Table 1: Ex1: Katsura-5 := [2*x[5] + 2*x[4] + 2*x[3] + 2*x[2] + 2*x[1] + x[6] - 1, 2*x[1]*x[2] + 2*x[1]*x[4] + 2*x[2]*x[5] + 3*x[3]*x[6] - x[3], 2*x[1]*x[3] + 2*x[1]*x[5] + x[2]^2 + x[2]*x[6] + 2*x[4]*x[6] - x[4], 2*x[1]*x[2] + 2*x[1]*x[6] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + x[5]*x[6] - x[1], 2*x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + x[6]^2 - x[6], x[1]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[2]*x[6] + 2*x[3]*x[5] + x[4]*x[6] - x[2]]; f := -x[1]^2*x[2]*x[4]^2*x[5]*x[6]^2 + x[1]^2*x[2]^2*x[4]*x[6] + x[1]^2*x[2]*x[3]*x[5]^2 + x[3]*x[4]*x[5]*x[6]; Ex2: Eco-7 := [x[1]*x[2]*x[7] + x[2]*x[3]*x[7] + x[3]*x[4]*x[7] + x[4]*x[5]*x[7] + x[5]*x[6]*x[7] + x[1]*x[7] - 1, x[1]*x[3]*x[7] + x[2]*x[4]*x[7] + x[3]*x[5]*x[7] + x[4]*x[6]*x[7] + x[2]*x[7] - 2, x[1]*x[4]*x[7] + x[2]*x[5]*x[7] + x[3]*x[6]*x[7] + x[3]*x[7] - 3, x[1]*x[5]*x[7] + x[2]*x[6]*x[7] + x[4]*x[7] - 4, x[1]*x[6]*x[7] + x[5]*x[7] - 5, x[6]*x[7] - 6, x[1] + x[2] + x[3] + x[4] + x[5] + x[6] + 1]; f := -x[5]^3; Ex3: Countercurrent reactors-10 := [-8*x[1]*x[2] - 2*x[1] - x[3] + 1, -8*x[1]*x[2] - 2*x[2] - 3*x[4], -8*x[3]*x[4] + x[1] - 2*x[3] - x[5], -8*x[3]*x[4] + x[2] - 2*x[4] - 3*x[6], -8*x[5]*x[6] + x[3] - 2*x[5] - x[7], -8*x[5]*x[6] + x[4] - 2*x[6] - 3*x[8], -8*x[7]*x[8] + x[5] - 2*x[7] - x[9], -8*x[7]*x[8] + x[6] - 2*x[8] - 3*x[10], -8*x[9]*x[10] + x[7] - 2*x[9], -8*x[9]*x[10] + x[8] - 2*x[10] - 3]; f := -x[1]*x[2]^2*x[4]^2*x[5]*x[6]*x[7]^2*x[9]^2*x[10] - x[1]^2*x[2]*x[5]*x[6]*x[7]^2*x[8]^2*x[9]*x[10] - x[1]*x[2]^2*x[3]^2*x[4]^2*x[6]^2*x[9]^2 + x[1]^2*x[3]*x[5]*x[8]^2*x[9]*x[10]; Ex4: Bellindo := [x[1]^2 + x[2]^2 + x[3]^2 - 12*x[1] - 68, x[4]^2 + x[5]^2 + x[6]^2 - 12*x[5] - 68, x[7]^2 + x[8]^2 + x[9]^2 - 24*x[8] - 12*x[9] + 100, x[1]*x[4] + x[2]*x[5] + x[3]*x[6] - 6*x[1] - 6*x[5] - 52, x[1]*x[7] + x[2]*x[8] + x[3]*x[9] - 6*x[1] - 12*x[8] - 6*x[9] + 64, x[4]*x[7] + x[5]*x[8] + x[6]*x[9] - 6*x[5] - 12*x[8] - 6*x[9] + 32, 2*x[2] + 2*x[3] - 2*x[6] - x[4] - x[5] - x[7] - x[9] + 18, x[1] + x[2] + 2*x[3] + 2*x[4] + 2*x[6] - 2*x[7] + x[8] - x[9] - 38, x[1] + x[3] + x[5] - x[6] + 2*x[7] - 2*x[8] - 2*x[4] + 8]; f:=-x[1]^2*x[2]^2*x[3]*x[4]^2*x[5]^2*x[6]*x[7]*x[9] - x[1]*x[4]*x[5]*x[6]^2*x[8]: Ex5: Katsura-6 := [2*x[6] + 2*x[5] + 2*x[4] + 2*x[3] + 2*x[2] + 2*x[1] + x[7] - 1, 2*x[1]*x[4] + 2*x[1]*x[6] + 