A LIST OF CHALLENGES FOR REAL ALGEBRAIC PLANE CURVE VISUALIZATION SOFTWARE by Oliver Labs (www.OliverLabs.net), October 2008 This list gives some explicit polynomials in low degree from the 20 challenges (each for infinitely many degrees) described in the article Oliver Labs: "A LIST OF CHALLENGES FOR REAL ALGEBRAIC PLANE CURVE VISUALIZATION SOFTWARE" p. 137-164 in: Nonlinear Computational Geometry, edited by I. Emiris and F. Sottile and T. Theobald, IMA Volume 151, Springer. ---------------- Challenge 1: many solitary points ---------------- KO_d: d = 4 g(d)= 3 KO_d: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+1 d = 5 g(d)= 6 KO_d: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+1 d = 6 g(d)= 10 KO_d: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+1 d = 7 g(d)= 15 KO_d: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+1 d = 8 g(d)= 21 KO_d: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+1 d = 9 g(d)= 28 KO_d: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+1 d = 10 g(d)= 36 KO_d: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+1 ---------------- Challenge 2: higher solitary points ---------------- SP_k_l: k: 1 l: 1 SP_k_l: x^2+y^2 k: 1 l: 2 SP_k_l: y^4+x^2 k: 1 l: 3 SP_k_l: y^6+x^2 k: 1 l: 4 SP_k_l: y^8+x^2 k: 1 l: 5 SP_k_l: y^10+x^2 k: 2 l: 1 SP_k_l: x^4+y^2 k: 2 l: 2 SP_k_l: x^4+y^4 k: 2 l: 3 SP_k_l: y^6+x^4 k: 2 l: 4 SP_k_l: y^8+x^4 k: 2 l: 5 SP_k_l: y^10+x^4 k: 3 l: 1 SP_k_l: x^6+y^2 k: 3 l: 2 SP_k_l: x^6+y^4 k: 3 l: 3 SP_k_l: x^6+y^6 k: 3 l: 4 SP_k_l: y^8+x^6 k: 3 l: 5 SP_k_l: y^10+x^6 k: 4 l: 1 SP_k_l: x^8+y^2 k: 4 l: 2 SP_k_l: x^8+y^4 k: 4 l: 3 SP_k_l: x^8+y^6 k: 4 l: 4 SP_k_l: x^8+y^8 k: 4 l: 5 SP_k_l: y^10+x^8 k: 5 l: 1 SP_k_l: x^10+y^2 k: 5 l: 2 SP_k_l: x^10+y^4 k: 5 l: 3 SP_k_l: x^10+y^6 k: 5 l: 4 SP_k_l: x^10+y^8 k: 5 l: 5 SP_k_l: x^10+y^10 f_k_l_p: k: 2 l: 2 f_k_l_p: x^4+y^4-2*x^2*y+y^2 k: 2 l: 4 f_k_l_p: x^8+y^8-4*x^6*y+6*x^4*y^2-4*x^2*y^3+y^4 k: 2 l: 6 f_k_l_p: x^12+y^12-6*x^10*y+15*x^8*y^2-20*x^6*y^3+15*x^4*y^4-6*x^2*y^5+y^6 k: 2 l: 8 f_k_l_p: x^16+y^16-8*x^14*y+28*x^12*y^2-56*x^10*y^3+70*x^8*y^4-56*x^6*y^5+28*x^4*y^6-8*x^2*y^7+y^8 k: 4 l: 2 f_k_l_p: x^8+y^8-2*x^4*y+y^2 k: 4 l: 4 f_k_l_p: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4 k: 4 l: 6 f_k_l_p: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6 k: 4 l: 8 f_k_l_p: x^32+y^32-8*x^28*y+28*x^24*y^2-56*x^20*y^3+70*x^16*y^4-56*x^12*y^5+28*x^8*y^6-8*x^4*y^7+y^8 k: 6 l: 2 f_k_l_p: x^12+y^12-2*x^6*y+y^2 k: 6 l: 4 f_k_l_p: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4 k: 6 l: 6 f_k_l_p: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6 k: 6 l: 8 f_k_l_p: x^48+y^48-8*x^42*y+28*x^36*y^2-56*x^30*y^3+70*x^24*y^4-56*x^18*y^5+28*x^12*y^6-8*x^6*y^7+y^8 k: 8 l: 2 f_k_l_p: x^16+y^16-2*x^8*y+y^2 k: 8 l: 4 f_k_l_p: x^32+y^32-4*x^24*y+6*x^16*y^2-4*x^8*y^3+y^4 k: 8 l: 6 f_k_l_p: x^48+y^48-6*x^40*y+15*x^32*y^2-20*x^24*y^3+15*x^16*y^4-6*x^8*y^5+y^6 k: 8 l: 8 f_k_l_p: x^64+y^64-8*x^56*y+28*x^48*y^2-56*x^40*y^3+70*x^32*y^4-56*x^24*y^5+28*x^16*y^6-8*x^8*y^7+y^8 ---------------- Challenge 3: many small ovals ---------------- KO_d_eps: d: 2 eps: 1/10 KO_d_eps: 4/5*x^2-8/5*x*y+4/5*y^2-9/5*x-9/5*y+1 d: 2 eps: 1/100 KO_d_eps: 98/125*x^2-196/125*x*y+98/125*y^2-891/500*x-891/500*y+1 d: 2 eps: 1/1000 KO_d_eps: 24451/31250*x^2-24451/15625*x*y+24451/31250*y^2-890109/500000*x-890109/500000*y+1 d: 2 eps: 1/10000 KO_d_eps: 122230549/156250000*x^2-122230549/78125000*x*y+122230549/156250000*y^2-8900199891/5000000000*x-8900199891/5000000000*y+1 d: 2 eps: 1/100000 KO_d_eps: 6111405219451/7812500000000*x^2-6111405219451/3906250000000*x*y+6111405219451/7812500000000*y^2-890011088900109/500000000000000*x-890011088900109/500000000000000*y+1 d: 3 eps: 1/10 KO_d_eps: 7/10*x^3+21/10*x^2*y+21/10*x*y^2+7/10*y^3+12/5*x^2-84/5*x*y+12/5*y^2+27/10*x+27/10*y+1 d: 3 eps: 1/100 KO_d_eps: 679/1000*x^3+2037/1000*x^2*y+2037/1000*x*y^2+679/1000*y^3+294/125*x^2-2058/125*x*y+294/125*y^2+2673/1000*x+2673/1000*y+1 d: 3 eps: 1/1000 KO_d_eps: 676963/1000000*x^3+2030889/1000000*x^2*y+2030889/1000000*x*y^2+676963/1000000*y^3+73353/31250*x^2-513471/31250*x*y+73353/31250*y^2+2670327/1000000*x+2670327/1000000*y+1 d: 3 eps: 1/10000 KO_d_eps: 6767599111/10000000000*x^3+20302797333/10000000000*x^2*y+20302797333/10000000000*x*y^2+6767599111/10000000000*y^3+366691647/156250000*x^2-2566841529/156250000*x*y+366691647/156250000*y^2+26700599673/10000000000*x+26700599673/10000000000*y+1 d: 3 eps: 1/100000 KO_d_eps: 676739608302667/1000000000000000*x^3+2030218824908001/1000000000000000*x^2*y+2030218824908001/1000000000000000*x*y^2+676739608302667/1000000000000000*y^3+18334215658353/7812500000000*x^2-128339509608471/7812500000000*x*y+18334215658353/7812500000000*y^2+2670033266700327/1000000000000000*x+2670033266700327/1000000000000000*y+1 d: 4 eps: 1/10 KO_d_eps: 3/5*x^4-12/5*x^3*y+18/5*x^2*y^2-12/5*x*y^3+3/5*y^4-14/5*x^3-434/5*x^2*y-434/5*x*y^2-14/5*y^3+24/5*x^2-496/5*x*y+24/5*y^2-18/5*x-18/5*y+1 d: 4 eps: 1/100 KO_d_eps: 72/125*x^4-288/125*x^3*y+432/125*x^2*y^2-288/125*x*y^3+72/125*y^4-679/250*x^3-21049/250*x^2*y-21049/250*x*y^2-679/250*y^3+588/125*x^2-12152/125*x*y+588/125*y^2-891/250*x-891/250*y+1 d: 4 eps: 1/1000 KO_d_eps: 8964/15625*x^4-35856/15625*x^3*y+53784/15625*x^2*y^2-35856/15625*x*y^3+8964/15625*y^4-676963/250000*x^3-20985853/250000*x^2*y-20985853/250000*x*y^2-676963/250000*y^3+73353/15625*x^2-1515962/15625*x*y+73353/15625*y^2-890109/250000*x-890109/250000*y+1 d: 4 eps: 1/10000 KO_d_eps: 5600259/9765625*x^4-22401036/9765625*x^3*y+33601554/9765625*x^2*y^2-22401036/9765625*x*y^3+5600259/9765625*y^4-6767599111/2500000000*x^3-209795572441/2500000000*x^2*y-209795572441/2500000000*x*y^2-6767599111/2500000000*y^3+366691647/78125000*x^2-3789147019/39062500*x*y+366691647/78125000*y^2-8900199891/2500000000*x-8900199891/2500000000*y+1 d: 4 eps: 1/100000 KO_d_eps: 140000874741/244140625000*x^4-140000874741/61035156250*x^3*y+420002624223/122070312500*x^2*y^2-140000874741/61035156250*x*y^3+140000874741/244140625000*y^4-676739608302667/250000000000000*x^3-20978927857382677/250000000000000*x^2*y-20978927857382677/250000000000000*x*y^2-676739608302667/250000000000000*y^3+18334215658353/3906250000000*x^2-189453561802981/1953125000000*x*y+18334215658353/3906250000000*y^2-890011088900109/250000000000000*x-890011088900109/250000000000000*y+1 d: 5 eps: 1/10 KO_d_eps: 1/2*x^5+5/2*x^4*y+5*x^3*y^2+5*x^2*y^3+5/2*x*y^4+1/2*y^5+3*x^4-363*x^3*y+1143*x^2*y^2-363*x*y^3+3*y^4+7*x^3+2667/2*x^2*y+2667/2*x*y^2+7*y^3+8*x^2-484*x*y+8*y^2+9/2*x+9/2*y+1 d: 5 eps: 1/100 KO_d_eps: 19/40*x^5+19/8*x^4*y+19/4*x^3*y^2+19/4*x^2*y^3+19/8*x*y^4+19/40*y^5+72/25*x^4-8712/25*x^3*y+27432/25*x^2*y^2-8712/25*x*y^3+72/25*y^4+679/100*x^3+258699/200*x^2*y+258699/200*x*y^2+679/100*y^3+196/25*x^2-11858/25*x*y+196/25*y^2+891/200*x+891/200*y+1 d: 5 eps: 1/1000 KO_d_eps: 3781/8000*x^5+3781/1600*x^4*y+3781/800*x^3*y^2+3781/800*x^2*y^3+3781/1600*x*y^4+3781/8000*y^5+8964/3125*x^4-1084644/3125*x^3*y+3415284/3125*x^2*y^2-1084644/3125*x*y^3+8964/3125*y^4+676963/100000*x^3+257922903/200000*x^2*y+257922903/200000*x*y^2+676963/100000*y^3+24451/3125*x^2-2958571/6250*x*y+24451/3125*y^2+890109/200000*x+890109/200000*y+1 d: 5 eps: 1/10000 KO_d_eps: 7558219/16000000*x^5+7558219/3200000*x^4*y+7558219/1600000*x^3*y^2+7558219/1600000*x^2*y^3+7558219/3200000*x*y^4+7558219/16000000*y^5+5600259/1953125*x^4-677631339/1953125*x^3*y+2133698679/1953125*x^2*y^2-677631339/1953125*x*y^3+5600259/1953125*y^4+6767599111/1000000000*x^3+2578455261291/2000000000*x^2*y+2578455261291/2000000000*x*y^2+6767599111/1000000000*y^3+122230549/15625000*x^2-14789896429/31250000*x*y+122230549/15625000*y^2+8900199891/2000000000*x+8900199891/2000000000*y+1 d: 5 eps: 1/100000 KO_d_eps: 151156821781/320000000000*x^5+151156821781/64000000000*x^4*y+151156821781/32000000000*x^3*y^2+151156821781/32000000000*x^2*y^3+151156821781/64000000000*x*y^4+151156821781/320000000000*y^5+140000874741/48828125000*x^4-16940105843661/48828125000*x^3*y+53340333276321/48828125000*x^2*y^2-16940105843661/48828125000*x*y^3+140000874741/48828125000*y^4+676739608302667/100000000000000*x^3+257837790763316127/200000000000000*x^2*y+257837790763316127/200000000000000*x*y^2+676739608302667/100000000000000*y^3+6111405219451/781250000000*x^2-739480031553571/1562500000000*x*y+6111405219451/781250000000*y^2+890011088900109/200000000000000*x+890011088900109/200000000000000*y+1 