2],[e1^2-720*c3-74,e1],[c3^2+c3+1,c3]] _______________________________________________________________________________ [7] x^7-2 0 1 using a factor (-84*c7^5)-112*c7^4-28*c7^3-56*c7^2-140*c7+A^7-70 over the cyclotomic_21 42 7 [7] 0.112 0.003 [[A-e1,A],[e1^7-84*c7^5-112*c7^4-28*c7^3-56*c7^2-140*c7-70,e1], [c7^6+c7^5+c7^4+c7^3+c7^2+c7+1,c7]] _______________________________________________________________________________ [8] x^8-2 0 1 16 16 [2,2,2,2] 0.088 0.007 [[A-e4,A],[e4^2+e3,e4],[e3^2+8*e2+6*e1,e3],[e2^2+1,e2],[e1^2+2,e1]] _______________________________________________________________________________ [9] x^9-2 0 1 using a factor 1296*c3+A^18*((-1008*c3)-504)+A^27+17172*A^9+648 over the cyclotomic_3 [112,96,2,26] 1 L: 0.002 [114,25,2,8] 2 L: 0.002 54 27 [3,3,3] 0.141 0.046 [[A-(e3+e2)/3,A],[e3^3+9*c3*e1-9*e1,e3],[e2^3-9*c3*e1-18*e1,e2], [e1^3-12*c3-6,e1],[c3^2+c3+1,c3]] _______________________________________________________________________________ [10] x^10-2 0 1 using a factor (-24640*c5^3)+26840*c5^2-30360*c5+A^10+10558 over the cyclotomic_5 40 10 [2,5] 0.126 0.004 [[A-e2,A],[e2^5-e1,e2],[e1^2-24640*c5^3+26840*c5^2-30360*c5+10558,e1], [c5^4+c5^3+c5^2+c5+1,c5]] _______________________________________________________________________________ [11] x^11-2 0 1 using a factor (-1254*c11^9)-220*c11^8-308*c11^7-990*c11^6+330*c11^5-352*c11^4-440*c11^3+594*c11^2-660*c11+A^11-330 over the cyclotomic_55 110 11 [11] 0.514 0.007 [[A-e1,A], [e1^11-1254*c11^9-220*c11^8-308*c11^7-990*c11^6+330*c11^5-352*c11^4-440*c11^3 +594*c11^2-660*c11-330,e1], [c11^10+c11^9+c11^8+c11^7+c11^6+c11^5+c11^4+c11^3+c11^2+c11+1,c11]] _______________________________________________________________________________ [12] x^12-2 0 1 using a factor (-5100480*c3)+A^12*((-744480*c3)-18500)+A^24-21345404 over the cyclotomic_3 48 24 [2,2,2,3] 0.204 0.017 [[A-e4,A],[e4^3-e3,e4],[e3^2+4*e2+3*e1,e3],[e2^2-11790*c3-352,e2], [e1^2-20400*c3-402,e1],[c3^2+c3+1,c3]] _______________________________________________________________________________ [13] x^13-2 0 1 using a factor (-3146*c13^11)-2730*c13^10+858*c13^9-2600*c13^8-4004*c13^7-1144*c13^6-2548*c13^5-6006*c13^4-2418*c13^3-2002*c13^2-5148*c13+A^13-2574 over the cyclotomic_39 156 13 [13] 0.896 0.007 [[A-e1,A], [e1^13-3146*c13^11-2730*c13^10+858*c13^9-2600*c13^8-4004*c13^7-1144*c13^6 -2548*c13^5-6006*c13^4-2418*c13^3-2002*c13^2-5148*c13-2574,e1], [c13^12+c13^11+c13^10+c13^9+c13^8+c13^7+c13^6+c13^5+c13^4+c13^3+c13^2+c13+1, c13]] _______________________________________________________________________________ [14] x^14-2 0 1 using a factor (-2996392*c7^5)-2076256*c7^4+590408*c7^3-1613920*c7^2-3503136*c7+A^14-613090 over the cyclotomic_21 84 14 [2,7] 0.465 0.008 [[A-e2,A],[e2^7-e1,e2], [e1^2-2996392*c7^5-2076256*c7^4+590408*c7^3-1613920*c7^2-3503136*c7-613090, e1],[c7^6+c7^5+c7^4+c7^3+c7^2+c7+1,c7]] _______________________________________________________________________________ [15] x^15-2 0 1 using a factor (-26520*c5^3)+c3*((-15780*c5^3)-15780*c5^2-25092)-3740*c5^2-14480*c5+A^15-19786 over the cyclotomic_15 120 15 [3,5] 0.684 0.01 [[A-e2,A],[e2^5-e1,e2], [e1^3-26520*c5^3+c3*((-15780*c5^3)-15780*c5^2-25092)-3740*c5^2-14480*c5 -19786,e1],[c3^2+c3+1,c3],[c5^4+c5^3+c5^2+c5+1,c5]] _______________________________________________________________________________ [16] x^16-2 0 1 64 64 [2,2,2,2,2,2] 0.389 0.074 [[A-e6,A],[e6^2+e5,e6],[e5^2+4*e4+e3,e5],[e4^2+2*e2+2*e1,e4], [e3^2+24*e2+38*e1,e3],[e2^2+1,e2],[e1^2+2,e1]] Evaluation took 0.9120 seconds (4.1410 elapsed) using 185.416 MB.