2*x[2]*x[3] + x[2]*x[7] + 2*x[5]*x[7] - x[5], 2*x[1]*x[3] + 2*x[1]*x[5] + x[2]^2 + 2*x[2]*x[6] + x[3]*x[7] + 2*x[4]*x[7] - x[4], 2*x[1]*x[2] + 2*x[1]*x[4] + 2*x[2]*x[5] + 2*x[3]*x[6] + 2*x[3]*x[7] + x[4]*x[7] - x[3], 2*x[1]*x[2] + 2*x[1]*x[7] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + 2*x[5]*x[6] + x[6]*x[7] - x[1], 2*x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + 2*x[6]^2 + x[7]^2 - x[7], x[1]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[2]*x[7] + 2*x[3]*x[5] + 2*x[4]*x[6] + x[5]*x[7] - x[2]]; f := -x[1]^2*x[2]^2*x[3]^2*x[5]^2 + x[1]^2*x[3]*x[5]^2*x[6]^2 + x[1]*x[2]^2*x[5]*x[6]^2*x[7]; Ex6: Broyden tridiagonal-7 := [-2*x[2]^2 - x[1] + 3*x[2] - 2*x[3] + 1, -2*x[3]^2 - x[2] + 3*x[3] - 2*x[4] + 1, -2*x[4]^2 - x[3] + 3*x[4] - 2*x[5] + 1, -2*x[5]^2 - x[4] + 3*x[5] - 2*x[6] + 1, -2*x[6]^2 - x[5] + 3*x[6] - 2*x[7] + 1, -2*x[7]^2 - x[6] + 3*x[7] - 2*x[8] + 1, -2*x[8]^2 - x[7] + 3*x[8] - 2*x[9] + 1, x[1], x[9]]; f := x[1]*x[2]*x[3]*x[6]*x[8]*x[9] + x[2]*x[4]*x[5]*x[6]*x[7]*x[8] + x[1]*x[4]*x[5]*x[7]*x[8] + x[1]*x[3]*x[6]*x[9] + x[1]*x[6]*x[7]; **************************************************************************************************** Table 2: Ex1: Eco-7 := [x[1]*x[2]*x[7] + x[2]*x[3]*x[7] + x[3]*x[4]*x[7] + x[4]*x[5]*x[7] + x[5]*x[6]*x[7] + x[1]*x[7] - 1, x[1]*x[3]*x[7] + x[2]*x[4]*x[7] + x[3]*x[5]*x[7] + x[4]*x[6]*x[7] + x[2]*x[7] - 2, x[1]*x[4]*x[7] + x[2]*x[5]*x[7] + x[3]*x[6]*x[7] + x[3]*x[7] - 3, x[1]*x[5]*x[7] + x[2]*x[6]*x[7] + x[4]*x[7] - 4, x[1]*x[6]*x[7] + x[5]*x[7] - 5, x[6]*x[7] - 6, x[1] + x[2] + x[3] + x[4] + x[5] + x[6] + 1]; Ex2: Katsura-5 := [2*x[5] + 2*x[4] + 2*x[3] + 2*x[2] + 2*x[1] + x[6] - 1, 2*x[1]*x[2] + 2*x[1]*x[4] + 2*x[2]*x[5] + 3*x[3]*x[6] - x[3], 2*x[1]*x[3] + 2*x[1]*x[5] + x[2]^2 + x[2]*x[6] + 2*x[4]*x[6] - x[4], 2*x[1]*x[2] + 2*x[1]*x[6] + 2*x[2]*x[3] + 2*x[3]*x[4] + 2*x[4]*x[5] + x[5]*x[6] - x[1], 2*x[1]^2 + 2*x[2]^2 + 2*x[3]^2 + 2*x[4]^2 + 2*x[5]^2 + x[6]^2 - x[6], x[1]^2 + 2*x[1]*x[3] + 2*x[2]*x[4] + 2*x[2]*x[6] + 2*x[3]*x[5] + x[4]*x[6] - x[2]]; Ex3: Bellindo := [x[1]^2 + x[2]^2 + x[3]^2 - 12*x[1] - 68, x[4]^2 + x[5]^2 + x[6]^2 - 12*x[5] - 68, x[7]^2 + x[8]^2 + x[9]^2 - 24*x[8] - 12*x[9] + 100, x[1]*x[4] + x[2]*x[5] + x[3]*x[6] - 6*x[1] - 6*x[5] - 52, x[1]*x[7] + x[2]*x[8] + x[3]*x[9] - 6*x[1] - 12*x[8] - 6*x[9] + 