d: 6 eps: 1/10 KO_d_eps: 2/5*x^6-12/5*x^5*y+6*x^4*y^2-8*x^3*y^3+6*x^2*y^4-12/5*x*y^5+2/5*y^6-3*x^5-1368*x^4*y-10293*x^3*y^2-10293*x^2*y^3-1368*x*y^4-3*y^5+9*x^4-61758/5*x^3*y+395181/5*x^2*y^2-61758/5*x*y^3+9*y^4-14*x^3-72051/5*x^2*y-72051/5*x*y^2-14*y^3+12*x^2-10944/5*x*y+12*y^2-27/5*x-27/5*y+1 d: 6 eps: 1/100 KO_d_eps: 47/125*x^6-282/125*x^5*y+141/25*x^4*y^2-188/25*x^3*y^3+141/25*x^2*y^4-282/125*x*y^5+47/125*y^6-57/20*x^5-6498/5*x^4*y-195567/20*x^3*y^2-195567/20*x^2*y^3-6498/5*x*y^4-57/20*y^5+216/25*x^4-1482192/125*x^3*y+9484344/125*x^2*y^2-1482192/125*x*y^3+216/25*y^4-679/50*x^3-6988947/500*x^2*y-6988947/500*x*y^2-679/50*y^3+294/25*x^2-268128/125*x*y+294/25*y^2-2673/500*x-2673/500*y+1 d: 6 eps: 1/1000 KO_d_eps: 23359/62500*x^6-70077/31250*x^5*y+70077/12500*x^4*y^2-23359/3125*x^3*y^3+70077/12500*x^2*y^4-70077/31250*x*y^5+23359/62500*y^6-11343/4000*x^5-646551/500*x^4*y-38917833/4000*x^3*y^2-38917833/4000*x^2*y^3-646551/500*x*y^4-11343/4000*y^5+26892/3125*x^4-184532904/15625*x^3*y+1180800828/15625*x^2*y^2-184532904/15625*x*y^3+26892/3125*y^4-676963/50000*x^3-6967980159/500000*x^2*y-6967980159/500000*x*y^2-676963/50000*y^3+73353/6250*x^2-33448968/15625*x*y+73353/6250*y^2-2670327/500000*x-2670327/500000*y+1 d: 6 eps: 1/10000 KO_d_eps: 116724923/312500000*x^6-350174769/156250000*x^5*y+350174769/62500000*x^4*y^2-116724923/15625000*x^3*y^3+350174769/62500000*x^2*y^4-350174769/156250000*x*y^5+116724923/312500000*y^6-22674657/8000000*x^5-1292455449/1000000*x^4*y-77796748167/8000000*x^3*y^2-77796748167/8000000*x^2*y^3-1292455449/1000000*x*y^4-22674657/8000000*y^5+16800777/1953125*x^4-115286931774/9765625*x^3*y+737705317293/9765625*x^2*y^2-115286931774/9765625*x*y^3+16800777/1953125*y^4-6767599111/500000000*x^3-69658897649523/5000000000*x^2*y-69658897649523/5000000000*x*y^2-6767599111/500000000*y^3+366691647/31250000*x^2-20901423879/9765625*x*y+366691647/31250000*y^2-26700599673/5000000000*x-26700599673/5000000000*y+1 d: 6 eps: 1/100000 KO_d_eps: 5835895975231/15625000000000*x^6-17507687925693/7812500000000*x^5*y+17507687925693/3125000000000*x^4*y^2-5835895975231/781250000000*x^3*y^3+17507687925693/3125000000000*x^2*y^4-17507687925693/7812500000000*x*y^5+5835895975231/15625000000000*y^6-453470465343/160000000000*x^5-25847816524551/20000000000*x^4*y-1555857166591833/160000000000*x^3*y^2-1555857166591833/160000000000*x^2*y^3-25847816524551/20000000000*x*y^4-453470465343/160000000000*y^5+420002624223/48828125000*x^4-1441029003709113/122070312500*x^3*y+18441895227007707/244140625000*x^2*y^2-1441029003709113/122070312500*x*y^3+420002624223/48828125000*y^4-676739608302667/50000000000000*x^3-6965680788259351431/500000000000000*x^2*y-6965680788259351431/500000000000000*x*y^2-676739608302667/50000000000000*y^3+18334215658353/1562500000000*x^2-1045050292526121/488281250000*x*y+18334215658353/1562500000000*y^2-2670033266700327/500000000000000*x-2670033266700327/500000000000000*y+1 d: 7 eps: 1/10 KO_d_eps: 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eps: 1/100000 KO_d_eps: 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d: 8 eps: 1/100000 KO_d_eps: 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91/1000*x^9+819/1000*x^8*y+819/250*x^7*y^2+1911/250*x^6*y^3+5733/500*x^5*y^4+5733/500*x^4*y^5+1911/250*x^3*y^6+819/250*x^2*y^7+819/1000*x*y^8+91/1000*y^9+207/125*x^8-5030307/125*x^7*y+278108847/125*x^6*y^2-2142537147/125*x^5*y^3+4059318231/125*x^4*y^4-2142537147/125*x^3*y^5+278108847/125*x^2*y^6-5030307/125*x*y^7+207/125*y^8+2511/250*x^7+3373581231/1000*x^6*y+1046485889199/1000*x^5*y^2+6083295561297/500*x^4*y^3+6083295561297/500*x^3*y^4+1046485889199/1000*x^2*y^5+3373581231/1000*x*y^6+2511/250*y^7+3948/125*x^6-4378228083/125*x^5*y+2049569113842/125*x^4*y^2-12828279003432/125*x^3*y^3+2049569113842/125*x^2*y^4-4378228083/125*x*y^5+3948/125*y^6+1197/20*x^5+3353349843/40*x^4*y+414274608117/20*x^3*y^2+414274608117/20*x^2*y^3+3353349843/40*x*y^4+1197/20*y^5+9072/125*x^4-6707072808/125*x^3*y+270060874632/125*x^2*y^2-6707072808/125*x*y^3+9072/125*y^4+14259/250*x^3+8210256831/1000*x^2*y+8210256831/1000*x*y^2+14259/250*y^3+3528/125*x^2-21433482/125*x*y+3528/125*y^2+8019/1000*x+8019/1000*y+1 d: 9 eps: 1/1000 KO_d_eps: 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d: 9 eps: 1/10000 KO_d_eps: 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d: 9 eps: 1/100000 KO_d_eps: 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d: 10 eps: 1/10 KO_d_eps: -x^9-92368*x^8*y-9091270*x^7*y^2-115921972*x^6*y^3-374894389*x^5*y^4-374894389*x^4*y^5-115921972*x^3*y^6-9091270*x^2*y^7-92368*x*y^8-y^9+9*x^8-18182540*x^7*y+16795809435*x^6*y^2-511082013774*x^5*y^3+1479810726865*x^4*y^4-511082013774*x^3*y^5+16795809435*x^2*y^6-18182540*x*y^7+9*y^8-36*x^7-347765916*x^6*y-766623020661*x^5*y^2-21782349939012*x^4*y^3-21782349939012*x^3*y^4-766623020661*x^2*y^5-347765916*x*y^6-36*y^7+84*x^6-1499577556*x^5*y+2959621453730*x^4*y^2-29043133252016*x^3*y^3+2959621453730*x^2*y^4-1499577556*x*y^5+84*y^6-126*x^5-1874471945*x^4*y-1277705034435*x^3*y^2-1277705034435*x^2*y^3-1874471945*x*y^4-126*y^5+126*x^4-695531832*x^3*y+50387428305*x^2*y^2-695531832*x*y^3+126*y^4-84*x^3-63638890*x^2*y-63638890*x*y^2-84*y^3+36*x^2-738944*x*y+36*y^2-9*x-9*y+1 d: 10 eps: 1/100 KO_d_eps: 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d: 10 eps: 1/1000 KO_d_eps: 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d: 10 eps: 1/10000 KO_d_eps: 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d: 10 eps: 1/100000 KO_d_eps: 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---------------- Challenge 4: nested ovals ---------------- nest_d_eps_k: d: 4 ieps: 1 k: 0 nest: x^4+2*x^2*y^2+y^4-11/100*x^2-11/100*y^2+1/100*x+1/100*y+1/1000 d: 4 ieps: 2 k: 0 nest: x^4+2*x^2*y^2+y^4-101/10000*x^2-101/10000*y^2+1/10000*x+1/10000*y+1/1000000 d: 4 ieps: 1 k: 1 nest: x^4+2*x^2*y^2+y^4-11/100*x^2-11/100*y^2+1/1000*x+1/1000*y+1/1000 d: 4 ieps: 2 k: 1 nest: x^4+2*x^2*y^2+y^4-101/10000*x^2-101/10000*y^2+1/100000*x+1/100000*y+1/1000000 d: 4 ieps: 1 k: 2 nest: x^4+2*x^2*y^2+y^4-11/100*x^2-11/100*y^2+1/10000*x+1/10000*y+1/1000 d: 4 ieps: 2 k: 2 nest: x^4+2*x^2*y^2+y^4-101/10000*x^2-101/10000*y^2+1/1000000*x+1/1000000*y+1/1000000 d: 6 ieps: 1 k: 0 nest: x^6+3*x^4*y^2+3*x^2*y^4+y^6-111/1000*x^4-111/500*x^2*y^2-111/1000*y^4+111/100000*x^2+111/100000*y^2+1/1000*x+1/1000*y-1/1000000 d: 6 ieps: 2 k: 0 nest: x^6+3*x^4*y^2+3*x^2*y^4+y^6-10101/1000000*x^4-10101/500000*x^2*y^2-10101/1000000*y^4+10101/10000000000*x^2+10101/10000000000*y^2+1/1000000*x+1/1000000*y-1/1000000000000 d: 6 ieps: 1 k: 1 nest: x^6+3*x^4*y^2+3*x^2*y^4+y^6-111/1000*x^4-111/500*x^2*y^2-111/1000*y^4+111/100000*x^2+111/100000*y^2+1/10000*x+1/10000*y-1/1000000 d: 6 ieps: 2 k: 1 nest: x^6+3*x^4*y^2+3*x^2*y^4+y^6-10101/1000000*x^4-10101/500000*x^2*y^2-10101/1000000*y^4+10101/10000000000*x^2+10101/10000000000*y^2+1/10000000*x+1/10000000*y-1/1000000000000 d: 6 ieps: 1 k: 2 nest: x^6+3*x^4*y^2+3*x^2*y^4+y^6-111/1000*x^4-111/500*x^2*y^2-111/1000*y^4+111/100000*x^2+111/100000*y^2+1/100000*x+1/100000*y-1/1000000 d: 6 ieps: 2 k: 2 nest: x^6+3*x^4*y^2+3*x^2*y^4+y^6-10101/1000000*x^4-10101/500000*x^2*y^2-10101/1000000*y^4+10101/10000000000*x^2+10101/10000000000*y^2+1/100000000*x+1/100000000*y-1/1000000000000 d: 8 ieps: 1 k: 0 nest: x^8+4*x^6*y^2+6*x^4*y^4+4*x^2*y^6+y^8-1111/10000*x^6-3333/10000*x^4*y^2-3333/10000*x^2*y^4-1111/10000*y^6+11211/10000000*x^4+11211/5000000*x^2*y^2+11211/10000000*y^4-1111/1000000000*x^2-1111/1000000000*y^2+1/10000*x+1/10000*y+1/10000000000 d: 8 ieps: 2 k: 0 nest: x^8+4*x^6*y^2+6*x^4*y^4+4*x^2*y^6+y^8-1010101/100000000*x^6-3030303/100000000*x^4*y^2-3030303/100000000*x^2*y^4-1010101/100000000*y^6+101020101/100000000000000*x^4+101020101/50000000000000*x^2*y^2+101020101/100000000000000*y^4-1010101/1000000000000000000*x^2-1010101/1000000000000000000*y^2+1/100000000*x+1/100000000*y+1/100000000000000000000 d: 8 ieps: 1 k: 1 nest: x^8+4*x^6*y^2+6*x^4*y^4+4*x^2*y^6+y^8-1111/10000*x^6-3333/10000*x^4*y^2-3333/10000*x^2*y^4-1111/10000*y^6+11211/10000000*x^4+11211/5000000*x^2*y^2+11211/10000000*y^4-1111/1000000000*x^2-1111/1000000000*y^2+1/100000*x+1/100000*y+1/10000000000 d: 8 ieps: 2 k: 1 nest: x^8+4*x^6*y^2+6*x^4*y^4+4*x^2*y^6+y^8-1010101/100000000*x^6-3030303/100000000*x^4*y^2-3030303/100000000*x^2*y^4-1010101/100000000*y^6+101020101/100000000000000*x^4+101020101/50000000000000*x^2*y^2+101020101/100000000000000*y^4-1010101/1000000000000000000*x^2-1010101/1000000000000000000*y^2+1/1000000000*x+1/1000000000*y+1/100000000000000000000 d: 8 ieps: 1 k: 2 nest: x^8+4*x^6*y^2+6*x^4*y^4+4*x^2*y^6+y^8-1111/10000*x^6-3333/10000*x^4*y^2-3333/10000*x^2*y^4-1111/10000*y^6+11211/10000000*x^4+11211/5000000*x^2*y^2+11211/10000000*y^4-1111/1000000000*x^2-1111/1000000000*y^2+1/1000000*x+1/1000000*y+1/10000000000 d: 8 ieps: 2 k: 2 nest: x^8+4*x^6*y^2+6*x^4*y^4+4*x^2*y^6+y^8-1010101/100000000*x^6-3030303/100000000*x^4*y^2-3030303/100000000*x^2*y^4-1010101/100000000*y^6+101020101/100000000000000*x^4+101020101/50000000000000*x^2*y^2+101020101/100000000000000*y^4-1010101/1000000000000000000*x^2-1010101/1000000000000000000*y^2+1/10000000000*x+1/10000000000*y+1/100000000000000000000 d: 10 ieps: 1 k: 0 nest: x^10+5*x^8*y^2+10*x^6*y^4+10*x^4*y^6+5*x^2*y^8+y^10-11111/100000*x^8-11111/25000*x^6*y^2-33333/50000*x^4*y^4-11111/25000*x^2*y^6-11111/100000*y^8+1122211/1000000000*x^6+3366633/1000000000*x^4*y^2+3366633/1000000000*x^2*y^4+1122211/1000000000*y^6-1122211/1000000000000*x^4-1122211/500000000000*x^2*y^2-1122211/1000000000000*y^4+11111/100000000000000*x^2+11111/100000000000000*y^2+1/100000*x+1/100000*y-1/1000000000000000 d: 10 ieps: 2 k: 0 nest: x^10+5*x^8*y^2+10*x^6*y^4+10*x^4*y^6+5*x^2*y^8+y^10-101010101/10000000000*x^8-101010101/2500000000*x^6*y^2-303030303/5000000000*x^4*y^4-101010101/2500000000*x^2*y^6-101010101/10000000000*y^8+1010202020101/1000000000000000000*x^6+3030606060303/1000000000000000000*x^4*y^2+3030606060303/1000000000000000000*x^2*y^4+1010202020101/1000000000000000000*y^6-1010202020101/1000000000000000000000000*x^4-1010202020101/500000000000000000000000*x^2*y^2-1010202020101/1000000000000000000000000*y^4+101010101/10000000000000000000000000000*x^2+101010101/10000000000000000000000000000*y^2+1/10000000000*x+1/10000000000*y-1/1000000000000000000000000000000 d: 10 ieps: 1 k: 1 nest: x^10+5*x^8*y^2+10*x^6*y^4+10*x^4*y^6+5*x^2*y^8+y^10-11111/100000*x^8-11111/25000*x^6*y^2-33333/50000*x^4*y^4-11111/25000*x^2*y^6-11111/100000*y^8+1122211/1000000000*x^6+3366633/1000000000*x^4*y^2+3366633/1000000000*x^2*y^4+1122211/1000000000*y^6-1122211/1000000000000*x^4-1122211/500000000000*x^2*y^2-1122211/1000000000000*y^4+11111/100000000000000*x^2+11111/100000000000000*y^2+1/1000000*x+1/1000000*y-1/1000000000000000 d: 10 ieps: 2 k: 1 nest: x^10+5*x^8*y^2+10*x^6*y^4+10*x^4*y^6+5*x^2*y^8+y^10-101010101/10000000000*x^8-101010101/2500000000*x^6*y^2-303030303/5000000000*x^4*y^4-101010101/2500000000*x^2*y^6-101010101/10000000000*y^8+1010202020101/1000000000000000000*x^6+3030606060303/1000000000000000000*x^4*y^2+3030606060303/1000000000000000000*x^2*y^4+1010202020101/1000000000000000000*y^6-1010202020101/1000000000000000000000000*x^4-1010202020101/500000000000000000000000*x^2*y^2-1010202020101/1000000000000000000000000*y^4+101010101/10000000000000000000000000000*x^2+101010101/10000000000000000000000000000*y^2+1/100000000000*x+1/100000000000*y-1/1000000000000000000000000000000 d: 10 ieps: 1 k: 2 nest: x^10+5*x^8*y^2+10*x^6*y^4+10*x^4*y^6+5*x^2*y^8+y^10-11111/100000*x^8-11111/25000*x^6*y^2-33333/50000*x^4*y^4-11111/25000*x^2*y^6-11111/100000*y^8+1122211/1000000000*x^6+3366633/1000000000*x^4*y^2+3366633/1000000000*x^2*y^4+1122211/1000000000*y^6-1122211/1000000000000*x^4-1122211/500000000000*x^2*y^2-1122211/1000000000000*y^4+11111/100000000000000*x^2+11111/100000000000000*y^2+1/10000000*x+1/10000000*y-1/1000000000000000 d: 10 ieps: 2 k: 2 nest: x^10+5*x^8*y^2+10*x^6*y^4+10*x^4*y^6+5*x^2*y^8+y^10-101010101/10000000000*x^8-101010101/2500000000*x^6*y^2-303030303/5000000000*x^4*y^4-101010101/2500000000*x^2*y^6-101010101/10000000000*y^8+1010202020101/1000000000000000000*x^6+3030606060303/1000000000000000000*x^4*y^2+3030606060303/1000000000000000000*x^2*y^4+1010202020101/1000000000000000000*y^6-1010202020101/1000000000000000000000000*x^4-1010202020101/500000000000000000000000*x^2*y^2-1010202020101/1000000000000000000000000*y^4+101010101/10000000000000000000000000000*x^2+101010101/10000000000000000000000000000*y^2+1/1000000000000*x+1/1000000000000*y-1/1000000000000000000000000000000 d: 12 ieps: 1 k: 0 nest: x^12+6*x^10*y^2+15*x^8*y^4+20*x^6*y^6+15*x^4*y^8+6*x^2*y^10+y^12-111111/1000000*x^10-111111/200000*x^8*y^2-111111/100000*x^6*y^4-111111/100000*x^4*y^6-111111/200000*x^2*y^8-111111/1000000*y^10+112232211/100000000000*x^8+112232211/25000000000*x^6*y^2+336696633/50000000000*x^4*y^4+112232211/25000000000*x^2*y^6+112232211/100000000000*y^8-1123333211/1000000000000000*x^6-3369999633/1000000000000000*x^4*y^2-3369999633/1000000000000000*x^2*y^4-1123333211/1000000000000000*y^6+112232211/1000000000000000000*x^4+112232211/500000000000000000*x^2*y^2+112232211/1000000000000000000*y^4-111111/100000000000000000000*x^2-111111/100000000000000000000*y^2+1/1000000*x+1/1000000*y+1/1000000000000000000000 d: 12 ieps: 2 k: 0 nest: x^12+6*x^10*y^2+15*x^8*y^4+20*x^6*y^6+15*x^4*y^8+6*x^2*y^10+y^12-10101010101/1000000000000*x^10-10101010101/200000000000*x^8*y^2-10101010101/100000000000*x^6*y^4-10101010101/100000000000*x^4*y^6-10101010101/200000000000*x^2*y^8-10101010101/1000000000000*y^10+10102020302020101/10000000000000000000000*x^8+10102020302020101/2500000000000000000000*x^6*y^2+30306060906060303/5000000000000000000000*x^4*y^4+10102020302020101/2500000000000000000000*x^2*y^6+10102020302020101/10000000000000000000000*y^8-1010203030303020101/1000000000000000000000000000000*x^6-3030609090909060303/1000000000000000000000000000000*x^4*y^2-3030609090909060303/1000000000000000000000000000000*x^2*y^4-1010203030303020101/1000000000000000000000000000000*y^6+10102020302020101/1000000000000000000000000000000000000*x^4+10102020302020101/500000000000000000000000000000000000*x^2*y^2+10102020302020101/1000000000000000000000000000000000000*y^4-10101010101/10000000000000000000000000000000000000000*x^2-10101010101/10000000000000000000000000000000000000000*y^2+1/1000000000000*x+1/1000000000000*y+1/1000000000000000000000000000000000000000000 d: 12 ieps: 1 k: 1 nest: x^12+6*x^10*y^2+15*x^8*y^4+20*x^6*y^6+15*x^4*y^8+6*x^2*y^10+y^12-111111/1000000*x^10-111111/200000*x^8*y^2-111111/100000*x^6*y^4-111111/100000*x^4*y^6-111111/200000*x^2*y^8-111111/1000000*y^10+112232211/100000000000*x^8+112232211/25000000000*x^6*y^2+336696633/50000000000*x^4*y^4+112232211/25000000000*x^2*y^6+112232211/100000000000*y^8-1123333211/1000000000000000*x^6-3369999633/1000000000000000*x^4*y^2-3369999633/1000000000000000*x^2*y^4-1123333211/1000000000000000*y^6+112232211/1000000000000000000*x^4+112232211/500000000000000000*x^2*y^2+112232211/1000000000000000000*y^4-111111/100000000000000000000*x^2-111111/100000000000000000000*y^2+1/10000000*x+1/10000000*y+1/1000000000000000000000 d: 12 ieps: 2 k: 1 nest: x^12+6*x^10*y^2+15*x^8*y^4+20*x^6*y^6+15*x^4*y^8+6*x^2*y^10+y^12-10101010101/1000000000000*x^10-10101010101/200000000000*x^8*y^2-10101010101/100000000000*x^6*y^4-10101010101/100000000000*x^4*y^6-10101010101/200000000000*x^2*y^8-10101010101/1000000000000*y^10+10102020302020101/10000000000000000000000*x^8+10102020302020101/2500000000000000000000*x^6*y^2+30306060906060303/5000000000000000000000*x^4*y^4+10102020302020101/2500000000000000000000*x^2*y^6+10102020302020101/10000000000000000000000*y^8-1010203030303020101/1000000000000000000000000000000*x^6-3030609090909060303/1000000000000000000000000000000*x^4*y^2-3030609090909060303/1000000000000000000000000000000*x^2*y^4-1010203030303020101/1000000000000000000000000000000*y^6+10102020302020101/1000000000000000000000000000000000000*x^4+10102020302020101/500000000000000000000000000000000000*x^2*y^2+10102020302020101/1000000000000000000000000000000000000*y^4-10101010101/10000000000000000000000000000000000000000*x^2-10101010101/10000000000000000000000000000000000000000*y^2+1/10000000000000*x+1/10000000000000*y+1/1000000000000000000000000000000000000000000 