64, x[4]*x[7] + x[5]*x[8] + x[6]*x[9] - 6*x[5] - 12*x[8] - 6*x[9] + 32, 2*x[2] + 2*x[3] - 2*x[6] - x[4] - x[5] - x[7] - x[9] + 18, x[1] + x[2] + 2*x[3] + 2*x[4] + 2*x[6] - 2*x[7] + x[8] - x[9] - 38, x[1] + x[3] + x[5] - x[6] + 2*x[7] - 2*x[8] - 2*x[4] + 8]; Ex4: Countercurrent reactors-11 := [-8*x[1]*x[2] - 2*x[1] - x[3] + 1, -8*x[1]*x[2] - 2*x[2] - 3*x[4], -8*x[3]*x[4] + x[1] - 2*x[3] - x[5], -8*x[3]*x[4] + x[2] - 2*x[4] - 3*x[6], -8*x[5]*x[6] + x[3] - 2*x[5] - x[7], -8*x[5]*x[6] + x[4] - 2*x[6] - 3*x[8], -8*x[7]*x[8] + x[5] - 2*x[7] - x[9], -8*x[7]*x[8] + x[6] - 2*x[8] - 3*x[10], -8*x[9]*x[10] + x[7] - 2*x[9] - x[11], -8*x[10]*x[11] + x[8] - 2*x[10], -8*x[10]*x[11] + x[9] - 2*x[11] - 3]; Ex5: x[2]^21 - 385*x[2]^19 + 61446*x[2]^17 - 5293970*x[2]^15 + 268880381*x[2]^13 - 8261931405*x[2]^11 + 151847872396*x[2]^9 - 1593719752240*x[2]^7 + 8689315795776*x[2]^5 - 20407635072000*x[2]^3 + 13168189440000*x[2], 10*x[1]^2*x[2]^19 + 15*x[1]*x[2]^20 + 80*x[1]^2*x[2]^18 + 15*x[1]*x[2]^19 - 42*x[2]^20 - 3120*x[1]^2*x[2]^17 - 5520*x[1]*x[2]^18 - 58*x[2]^19 - 24240*x[1]^2*x[2]^16 - 3600*x[1]*x[2]^17 + 15328*x[2]^18 + 392460*x[1]^2*x[2]^15 + 843210*x[1]*x[2]^16 + 15072*x[2]^17 + 2921520*x[1]^2*x[2]^14 + 261450*x[1]*x[2]^15 - 2322204*x[2]^16 - 26035400*x[1]^2*x[2]^13 - 69729060*x[1]*x[2]^14 - 1359996*x[2]^15 - 181989520*x[1]^2*x[2]^12 + 387420*x[1]*x[2]^13 + 190566936*x[2]^14 + 998569050*x[1]^2*x[2]^11 + 3408743535*x[1]*x[2]^12 + 40571864*x[2]^13 + 6350646720*x[1]^2*x[2]^10 - 959004945*x[1]*x[2]^11 - 9253298666*x[2]^12 - 22827018840*x[1]^2*x[2]^9 - 100922318820*x[1]*x[2]^10 + 1087503366*x[2]^11 - 125460330240*x[1]^2*x[2]^8 + 51493202460*x[1]*x[2]^9 + 272421457944*x[2]^10 + 309352912480*x[1]^2*x[2]^7 + 1781362836240*x[1]*x[2]^8 - 107657736744*x[2]^9 + 1345680327680*x[1]^2*x[2]^6 - 1229685089520*x[1]*x[2]^7 - 4787079413088*x[2]^8 - 2387578688640*x[1]^2*x[2]^5 - 17711011473600*x[1]*x[2]^6 + 2948153590688*x[2]^7 - 6989506560000*x[1]^2*x[2]^4 + 14585316390720*x[1]*x[2]^5 + 47437743601792*x[2]^6 + 9488897280000*x[1]^2*x[2]^3 + 87623164800000*x[1]*x[2]^4 - 37018759992192*x[2]^5 + 13005619200000*x[1]^2*x[2]^2 - 80124992640000*x[1]*x[2]^3 - 234161650944000*x[2]^4 - 14631321600000*x[1]^2*x[2] - 158505984000000*x[1]*x[2]^2 + 209167743744000*x[2]^3 + 153628876800000*x[1]*x[2] + 423007764480000*x[2]^2 - 406750740480000*x[2], -107*x[1]*x[2]^20 + 8680*x[1]^2*x[2]^18 + 16417*x[1]*x[2]^19 + 3095*x[2]^20 + 4200*x[1]^3*x[2]^16 + 94920*x[1]^2*x[2]^17 + 105768*x[1]*x[2]^18 - 43345*x[2]^19 + 79800*x[1]^3*x[2]^15 - 2441040*x[1]^2*x[2]^16 - 5898408*x[1]*x[2]^17 - 1394560*x[2]^18 - 575400*x[1]^3*x[2]^14 - 28445760*x[1]^2*x[2]^15 - 28492074*x[1]*x[2]^16 + 15201360*x[2]^17 - 19122600*x[1]^3*x[2]^13 + 258331920*x[1]^2*x[2]^14 + 869072094*x[1]*x[2]^15 + 257250330*x[2]^16 - 24036600*x[1]^3*x[2]^12 + 3349518480*x[1]^2*x[2]^13 + 3589324876*x[1]*x[2]^14 - 2179126230*x[2]^15 + 1598994600*x[1]^3*x[2]^11 - 12604749920*x[1]^2*x[2]^12 - 68153606756*x[1]*x[2]^13 - 25321810180*x[2]^14 + 7012374600*x[1]^3*x[2]^10 - 199232100480*x[1]^2*x[2]^11 - 248179217331*x[1]*x[2]^12 + 165834648380*x[2]^13 - 54242172600*x[1]^3*x[2]^9 + 254692866120*x[1]^2*x[2]^10 + 3086896814361*x[1]*x[2]^11 + 1452936824855*x[2]^12 - 377309763600*x[1]^3*x[2]^8 + 6373674818280*x[1]^2*x[2]^9 + 9923405908644*x[1]*x[2]^10 - 7282463404305*x[2]^11 + 529395081600*x[1]^3*x[2]^7 + 201737166960*x[1]^2*x[2]^8 - 82051489115964*x[1]*x[2]^9 - 49767577944660*x[2]^10 + 7762717804800*x[1]^3*x[2]^6 - 107872388789760*x[1]^2*x[2]^7 - 228106280601488*x[1]*x[2]^8 + 188295140800860*x[2]^9 + 5641690051200*x[1]^3*x[2]^5 - 72071176190720*x[1]^2*x[2]^6 + 1247569692278128*x[1]*x[2]^7 + 999880452464720*x[2]^8 - 59240109600000*x[1]^3*x[2]^4 + 902204009992320*x[1]^2*x[2]^5 + 2838169072235712*x[1]*x[2]^6 - 2817733829659120*x[2]^7 - 91967702400000*x[1]^3*x[2]^3 + 710211126240000*x[1]^2*x[2]^4 - 10191152119063872*x[1]*x[2]^5 - 11095988731057600*x[2]^6 + 135136512000000*x[1]^3*x[2]^2 - 3433708333440000*x[1]^2*x[2]^3 - 16543659101184000*x[1]*x[2]^4 + 23155394326766400*x[2]^5 + 256048128000000*x[1]^3*x[2] - 1753929676800000*x[1]^2*x[2]^2 + 40610723186304000*x[1]*x[2]^3 + 59596510464000000*x[2]^4 + 4762495180800000*x[1]^2*x[2] + 33062234849280000*x[1]*x[2]^2 - 94729046313600000*x[2]^3 - 61119419719680000*x[1]*x[2] - 113490284544000000*x[2]^2 + 147373986816000000*x[2], 4733123659*x[1]*x[2]^20 - 2464269570*x[1]^2*x[2]^18 - 6298620389*x[1]*x[2]^19 - 19591909206*x[2]^20 - 21450793280*x[1]^2*x[2]^17 - 1828265458896*x[1]*x[2]^18 + 20248484546*x[2]^19 - 13155542400*x[1]^3*x[2]^15 + 747681710160*x[1]^2*x[2]^16 + 2351793096816*x[1]*x[2]^17 + 7561243189064*x[2]^18 - 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