d: 12 ieps: 1 k: 2 nest: x^12+6*x^10*y^2+15*x^8*y^4+20*x^6*y^6+15*x^4*y^8+6*x^2*y^10+y^12-111111/1000000*x^10-111111/200000*x^8*y^2-111111/100000*x^6*y^4-111111/100000*x^4*y^6-111111/200000*x^2*y^8-111111/1000000*y^10+112232211/100000000000*x^8+112232211/25000000000*x^6*y^2+336696633/50000000000*x^4*y^4+112232211/25000000000*x^2*y^6+112232211/100000000000*y^8-1123333211/1000000000000000*x^6-3369999633/1000000000000000*x^4*y^2-3369999633/1000000000000000*x^2*y^4-1123333211/1000000000000000*y^6+112232211/1000000000000000000*x^4+112232211/500000000000000000*x^2*y^2+112232211/1000000000000000000*y^4-111111/100000000000000000000*x^2-111111/100000000000000000000*y^2+1/100000000*x+1/100000000*y+1/1000000000000000000000 d: 12 ieps: 2 k: 2 nest: x^12+6*x^10*y^2+15*x^8*y^4+20*x^6*y^6+15*x^4*y^8+6*x^2*y^10+y^12-10101010101/1000000000000*x^10-10101010101/200000000000*x^8*y^2-10101010101/100000000000*x^6*y^4-10101010101/100000000000*x^4*y^6-10101010101/200000000000*x^2*y^8-10101010101/1000000000000*y^10+10102020302020101/10000000000000000000000*x^8+10102020302020101/2500000000000000000000*x^6*y^2+30306060906060303/5000000000000000000000*x^4*y^4+10102020302020101/2500000000000000000000*x^2*y^6+10102020302020101/10000000000000000000000*y^8-1010203030303020101/1000000000000000000000000000000*x^6-3030609090909060303/1000000000000000000000000000000*x^4*y^2-3030609090909060303/1000000000000000000000000000000*x^2*y^4-1010203030303020101/1000000000000000000000000000000*y^6+10102020302020101/1000000000000000000000000000000000000*x^4+10102020302020101/500000000000000000000000000000000000*x^2*y^2+10102020302020101/1000000000000000000000000000000000000*y^4-10101010101/10000000000000000000000000000000000000000*x^2-10101010101/10000000000000000000000000000000000000000*y^2+1/100000000000000*x+1/100000000000000*y+1/1000000000000000000000000000000000000000000 ---------------- Challenge 5: one small non-real oval ---------------- SP_k_l_eps: k: 1 l: 1 ieps: 1 SP_k_l_eps: x^2+y^2+1/10 k: 1 l: 1 ieps: 2 SP_k_l_eps: x^2+y^2+1/100 k: 1 l: 1 ieps: 3 SP_k_l_eps: x^2+y^2+1/1000 k: 1 l: 1 ieps: 4 SP_k_l_eps: x^2+y^2+1/10000 k: 1 l: 1 ieps: 5 SP_k_l_eps: x^2+y^2+1/100000 k: 1 l: 1 ieps: 6 SP_k_l_eps: x^2+y^2+1/1000000 k: 1 l: 1 ieps: 7 SP_k_l_eps: x^2+y^2+1/10000000 k: 1 l: 1 ieps: 8 SP_k_l_eps: x^2+y^2+1/100000000 k: 1 l: 2 ieps: 1 SP_k_l_eps: y^4+x^2+1/10 k: 1 l: 2 ieps: 2 SP_k_l_eps: y^4+x^2+1/100 k: 1 l: 2 ieps: 3 SP_k_l_eps: y^4+x^2+1/1000 k: 1 l: 2 ieps: 4 SP_k_l_eps: y^4+x^2+1/10000 k: 1 l: 2 ieps: 5 SP_k_l_eps: y^4+x^2+1/100000 k: 1 l: 2 ieps: 6 SP_k_l_eps: y^4+x^2+1/1000000 k: 1 l: 2 ieps: 7 SP_k_l_eps: y^4+x^2+1/10000000 k: 1 l: 2 ieps: 8 SP_k_l_eps: y^4+x^2+1/100000000 k: 1 l: 3 ieps: 1 SP_k_l_eps: y^6+x^2+1/10 k: 1 l: 3 ieps: 2 SP_k_l_eps: y^6+x^2+1/100 k: 1 l: 3 ieps: 3 SP_k_l_eps: y^6+x^2+1/1000 k: 1 l: 3 ieps: 4 SP_k_l_eps: y^6+x^2+1/10000 k: 1 l: 3 ieps: 5 SP_k_l_eps: y^6+x^2+1/100000 k: 1 l: 3 ieps: 6 SP_k_l_eps: y^6+x^2+1/1000000 k: 1 l: 3 ieps: 7 SP_k_l_eps: y^6+x^2+1/10000000 k: 1 l: 3 ieps: 8 SP_k_l_eps: y^6+x^2+1/100000000 k: 1 l: 4 ieps: 1 SP_k_l_eps: y^8+x^2+1/10 k: 1 l: 4 ieps: 2 SP_k_l_eps: y^8+x^2+1/100 k: 1 l: 4 ieps: 3 SP_k_l_eps: y^8+x^2+1/1000 k: 1 l: 4 ieps: 4 SP_k_l_eps: y^8+x^2+1/10000 k: 1 l: 4 ieps: 5 SP_k_l_eps: y^8+x^2+1/100000 k: 1 l: 4 ieps: 6 SP_k_l_eps: y^8+x^2+1/1000000 k: 1 l: 4 ieps: 7 SP_k_l_eps: y^8+x^2+1/10000000 k: 1 l: 4 ieps: 8 SP_k_l_eps: y^8+x^2+1/100000000 k: 1 l: 5 ieps: 1 SP_k_l_eps: y^10+x^2+1/10 k: 1 l: 5 ieps: 2 SP_k_l_eps: y^10+x^2+1/100 k: 1 l: 5 ieps: 3 SP_k_l_eps: y^10+x^2+1/1000 k: 1 l: 5 ieps: 4 SP_k_l_eps: y^10+x^2+1/10000 k: 1 l: 5 ieps: 5 SP_k_l_eps: y^10+x^2+1/100000 k: 1 l: 5 ieps: 6 SP_k_l_eps: y^10+x^2+1/1000000 k: 1 l: 5 ieps: 7 SP_k_l_eps: y^10+x^2+1/10000000 k: 1 l: 5 ieps: 8 SP_k_l_eps: y^10+x^2+1/100000000 k: 1 l: 6 ieps: 1 SP_k_l_eps: y^12+x^2+1/10 k: 1 l: 6 ieps: 2 SP_k_l_eps: y^12+x^2+1/100 k: 1 l: 6 ieps: 3 SP_k_l_eps: y^12+x^2+1/1000 k: 1 l: 6 ieps: 4 SP_k_l_eps: y^12+x^2+1/10000 k: 1 l: 6 ieps: 5 SP_k_l_eps: y^12+x^2+1/100000 k: 1 l: 6 ieps: 6 SP_k_l_eps: y^12+x^2+1/1000000 k: 1 l: 6 ieps: 7 SP_k_l_eps: y^12+x^2+1/10000000 k: 1 l: 6 ieps: 8 SP_k_l_eps: y^12+x^2+1/100000000 k: 2 l: 1 ieps: 1 SP_k_l_eps: x^4+y^2+1/10 k: 2 l: 1 ieps: 2 SP_k_l_eps: x^4+y^2+1/100 k: 2 l: 1 ieps: 3 SP_k_l_eps: x^4+y^2+1/1000 k: 2 l: 1 ieps: 4 SP_k_l_eps: x^4+y^2+1/10000 k: 2 l: 1 ieps: 5 SP_k_l_eps: x^4+y^2+1/100000 k: 2 l: 1 ieps: 6 SP_k_l_eps: x^4+y^2+1/1000000 k: 2 l: 1 ieps: 7 SP_k_l_eps: x^4+y^2+1/10000000 k: 2 l: 1 ieps: 8 SP_k_l_eps: x^4+y^2+1/100000000 k: 2 l: 2 ieps: 1 SP_k_l_eps: x^4+y^4+1/10 k: 2 l: 2 ieps: 2 SP_k_l_eps: x^4+y^4+1/100 k: 2 l: 2 ieps: 3 SP_k_l_eps: x^4+y^4+1/1000 k: 2 l: 2 ieps: 4 SP_k_l_eps: x^4+y^4+1/10000 k: 2 l: 2 ieps: 5 SP_k_l_eps: x^4+y^4+1/100000 k: 2 l: 2 ieps: 6 SP_k_l_eps: x^4+y^4+1/1000000 k: 2 l: 2 ieps: 7 SP_k_l_eps: x^4+y^4+1/10000000 k: 2 l: 2 ieps: 8 SP_k_l_eps: x^4+y^4+1/100000000 k: 2 l: 3 ieps: 1 SP_k_l_eps: y^6+x^4+1/10 k: 2 l: 3 ieps: 2 SP_k_l_eps: y^6+x^4+1/100 k: 2 l: 3 ieps: 3 SP_k_l_eps: y^6+x^4+1/1000 k: 2 l: 3 ieps: 4 SP_k_l_eps: y^6+x^4+1/10000 k: 2 l: 3 ieps: 5 SP_k_l_eps: y^6+x^4+1/100000 k: 2 l: 3 ieps: 6 SP_k_l_eps: y^6+x^4+1/1000000 k: 2 l: 3 ieps: 7 SP_k_l_eps: y^6+x^4+1/10000000 k: 2 l: 3 ieps: 8 SP_k_l_eps: y^6+x^4+1/100000000 k: 2 l: 4 ieps: 1 SP_k_l_eps: y^8+x^4+1/10 k: 2 l: 4 ieps: 2 SP_k_l_eps: y^8+x^4+1/100 k: 2 l: 4 ieps: 3 SP_k_l_eps: y^8+x^4+1/1000 k: 2 l: 4 ieps: 4 SP_k_l_eps: y^8+x^4+1/10000 k: 2 l: 4 ieps: 5 SP_k_l_eps: y^8+x^4+1/100000 k: 2 l: 4 ieps: 6 SP_k_l_eps: y^8+x^4+1/1000000 k: 2 l: 4 ieps: 7 SP_k_l_eps: y^8+x^4+1/10000000 k: 2 l: 4 ieps: 8 SP_k_l_eps: y^8+x^4+1/100000000 k: 2 l: 5 ieps: 1 SP_k_l_eps: y^10+x^4+1/10 k: 2 l: 5 ieps: 2 SP_k_l_eps: y^10+x^4+1/100 k: 2 l: 5 ieps: 3 SP_k_l_eps: y^10+x^4+1/1000 k: 2 l: 5 ieps: 4 SP_k_l_eps: y^10+x^4+1/10000 k: 2 l: 5 ieps: 5 SP_k_l_eps: y^10+x^4+1/100000 k: 2 l: 5 ieps: 6 SP_k_l_eps: y^10+x^4+1/1000000 k: 2 l: 5 ieps: 7 SP_k_l_eps: y^10+x^4+1/10000000 k: 2 l: 5 ieps: 8 SP_k_l_eps: y^10+x^4+1/100000000 k: 2 l: 6 ieps: 1 SP_k_l_eps: y^12+x^4+1/10 k: 2 l: 6 ieps: 2 SP_k_l_eps: y^12+x^4+1/100 k: 2 l: 6 ieps: 3 SP_k_l_eps: y^12+x^4+1/1000 k: 2 l: 6 ieps: 4 SP_k_l_eps: y^12+x^4+1/10000 k: 2 l: 6 ieps: 5 SP_k_l_eps: y^12+x^4+1/100000 k: 2 l: 6 ieps: 6 SP_k_l_eps: y^12+x^4+1/1000000 k: 2 l: 6 ieps: 7 SP_k_l_eps: y^12+x^4+1/10000000 k: 2 l: 6 ieps: 8 SP_k_l_eps: y^12+x^4+1/100000000 k: 3 l: 1 ieps: 1 SP_k_l_eps: x^6+y^2+1/10 k: 3 l: 1 ieps: 2 SP_k_l_eps: x^6+y^2+1/100 k: 3 l: 1 ieps: 3 SP_k_l_eps: x^6+y^2+1/1000 k: 3 l: 1 ieps: 4 SP_k_l_eps: x^6+y^2+1/10000 k: 3 l: 1 ieps: 5 SP_k_l_eps: x^6+y^2+1/100000 k: 3 l: 1 ieps: 6 SP_k_l_eps: x^6+y^2+1/1000000 k: 3 l: 1 ieps: 7 SP_k_l_eps: x^6+y^2+1/10000000 k: 3 l: 1 ieps: 8 SP_k_l_eps: x^6+y^2+1/100000000 k: 3 l: 2 ieps: 1 SP_k_l_eps: x^6+y^4+1/10 k: 3 l: 2 ieps: 2 SP_k_l_eps: x^6+y^4+1/100 k: 3 l: 2 ieps: 3 SP_k_l_eps: x^6+y^4+1/1000 k: 3 l: 2 ieps: 4 SP_k_l_eps: x^6+y^4+1/10000 k: 3 l: 2 ieps: 5 SP_k_l_eps: x^6+y^4+1/100000 k: 3 l: 2 ieps: 6 SP_k_l_eps: x^6+y^4+1/1000000 k: 3 l: 2 ieps: 7 SP_k_l_eps: x^6+y^4+1/10000000 k: 3 l: 2 ieps: 8 SP_k_l_eps: x^6+y^4+1/100000000 k: 3 l: 3 ieps: 1 SP_k_l_eps: x^6+y^6+1/10 k: 3 l: 3 ieps: 2 SP_k_l_eps: x^6+y^6+1/100 k: 3 l: 3 ieps: 3 SP_k_l_eps: x^6+y^6+1/1000 k: 3 l: 3 ieps: 4 SP_k_l_eps: x^6+y^6+1/10000 k: 3 l: 3 ieps: 5 SP_k_l_eps: x^6+y^6+1/100000 k: 3 l: 3 ieps: 6 SP_k_l_eps: x^6+y^6+1/1000000 k: 3 l: 3 ieps: 7 SP_k_l_eps: x^6+y^6+1/10000000 k: 3 l: 3 ieps: 8 SP_k_l_eps: x^6+y^6+1/100000000 k: 3 l: 4 ieps: 1 SP_k_l_eps: y^8+x^6+1/10 k: 3 l: 4 ieps: 2 SP_k_l_eps: y^8+x^6+1/100 k: 3 l: 4 ieps: 3 SP_k_l_eps: y^8+x^6+1/1000 k: 3 l: 4 ieps: 4 SP_k_l_eps: y^8+x^6+1/10000 k: 3 l: 4 ieps: 5 SP_k_l_eps: y^8+x^6+1/100000 k: 3 l: 4 ieps: 6 SP_k_l_eps: y^8+x^6+1/1000000 k: 3 l: 4 ieps: 7 SP_k_l_eps: y^8+x^6+1/10000000 k: 3 l: 4 ieps: 8 SP_k_l_eps: y^8+x^6+1/100000000 k: 3 l: 5 ieps: 1 SP_k_l_eps: y^10+x^6+1/10 k: 3 l: 5 ieps: 2 SP_k_l_eps: y^10+x^6+1/100 k: 3 l: 5 ieps: 3 SP_k_l_eps: y^10+x^6+1/1000 k: 3 l: 5 ieps: 4 SP_k_l_eps: y^10+x^6+1/10000 k: 3 l: 5 ieps: 5 SP_k_l_eps: y^10+x^6+1/100000 k: 3 l: 5 ieps: 6 SP_k_l_eps: y^10+x^6+1/1000000 k: 3 l: 5 ieps: 7 SP_k_l_eps: y^10+x^6+1/10000000 k: 3 l: 5 ieps: 8 SP_k_l_eps: y^10+x^6+1/100000000 k: 3 l: 6 ieps: 1 SP_k_l_eps: y^12+x^6+1/10 k: 3 l: 6 ieps: 2 SP_k_l_eps: y^12+x^6+1/100 k: 3 l: 6 ieps: 3 SP_k_l_eps: y^12+x^6+1/1000 k: 3 l: 6 ieps: 4 SP_k_l_eps: y^12+x^6+1/10000 k: 3 l: 6 ieps: 5 SP_k_l_eps: y^12+x^6+1/100000 k: 3 l: 6 ieps: 6 SP_k_l_eps: y^12+x^6+1/1000000 k: 3 l: 6 ieps: 7 SP_k_l_eps: y^12+x^6+1/10000000 k: 3 l: 6 ieps: 8 SP_k_l_eps: y^12+x^6+1/100000000 k: 4 l: 1 ieps: 1 SP_k_l_eps: x^8+y^2+1/10 k: 4 l: 1 ieps: 2 SP_k_l_eps: x^8+y^2+1/100 k: 4 l: 1 ieps: 3 SP_k_l_eps: x^8+y^2+1/1000 k: 4 l: 1 ieps: 4 SP_k_l_eps: x^8+y^2+1/10000 k: 4 l: 1 ieps: 5 SP_k_l_eps: x^8+y^2+1/100000 k: 4 l: 1 ieps: 6 SP_k_l_eps: x^8+y^2+1/1000000 k: 4 l: 1 ieps: 7 SP_k_l_eps: x^8+y^2+1/10000000 k: 4 l: 1 ieps: 8 SP_k_l_eps: x^8+y^2+1/100000000 k: 4 l: 2 ieps: 1 SP_k_l_eps: x^8+y^4+1/10 k: 4 l: 2 ieps: 2 SP_k_l_eps: x^8+y^4+1/100 k: 4 l: 2 ieps: 3 SP_k_l_eps: x^8+y^4+1/1000 k: 4 l: 2 ieps: 4 SP_k_l_eps: x^8+y^4+1/10000 k: 4 l: 2 ieps: 5 SP_k_l_eps: x^8+y^4+1/100000 k: 4 l: 2 ieps: 6 SP_k_l_eps: x^8+y^4+1/1000000 k: 4 l: 2 ieps: 7 SP_k_l_eps: x^8+y^4+1/10000000 k: 4 l: 2 ieps: 8 SP_k_l_eps: x^8+y^4+1/100000000 k: 4 l: 3 ieps: 1 SP_k_l_eps: x^8+y^6+1/10 k: 4 l: 3 ieps: 2 SP_k_l_eps: x^8+y^6+1/100 k: 4 l: 3 ieps: 3 SP_k_l_eps: x^8+y^6+1/1000 k: 4 l: 3 ieps: 4 SP_k_l_eps: x^8+y^6+1/10000 k: 4 l: 3 ieps: 5 SP_k_l_eps: x^8+y^6+1/100000 k: 4 l: 3 ieps: 6 SP_k_l_eps: x^8+y^6+1/1000000 k: 4 l: 3 ieps: 7 SP_k_l_eps: x^8+y^6+1/10000000 k: 4 l: 3 ieps: 8 SP_k_l_eps: x^8+y^6+1/100000000 k: 4 l: 4 ieps: 1 SP_k_l_eps: x^8+y^8+1/10 k: 4 l: 4 ieps: 2 SP_k_l_eps: x^8+y^8+1/100 k: 4 l: 4 ieps: 3 SP_k_l_eps: x^8+y^8+1/1000 k: 4 l: 4 ieps: 4 SP_k_l_eps: x^8+y^8+1/10000 k: 4 l: 4 ieps: 5 SP_k_l_eps: x^8+y^8+1/100000 k: 4 l: 4 ieps: 6 SP_k_l_eps: x^8+y^8+1/1000000 k: 4 l: 4 ieps: 7 SP_k_l_eps: x^8+y^8+1/10000000 k: 4 l: 4 ieps: 8 SP_k_l_eps: x^8+y^8+1/100000000 k: 4 l: 5 ieps: 1 SP_k_l_eps: y^10+x^8+1/10 k: 4 l: 5 ieps: 2 SP_k_l_eps: y^10+x^8+1/100 k: 4 l: 5 ieps: 3 SP_k_l_eps: y^10+x^8+1/1000 k: 4 l: 5 ieps: 4 SP_k_l_eps: y^10+x^8+1/10000 k: 4 l: 5 ieps: 5 SP_k_l_eps: y^10+x^8+1/100000 k: 4 l: 5 ieps: 6 SP_k_l_eps: y^10+x^8+1/1000000 k: 4 l: 5 ieps: 7 SP_k_l_eps: y^10+x^8+1/10000000 k: 4 l: 5 ieps: 8 SP_k_l_eps: y^10+x^8+1/100000000 k: 4 l: 6 ieps: 1 SP_k_l_eps: y^12+x^8+1/10 k: 4 l: 6 ieps: 2 SP_k_l_eps: y^12+x^8+1/100 k: 4 l: 6 ieps: 3 SP_k_l_eps: y^12+x^8+1/1000 k: 4 l: 6 ieps: 4 SP_k_l_eps: y^12+x^8+1/10000 k: 4 l: 6 ieps: 5 SP_k_l_eps: y^12+x^8+1/100000 k: 4 l: 6 ieps: 6 SP_k_l_eps: 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x^8+y^8-2*x^4*y+y^2+1/10000000 k: 4 l: 2 ieps: 8 f_k_l_p_eps: x^8+y^8-2*x^4*y+y^2+1/100000000 k: 4 l: 4 ieps: 1 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/10 k: 4 l: 4 ieps: 2 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/100 k: 4 l: 4 ieps: 3 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/1000 k: 4 l: 4 ieps: 4 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/10000 k: 4 l: 4 ieps: 5 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/100000 k: 4 l: 4 ieps: 6 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/1000000 k: 4 l: 4 ieps: 7 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/10000000 k: 4 l: 4 ieps: 8 f_k_l_p_eps: x^16+y^16-4*x^12*y+6*x^8*y^2-4*x^4*y^3+y^4+1/100000000 k: 4 l: 6 ieps: 1 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/10 k: 4 l: 6 ieps: 2 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/100 k: 4 l: 6 ieps: 3 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/1000 k: 4 l: 6 ieps: 4 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/10000 k: 4 l: 6 ieps: 5 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/100000 k: 4 l: 6 ieps: 6 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/1000000 k: 4 l: 6 ieps: 7 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/10000000 k: 4 l: 6 ieps: 8 f_k_l_p_eps: x^24+y^24-6*x^20*y+15*x^16*y^2-20*x^12*y^3+15*x^8*y^4-6*x^4*y^5+y^6+1/100000000 k: 5 l: 2 ieps: 1 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/10 k: 5 l: 2 ieps: 2 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/100 k: 5 l: 2 ieps: 3 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/1000 k: 5 l: 2 ieps: 4 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/10000 k: 5 l: 2 ieps: 5 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/100000 k: 5 l: 2 ieps: 6 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/1000000 k: 5 l: 2 ieps: 7 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/10000000 k: 5 l: 2 ieps: 8 f_k_l_p_eps: x^10+y^10-2*x^5*y+y^2+1/100000000 k: 5 l: 4 ieps: 1 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/10 k: 5 l: 4 ieps: 2 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/100 k: 5 l: 4 ieps: 3 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/1000 k: 5 l: 4 ieps: 4 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/10000 k: 5 l: 4 ieps: 5 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/100000 k: 5 l: 4 ieps: 6 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/1000000 k: 5 l: 4 ieps: 7 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/10000000 k: 5 l: 4 ieps: 8 f_k_l_p_eps: x^20+y^20-4*x^15*y+6*x^10*y^2-4*x^5*y^3+y^4+1/100000000 k: 5 l: 6 ieps: 1 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/10 k: 5 l: 6 ieps: 2 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/100 k: 5 l: 6 ieps: 3 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/1000 k: 5 l: 6 ieps: 4 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/10000 k: 5 l: 6 ieps: 5 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/100000 k: 5 l: 6 ieps: 6 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/1000000 k: 5 l: 6 ieps: 7 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/10000000 k: 5 l: 6 ieps: 8 f_k_l_p_eps: x^30+y^30-6*x^25*y+15*x^20*y^2-20*x^15*y^3+15*x^10*y^4-6*x^5*y^5+y^6+1/100000000 k: 6 l: 2 ieps: 1 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/10 k: 6 l: 2 ieps: 2 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/100 k: 6 l: 2 ieps: 3 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/1000 k: 6 l: 2 ieps: 4 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/10000 k: 6 l: 2 ieps: 5 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/100000 k: 6 l: 2 ieps: 6 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/1000000 k: 6 l: 2 ieps: 7 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/10000000 k: 6 l: 2 ieps: 8 f_k_l_p_eps: x^12+y^12-2*x^6*y+y^2+1/100000000 k: 6 l: 4 ieps: 1 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/10 k: 6 l: 4 ieps: 2 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/100 k: 6 l: 4 ieps: 3 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/1000 k: 6 l: 4 ieps: 4 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/10000 k: 6 l: 4 ieps: 5 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/100000 k: 6 l: 4 ieps: 6 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/1000000 k: 6 l: 4 ieps: 7 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/10000000 k: 6 l: 4 ieps: 8 f_k_l_p_eps: x^24+y^24-4*x^18*y+6*x^12*y^2-4*x^6*y^3+y^4+1/100000000 k: 6 l: 6 ieps: 1 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/10 k: 6 l: 6 ieps: 2 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/100 k: 6 l: 6 ieps: 3 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/1000 k: 6 l: 6 ieps: 4 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/10000 k: 6 l: 6 ieps: 5 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/100000 k: 6 l: 6 ieps: 6 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/1000000 k: 6 l: 6 ieps: 7 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/10000000 k: 6 l: 6 ieps: 8 f_k_l_p_eps: x^36+y^36-6*x^30*y+15*x^24*y^2-20*x^18*y^3+15*x^12*y^4-6*x^6*y^5+y^6+1/100000000 ---------------- Challenge 6: many small non-real ovals ---------------- KO_d_eps_m: d: 3 eps: 1/10 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+9/10 d: 3 eps: 1/100 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+89/100 d: 3 eps: 1/1000 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+889/1000 d: 3 eps: 1/10000 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+8889/10000 d: 3 eps: 1/100000 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+88889/100000 d: 3 eps: 1/1000000 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+888889/1000000 d: 3 eps: 1/10000000 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+8888889/10000000 d: 3 eps: 1/100000000 KO_d_eps_m: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+88888889/100000000 d: 4 eps: 1/10 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+9/10 d: 4 eps: 1/100 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+89/100 d: 4 eps: 1/1000 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+889/1000 d: 4 eps: 1/10000 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+8889/10000 d: 4 eps: 1/100000 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+88889/100000 d: 4 eps: 1/1000000 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+888889/1000000 d: 4 eps: 1/10000000 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+8888889/10000000 d: 4 eps: 1/100000000 KO_d_eps_m: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+88888889/100000000 d: 5 eps: 1/10 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+9/10 d: 5 eps: 1/100 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+89/100 d: 5 eps: 1/1000 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+889/1000 d: 5 eps: 1/10000 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+8889/10000 d: 5 eps: 1/100000 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+88889/100000 d: 5 eps: 1/1000000 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+888889/1000000 d: 5 eps: 1/10000000 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+8888889/10000000 d: 5 eps: 1/100000000 KO_d_eps_m: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+88888889/100000000 d: 6 eps: 1/10 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+9/10 d: 6 eps: 1/100 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+89/100 d: 6 eps: 1/1000 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+889/1000 d: 6 eps: 1/10000 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+8889/10000 d: 6 eps: 1/100000 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+88889/100000 d: 6 eps: 1/1000000 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+888889/1000000 d: 6 eps: 1/10000000 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+8888889/10000000 d: 6 eps: 1/100000000 KO_d_eps_m: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+88888889/100000000 d: 7 eps: 1/10 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+9/10 d: 7 eps: 1/100 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+89/100 d: 7 eps: 1/1000 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+889/1000 d: 7 eps: 1/10000 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+8889/10000 d: 7 eps: 1/100000 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+88889/100000 d: 7 eps: 1/1000000 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+888889/1000000 d: 7 eps: 1/10000000 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+8888889/10000000 d: 7 eps: 1/100000000 KO_d_eps_m: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+88888889/100000000 d: 8 eps: 1/10 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+9/10 d: 8 eps: 1/100 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+89/100 d: 8 eps: 1/1000 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+889/1000 d: 8 eps: 1/10000 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+8889/10000 d: 8 eps: 1/100000 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+88889/100000 d: 8 eps: 1/1000000 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+888889/1000000 d: 8 eps: 1/10000000 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+8888889/10000000 d: 8 eps: 1/100000000 KO_d_eps_m: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+88888889/100000000 d: 9 eps: 1/10 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+9/10 d: 9 eps: 1/100 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+89/100 d: 9 eps: 1/1000 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+889/1000 d: 9 eps: 1/10000 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+8889/10000 d: 9 eps: 1/100000 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+88889/100000 d: 9 eps: 1/1000000 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+888889/1000000 d: 9 eps: 1/10000000 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+8888889/10000000 d: 9 eps: 1/100000000 KO_d_eps_m: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+88888889/100000000 d: 10 eps: 1/10 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+9/10 d: 10 eps: 1/100 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+89/100 d: 10 eps: 1/1000 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+889/1000 d: 10 eps: 1/10000 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+8889/10000 d: 10 eps: 1/100000 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+88889/100000 d: 10 eps: 1/1000000 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+888889/1000000 d: 10 eps: 1/10000000 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+8888889/10000000 d: 10 eps: 1/100000000 KO_d_eps_m: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+88888889/100000000 KO_d_eps_p: d: 3 eps: 1/10 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+11/10 d: 3 eps: 1/100 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+111/100 d: 3 eps: 1/1000 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+1111/1000 d: 3 eps: 1/10000 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+11111/10000 d: 3 eps: 1/100000 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+111111/100000 d: 3 eps: 1/1000000 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+1111111/1000000 d: 3 eps: 1/10000000 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+11111111/10000000 d: 3 eps: 1/100000000 KO_d_eps_p: x^3+3*x^2*y+3*x*y^2+y^3+3*x^2-21*x*y+3*y^2+3*x+3*y+111111111/100000000 d: 4 eps: 1/10 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+11/10 d: 4 eps: 1/100 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+111/100 d: 4 eps: 1/1000 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+1111/1000 d: 4 eps: 1/10000 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+11111/10000 d: 4 eps: 1/100000 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+111111/100000 d: 4 eps: 1/1000000 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+1111111/1000000 d: 4 eps: 1/10000000 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+11111111/10000000 d: 4 eps: 1/100000000 KO_d_eps_p: x^4-4*x^3*y+6*x^2*y^2-4*x*y^3+y^4-4*x^3-124*x^2*y-124*x*y^2-4*y^3+6*x^2-124*x*y+6*y^2-4*x-4*y+111111111/100000000 d: 5 eps: 1/10 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+11/10 d: 5 eps: 1/100 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+111/100 d: 5 eps: 1/1000 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+1111/1000 d: 5 eps: 1/10000 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+11111/10000 d: 5 eps: 1/100000 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+111111/100000 d: 5 eps: 1/1000000 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+1111111/1000000 d: 5 eps: 1/10000000 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+11111111/10000000 d: 5 eps: 1/100000000 KO_d_eps_p: x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5+5*x^4-605*x^3*y+1905*x^2*y^2-605*x*y^3+5*y^4+10*x^3+1905*x^2*y+1905*x*y^2+10*y^3+10*x^2-605*x*y+10*y^2+5*x+5*y+111111111/100000000 d: 6 eps: 1/10 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+11/10 d: 6 eps: 1/100 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+111/100 d: 6 eps: 1/1000 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+1111/1000 d: 6 eps: 1/10000 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+11111/10000 d: 6 eps: 1/100000 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+111111/100000 d: 6 eps: 1/1000000 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+1111111/1000000 d: 6 eps: 1/10000000 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+11111111/10000000 d: 6 eps: 1/100000000 KO_d_eps_p: x^6-6*x^5*y+15*x^4*y^2-20*x^3*y^3+15*x^2*y^4-6*x*y^5+y^6-6*x^5-2736*x^4*y-20586*x^3*y^2-20586*x^2*y^3-2736*x*y^4-6*y^5+15*x^4-20586*x^3*y+131727*x^2*y^2-20586*x*y^3+15*y^4-20*x^3-20586*x^2*y-20586*x*y^2-20*y^3+15*x^2-2736*x*y+15*y^2-6*x-6*y+111111111/100000000 d: 7 eps: 1/10 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+11/10 d: 7 eps: 1/100 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+111/100 d: 7 eps: 1/1000 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+1111/1000 d: 7 eps: 1/10000 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+11111/10000 d: 7 eps: 1/100000 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+111111/100000 d: 7 eps: 1/1000000 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+1111111/1000000 d: 7 eps: 1/10000000 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+11111111/10000000 d: 7 eps: 1/100000000 KO_d_eps_p: x^7+7*x^6*y+21*x^5*y^2+35*x^4*y^3+35*x^3*y^4+21*x^2*y^5+7*x*y^6+y^7+7*x^6-11963*x^5*y+187383*x^4*y^2-424837*x^3*y^3+187383*x^2*y^4-11963*x*y^5+7*y^6+21*x^5+187383*x^4*y+5150355*x^3*y^2+5150355*x^2*y^3+187383*x*y^4+21*y^5+35*x^4-424837*x^3*y+5150355*x^2*y^2-424837*x*y^3+35*y^4+35*x^3+187383*x^2*y+187383*x*y^2+35*y^3+21*x^2-11963*x*y+21*y^2+7*x+7*y+111111111/100000000 d: 8 eps: 1/10 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+11/10 d: 8 eps: 1/100 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+111/100 d: 8 eps: 1/1000 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+1111/1000 d: 8 eps: 1/10000 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+11111/10000 d: 8 eps: 1/100000 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+111111/100000 d: 8 eps: 1/1000000 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+1111111/1000000 d: 8 eps: 1/10000000 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+11111111/10000000 d: 8 eps: 1/100000000 KO_d_eps_p: x^8-8*x^7*y+28*x^6*y^2-56*x^5*y^3+70*x^4*y^4-56*x^3*y^5+28*x^2*y^6-8*x*y^7+y^8-8*x^7-51416*x^6*y-1549640*x^5*y^2-6787544*x^4*y^3-6787544*x^3*y^4-1549640*x^2*y^5-51416*x*y^6-8*y^7+28*x^6-1549640*x^5*y+151020580*x^4*y^2-581991920*x^3*y^3+151020580*x^2*y^4-1549640*x*y^5+28*y^6-56*x^5-6787544*x^4*y-581991920*x^3*y^2-581991920*x^2*y^3-6787544*x*y^4-56*y^5+70*x^4-6787544*x^3*y+151020580*x^2*y^2-6787544*x*y^3+70*y^4-56*x^3-1549640*x^2*y-1549640*x*y^2-56*y^3+28*x^2-51416*x*y+28*y^2-8*x-8*y+111111111/100000000 d: 9 eps: 1/10 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+11/10 d: 9 eps: 1/100 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+111/100 d: 9 eps: 1/1000 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+1111/1000 d: 9 eps: 1/10000 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+11111/10000 d: 9 eps: 1/100000 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+111111/100000 d: 9 eps: 1/1000000 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+1111111/1000000 d: 9 eps: 1/10000000 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+11111111/10000000 d: 9 eps: 1/100000000 KO_d_eps_p: x^9+9*x^8*y+36*x^7*y^2+84*x^6*y^3+126*x^5*y^4+126*x^4*y^5+84*x^3*y^6+36*x^2*y^7+9*x*y^8+y^9+9*x^8-218709*x^7*y+12091689*x^6*y^2-93153789*x^5*y^3+176492097*x^4*y^4-93153789*x^3*y^5+12091689*x^2*y^6-218709*x*y^7+9*y^8+36*x^7+12091689*x^6*y+3750845481*x^5*y^2+43607853486*x^4*y^3+43607853486*x^3*y^4+3750845481*x^2*y^5+12091689*x*y^6+36*y^7+84*x^6-93153789*x^5*y+43607853486*x^4*y^2-272942106456*x^3*y^3+43607853486*x^2*y^4-93153789*x*y^5+84*y^6+126*x^5+176492097*x^4*y+43607853486*x^3*y^2+43607853486*x^2*y^3+176492097*x*y^4+126*y^5+126*x^4-93153789*x^3*y+3750845481*x^2*y^2-93153789*x*y^3+126*y^4+84*x^3+12091689*x^2*y+12091689*x*y^2+84*y^3+36*x^2-218709*x*y+36*y^2+9*x+9*y+111111111/100000000 d: 10 eps: 1/10 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+11/10 d: 10 eps: 1/100 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+111/100 d: 10 eps: 1/1000 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+1111/1000 d: 10 eps: 1/10000 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+11111/10000 d: 10 eps: 1/100000 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+111111/100000 d: 10 eps: 1/1000000 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+1111111/1000000 d: 10 eps: 1/10000000 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+11111111/10000000 d: 10 eps: 1/100000000 KO_d_eps_p: x^10-10*x^9*y+45*x^8*y^2-120*x^7*y^3+210*x^6*y^4-252*x^5*y^5+210*x^4*y^6-120*x^3*y^7+45*x^2*y^8-10*x*y^9+y^10-10*x^9-923680*x^8*y-90912700*x^7*y^2-1159219720*x^6*y^3-3748943890*x^5*y^4-3748943890*x^4*y^5-1159219720*x^3*y^6-90912700*x^2*y^7-923680*x*y^8-10*y^9+45*x^8-90912700*x^7*y+83979047175*x^6*y^2-2555410068870*x^5*y^3+7399053634325*x^4*y^4-2555410068870*x^3*y^5+83979047175*x^2*y^6-90912700*x*y^7+45*y^8-120*x^7-1159219720*x^6*y-2555410068870*x^5*y^2-72607833130040*x^4*y^3-72607833130040*x^3*y^4-2555410068870*x^2*y^5-1159219720*x*y^6-120*y^7+210*x^6-3748943890*x^5*y+7399053634325*x^4*y^2-72607833130040*x^3*y^3+7399053634325*x^2*y^4-3748943890*x*y^5+210*y^6-252*x^5-3748943890*x^4*y-2555410068870*x^3*y^2-2555410068870*x^2*y^3-3748943890*x*y^4-252*y^5+210*x^4-1159219720*x^3*y+83979047175*x^2*y^2-1159219720*x*y^3+210*y^4-120*x^3-90912700*x^2*y-90912700*x*y^2-120*y^3+45*x^2-923680*x*y+45*y^2-10*x-10*y+111111111/100000000 ---------------- Challenge 7 high tangencies at isolated singularities ---------------- fkl_m: k: 2 l: 2 fkl_m: x^4-y^4-2*x^2*y+y^2 k: 3 l: 2 fkl_m: x^6-y^6-2*x^3*y+y^2 k: 4 l: 2 fkl_m: x^8-y^8-2*x^4*y+y^2 k: 5 l: 2 fkl_m: x^10-y^10-2*x^5*y+y^2 k: 6 l: 2 fkl_m: x^12-y^12-2*x^6*y+y^2 k: 7 l: 2 fkl_m: x^14-y^14-2*x^7*y+y^2 k: 8 l: 2 fkl_m: x^16-y^16-2*x^8*y+y^2 k: 9 l: 2 fkl_m: x^18-y^18-2*x^9*y+y^2 k: 10 l: 2 fkl_m: x^20-y^20-2*x^10*y+y^2 k: 11 l: 2 fkl_m: x^22-y^22-2*x^11*y+y^2 k: 12 l: 2 fkl_m: x^24-y^24-2*x^12*y+y^2 ---------------- Challenge 8 high tangencies at non-isolated singularities ---------------- ni_m: m: 2 ni_m: x^2 m: 3 ni_m: x^3 m: 4 ni_m: x^4 m: 5 ni_m: x^5 m: 6 ni_m: x^6 m: 7 ni_m: x^7 m: 8 ni_m: x^8 ni_m_k: k: 0 m: 2 ni_m_k: x^2 k: 1 m: 2 ni_m_k: x^2*y k: 2 m: 2 ni_m_k: x^2*y^2 k: 3 m: 2 ni_m_k: x^2*y^3 k: 4 m: 2 ni_m_k: x^2*y^4 k: 5 m: 2 ni_m_k: x^2*y^5 k: 6 m: 2 ni_m_k: x^2*y^6 k: 7 m: 2 ni_m_k: x^2*y^7 k: 8 m: 2 ni_m_k: x^2*y^8 k: 0 m: 3 ni_m_k: x^3 k: 1 m: 3 ni_m_k: x^3*y k: 2 m: 3 ni_m_k: x^3*y^2 k: 3 m: 3 ni_m_k: x^3*y^3 k: 4 m: 3 ni_m_k: x^3*y^4 k: 5 m: 3 ni_m_k: x^3*y^5 k: 6 m: 3 ni_m_k: x^3*y^6 k: 7 m: 3 ni_m_k: x^3*y^7 k: 8 m: 3 ni_m_k: x^3*y^8 k: 0 m: 4 ni_m_k: x^4 k: 1 m: 4 ni_m_k: x^4*y k: 2 m: 4 ni_m_k: x^4*y^2 k: 3 m: 4 ni_m_k: x^4*y^3 k: 4 m: 4 ni_m_k: x^4*y^4 k: 5 m: 4 ni_m_k: x^4*y^5 k: 6 m: 4 ni_m_k: x^4*y^6 k: 7 m: 4 ni_m_k: x^4*y^7 k: 8 m: 4 ni_m_k: x^4*y^8 k: 0 m: 5 ni_m_k: x^5 k: 1 m: 5 ni_m_k: x^5*y k: 2 m: 5 ni_m_k: x^5*y^2 k: 3 m: 5 ni_m_k: x^5*y^3 k: 4 m: 5 ni_m_k: x^5*y^4 k: 5 m: 5 ni_m_k: x^5*y^5 k: 6 m: 5 ni_m_k: x^5*y^6 k: 7 m: 5 ni_m_k: x^5*y^7 k: 8 m: 5 ni_m_k: x^5*y^8 k: 0 m: 6 ni_m_k: x^6 k: 1 m: 6 ni_m_k: x^6*y k: 2 m: 6 ni_m_k: x^6*y^2 k: 3 m: 6 ni_m_k: x^6*y^3 k: 4 m: 6 ni_m_k: x^6*y^4 k: 5 m: 6 ni_m_k: x^6*y^5 k: 6 m: 6 ni_m_k: x^6*y^6 k: 7 m: 6 ni_m_k: x^6*y^7 k: 8 m: 6 ni_m_k: x^6*y^8 k: 0 m: 7 ni_m_k: x^7 k: 1 m: 7 ni_m_k: x^7*y k: 2 m: 7 ni_m_k: x^7*y^2 k: 3 m: 7 ni_m_k: x^7*y^3 k: 4 m: 7 ni_m_k: x^7*y^4 k: 5 m: 7 ni_m_k: x^7*y^5 k: 6 m: 7 ni_m_k: x^7*y^6 k: 7 m: 7 ni_m_k: x^7*y^7 k: 8 m: 7 ni_m_k: x^7*y^8 k: 0 m: 8 ni_m_k: x^8 k: 1 m: 8 ni_m_k: x^8*y k: 2 m: 8 ni_m_k: x^8*y^2 k: 3 m: 8 ni_m_k: x^8*y^3 k: 4 m: 8 ni_m_k: x^8*y^4 k: 5 m: 8 ni_m_k: x^8*y^5 k: 6 m: 8 ni_m_k: x^8*y^6 k: 7 m: 8 ni_m_k: x^8*y^7 k: 8 m: 8 ni_m_k: x^8*y^8 nix_m_n_k_l: m: 2 n: 2 k: 2 l: 2 nix_m_n_k_l: x^10-2*x^6*y^4+x^2*y^8-4*x^8*y+4*x^4*y^5+6*x^6*y^2-2*x^2*y^6-4*x^4*y^3+x^2*y^4 m: 2 n: 2 k: 2 l: 3 nix_m_n_k_l: x^14+2*x^8*y^6+x^2*y^12-6*x^12*y-6*x^6*y^7+15*x^10*y^2+6*x^4*y^8-20*x^8*y^3-2*x^2*y^9+15*x^6*y^4-6*x^4*y^5+x^2*y^6 m: 2 n: 2 k: 2 l: 4 nix_m_n_k_l: x^18-2*x^10*y^8+x^2*y^16-8*x^16*y+8*x^8*y^9+28*x^14*y^2-12*x^6*y^10-56*x^12*y^3+8*x^4*y^11+70*x^10*y^4-2*x^2*y^12-56*x^8*y^5+28*x^6*y^6-8*x^4*y^7+x^2*y^8 m: 2 n: 2 k: 2 l: 5 nix_m_n_k_l: x^22+2*x^12*y^10+x^2*y^20-10*x^20*y-10*x^10*y^11+45*x^18*y^2+20*x^8*y^12-120*x^16*y^3-20*x^6*y^13+210*x^14*y^4+10*x^4*y^14-252*x^12*y^5-2*x^2*y^15+210*x^10*y^6-120*x^8*y^7+45*x^6*y^8-10*x^4*y^9+x^2*y^10 m: 2 n: 2 k: 3 l: 2 nix_m_n_k_l: x^14-2*x^8*y^6+x^2*y^12-4*x^11*y+4*x^5*y^7+6*x^8*y^2-2*x^2*y^8-4*x^5*y^3+x^2*y^4 m: 2 n: 2 k: 3 l: 3 nix_m_n_k_l: x^20+2*x^11*y^9+x^2*y^18-6*x^17*y-6*x^8*y^10+15*x^14*y^2+6*x^5*y^11-20*x^11*y^3-2*x^2*y^12+15*x^8*y^4-6*x^5*y^5+x^2*y^6 m: 2 n: 2 k: 3 l: 4 nix_m_n_k_l: x^26-2*x^14*y^12+x^2*y^24-8*x^23*y+8*x^11*y^13+28*x^20*y^2-12*x^8*y^14-56*x^17*y^3+8*x^5*y^15+70*x^14*y^4-2*x^2*y^16-56*x^11*y^5+28*x^8*y^6-8*x^5*y^7+x^2*y^8 m: 2 n: 2 k: 3 l: 5 nix_m_n_k_l: x^32+2*x^17*y^15+x^2*y^30-10*x^29*y-10*x^14*y^16+45*x^26*y^2+20*x^11*y^17-120*x^23*y^3-20*x^8*y^18+210*x^20*y^4+10*x^5*y^19-252*x^17*y^5-2*x^2*y^20+210*x^14*y^6-120*x^11*y^7+45*x^8*y^8-10*x^5*y^9+x^2*y^10 m: 2 n: 2 k: 4 l: 2 nix_m_n_k_l: x^18-2*x^10*y^8+x^2*y^16-4*x^14*y+4*x^6*y^9+6*x^10*y^2-2*x^2*y^10-4*x^6*y^3+x^2*y^4 m: 2 n: 2 k: 4 l: 3 nix_m_n_k_l: x^26+2*x^14*y^12+x^2*y^24-6*x^22*y-6*x^10*y^13+15*x^18*y^2+6*x^6*y^14-20*x^14*y^3-2*x^2*y^15+15*x^10*y^4-6*x^6*y^5+x^2*y^6 m: 2 n: 2 k: 4 l: 4 nix_m_n_k_l: x^34-2*x^18*y^16+x^2*y^32-8*x^30*y+8*x^14*y^17+28*x^26*y^2-12*x^10*y^18-56*x^22*y^3+8*x^6*y^19+70*x^18*y^4-2*x^2*y^20-56*x^14*y^5+28*x^10*y^6-8*x^6*y^7+x^2*y^8 m: 2 n: 2 k: 4 l: 5 nix_m_n_k_l: x^42+2*x^22*y^20+x^2*y^40-10*x^38*y-10*x^18*y^21+45*x^34*y^2+20*x^14*y^22-120*x^30*y^3-20*x^10*y^23+210*x^26*y^4+10*x^6*y^24-252*x^22*y^5-2*x^2*y^25+210*x^18*y^6-120*x^14*y^7+45*x^10*y^8-10*x^6*y^9+x^2*y^10 m: 2 n: 2 k: 5 l: 2 nix_m_n_k_l: x^22-2*x^12*y^10+x^2*y^20-4*x^17*y+4*x^7*y^11+6*x^12*y^2-2*x^2*y^12-4*x^7*y^3+x^2*y^4 m: 2 n: 2 k: 5 l: 3 nix_m_n_k_l: x^32+2*x^17*y^15+x^2*y^30-6*x^27*y-6*x^12*y^16+15*x^22*y^2+6*x^7*y^17-20*x^17*y^3-2*x^2*y^18+15*x^12*y^4-6*x^7*y^5+x^2*y^6 m: 2 n: 2 k: 5 l: 4 nix_m_n_k_l: x^42-2*x^22*y^20+x^2*y^40-8*x^37*y+8*x^17*y^21+28*x^32*y^2-12*x^12*y^22-56*x^27*y^3+8*x^7*y^23+70*x^22*y^4-2*x^2*y^24-56*x^17*y^5+28*x^12*y^6-8*x^7*y^7+x^2*y^8 m: 2 n: 2 k: 5 l: 5 nix_m_n_k_l: x^52+2*x^27*y^25+x^2*y^50-10*x^47*y-10*x^22*y^26+45*x^42*y^2+20*x^17*y^27-120*x^37*y^3-20*x^12*y^28+210*x^32*y^4+10*x^7*y^29-252*x^27*y^5-2*x^2*y^30+210*x^22*y^6-120*x^17*y^7+45*x^12*y^8-10*x^7*y^9+x^2*y^10 m: 2 n: 3 k: 2 l: 2 nix_m_n_k_l: x^14-3*x^10*y^4+3*x^6*y^8-x^2*y^12-6*x^12*y+12*x^8*y^5-6*x^4*y^9+15*x^10*y^2-18*x^6*y^6+3*x^2*y^10-20*x^8*y^3+12*x^4*y^7+15*x^6*y^4-3*x^2*y^8-6*x^4*y^5+x^2*y^6 m: 2 n: 3 k: 2 l: 3 nix_m_n_k_l: -x^20-3*x^14*y^6-3*x^8*y^12-x^2*y^18+9*x^18*y+18*x^12*y^7+9*x^6*y^13-36*x^16*y^2-45*x^10*y^8-9*x^4*y^14+84*x^14*y^3+60*x^8*y^9+3*x^2*y^15-126*x^12*y^4-45*x^6*y^10+126*x^10*y^5+18*x^4*y^11-84*x^8*y^6-3*x^2*y^12+36*x^6*y^7-9*x^4*y^8+x^2*y^9 m: 2 n: 3 k: 2 l: 4 nix_m_n_k_l: x^26-3*x^18*y^8+3*x^10*y^16-x^2*y^24-12*x^24*y+24*x^16*y^9-12*x^8*y^17+66*x^22*y^2-84*x^14*y^10+18*x^6*y^18-220*x^20*y^3+168*x^12*y^11-12*x^4*y^19+495*x^18*y^4-210*x^10*y^12+3*x^2*y^20-792*x^16*y^5+168*x^8*y^13+924*x^14*y^6-84*x^6*y^14-792*x^12*y^7+24*x^4*y^15+495*x^10*y^8-3*x^2*y^16-220*x^8*y^9+66*x^6*y^10-12*x^4*y^11+x^2*y^12 m: 2 n: 3 k: 2 l: 5 nix_m_n_k_l: -x^32-3*x^22*y^10-3*x^12*y^20-x^2*y^30+15*x^30*y+30*x^20*y^11+15*x^10*y^21-105*x^28*y^2-135*x^18*y^12-30*x^8*y^22+455*x^26*y^3+360*x^16*y^13+30*x^6*y^23-1365*x^24*y^4-630*x^14*y^14-15*x^4*y^24+3003*x^22*y^5+756*x^12*y^15+3*x^2*y^25-5005*x^20*y^6-630*x^10*y^16+6435*x^18*y^7+360*x^8*y^17-6435*x^16*y^8-135*x^6*y^18+5005*x^14*y^9+30*x^4*y^19-3003*x^12*y^10-3*x^2*y^20+1365*x^10*y^11-455*x^8*y^12+105*x^6*y^13-15*x^4*y^14+x^2*y^15 m: 2 n: 3 k: 3 l: 2 nix_m_n_k_l: x^20-3*x^14*y^6+3*x^8*y^12-x^2*y^18-6*x^17*y+12*x^11*y^7-6*x^5*y^13+15*x^14*y^2-18*x^8*y^8+3*x^2*y^14-20*x^11*y^3+12*x^5*y^9+15*x^8*y^4-3*x^2*y^10-6*x^5*y^5+x^2*y^6 m: 2 n: 3 k: 3 l: 3 nix_m_n_k_l: -x^29-3*x^20*y^9-3*x^11*y^18-x^2*y^27+9*x^26*y+18*x^17*y^10+9*x^8*y^19-36*x^23*y^2-45*x^14*y^11-9*x^5*y^20+84*x^20*y^3+60*x^11*y^12+3*x^2*y^21-126*x^17*y^4-45*x^8*y^13+126*x^14*y^5+18*x^5*y^14-84*x^11*y^6-3*x^2*y^15+36*x^8*y^7-9*x^5*y^8+x^2*y^9 m: 2 n: 3 k: 3 l: 4 nix_m_n_k_l: x^38-3*x^26*y^12+3*x^14*y^24-x^2*y^36-12*x^35*y+24*x^23*y^13-12*x^11*y^25+66*x^32*y^2-84*x^20*y^14+18*x^8*y^26-220*x^29*y^3+168*x^17*y^15-12*x^5*y^27+495*x^26*y^4-210*x^14*y^16+3*x^2*y^28-792*x^23*y^5+168*x^11*y^17+924*x^20*y^6-84*x^8*y^18-792*x^17*y^7+24*x^5*y^19+495*x^14*y^8-3*x^2*y^20-220*x^11*y^9+66*x^8*y^10-12*x^5*y^11+x^2*y^12 m: 2 n: 3 k: 3 l: 5 nix_m_n_k_l: -x^47-3*x^32*y^15-3*x^17*y^30-x^2*y^45+15*x^44*y+30*x^29*y^16+15*x^14*y^31-105*x^41*y^2-135*x^26*y^17-30*x^11*y^32+455*x^38*y^3+360*x^23*y^18+30*x^8*y^33-1365*x^35*y^4-630*x^20*y^19-15*x^5*y^34+3003*x^32*y^5+756*x^17*y^20+3*x^2*y^35-5005*x^29*y^6-630*x^14*y^21+6435*x^26*y^7+360*x^11*y^22-6435*x^23*y^8-135*x^8*y^23+5005*x^20*y^9+30*x^5*y^24-3003*x^17*y^10-3*x^2*y^25+1365*x^14*y^11-455*x^11*y^12+105*x^8*y^13-15*x^5*y^14+x^2*y^15 m: 2 n: 3 k: 4 l: 2 nix_m_n_k_l: x^26-3*x^18*y^8+3*x^10*y^16-x^2*y^24-6*x^22*y+12*x^14*y^9-6*x^6*y^17+15*x^18*y^2-18*x^10*y^10+3*x^2*y^18-20*x^14*y^3+12*x^6*y^11+15*x^10*y^4-3*x^2*y^12-6*x^6*y^5+x^2*y^6 m: 2 n: 3 k: 4 l: 3 nix_m_n_k_l: -x^38-3*x^26*y^12-3*x^14*y^24-x^2*y^36+9*x^34*y+18*x^22*y^13+9*x^10*y^25-36*x^30*y^2-45*x^18*y^14-9*x^6*y^26+84*x^26*y^3+60*x^14*y^15+3*x^2*y^27-126*x^22*y^4-45*x^10*y^16+126*x^18*y^5+18*x^6*y^17-84*x^14*y^6-3*x^2*y^18+36*x^10*y^7-9*x^6*y^8+x^2*y^9 m: 2 n: 3 k: 4 l: 4 nix_m_n_k_l: 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x^30*y^5-5*x^24*y^11+10*x^18*y^17-10*x^12*y^23+5*x^6*y^29-y^35-10*x^27*y^6+40*x^21*y^12-60*x^15*y^18+40*x^9*y^24-10*x^3*y^30+45*x^24*y^7-140*x^18*y^13+150*x^12*y^19-60*x^6*y^25+5*y^31-120*x^21*y^8+280*x^15*y^14-200*x^9*y^20+40*x^3*y^26+210*x^18*y^9-350*x^12*y^15+150*x^6*y^21-10*y^27-252*x^15*y^10+280*x^9*y^16-60*x^3*y^22+210*x^12*y^11-140*x^6*y^17+10*y^23-120*x^9*y^12+40*x^3*y^18+45*x^6*y^13-5*y^19-10*x^3*y^14+y^15 m: 5 n: 5 k: 3 l: 4 niy_m_n_k_l: x^60*y^5-5*x^48*y^17+10*x^36*y^29-10*x^24*y^41+5*x^12*y^53-y^65-20*x^57*y^6+80*x^45*y^18-120*x^33*y^30+80*x^21*y^42-20*x^9*y^54+190*x^54*y^7-600*x^42*y^19+660*x^30*y^31-280*x^18*y^43+30*x^6*y^55-1140*x^51*y^8+2800*x^39*y^20-2200*x^27*y^32+560*x^15*y^44-20*x^3*y^56+4845*x^48*y^9-9100*x^36*y^21+4950*x^24*y^33-700*x^12*y^45+5*y^57-15504*x^45*y^10+21840*x^33*y^22-7920*x^21*y^34+560*x^9*y^46+38760*x^42*y^11-40040*x^30*y^23+9240*x^18*y^35-280*x^6*y^47-77520*x^39*y^12+57200*x^27*y^24-7920*x^15*y^36+80*x^3*y^48+125970*x^36*y^13-64350*x^24*y^25+4950*x^12*y^37-10*y^49-167960*x^33*y^14+57200*x^21*y^26-2200*x^9*y^38+184756*x^30*y^15-40040*x^18*y^27+660*x^6*y^39-167960*x^27*y^16+21840*x^15*y^28-120*x^3*y^40+125970*x^24*y^17-9100*x^12*y^29+10*y^41-77520*x^21*y^18+2800*x^9*y^30+38760*x^18*y^19-600*x^6*y^31-15504*x^15*y^20+80*x^3*y^32+4845*x^12*y^21-5*y^33-1140*x^9*y^22+190*x^6*y^23-20*x^3*y^24+y^25 m: 5 n: 5 k: 4 l: 2 niy_m_n_k_l: x^40*y^5-5*x^32*y^13+10*x^24*y^21-10*x^16*y^29+5*x^8*y^37-y^45-10*x^36*y^6+40*x^28*y^14-60*x^20*y^22+40*x^12*y^30-10*x^4*y^38+45*x^32*y^7-140*x^24*y^15+150*x^16*y^23-60*x^8*y^31+5*y^39-120*x^28*y^8+280*x^20*y^16-200*x^12*y^24+40*x^4*y^32+210*x^24*y^9-350*x^16*y^17+150*x^8*y^25-10*y^33-252*x^20*y^10+280*x^12*y^18-60*x^4*y^26+210*x^16*y^11-140*x^8*y^19+10*y^27-120*x^12*y^12+40*x^4*y^20+45*x^8*y^13-5*y^21-10*x^4*y^14+y^15 m: 5 n: 5 k: 4 l: 4 niy_m_n_k_l: x^80*y^5-5*x^64*y^21+10*x^48*y^37-10*x^32*y^53+5*x^16*y^69-y^85-20*x^76*y^6+80*x^60*y^22-120*x^44*y^38+80*x^28*y^54-20*x^12*y^70+190*x^72*y^7-600*x^56*y^23+660*x^40*y^39-280*x^24*y^55+30*x^8*y^71-1140*x^68*y^8+2800*x^52*y^24-2200*x^36*y^40+560*x^20*y^56-20*x^4*y^72+4845*x^64*y^9-9100*x^48*y^25+4950*x^32*y^41-700*x^16*y^57+5*y^73-15504*x^60*y^10+21840*x^44*y^26-7920*x^28*y^42+560*x^12*y^58+38760*x^56*y^11-40040*x^40*y^27+9240*x^24*y^43-280*x^8*y^59-77520*x^52*y^12+57200*x^36*y^28-7920*x^20*y^44+80*x^4*y^60+125970*x^48*y^13-64350*x^32*y^29+4950*x^16*y^45-10*y^61-167960*x^44*y^14+57200*x^28*y^30-2200*x^12*y^46+184756*x^40*y^15-40040*x^24*y^31+660*x^8*y^47-167960*x^36*y^16+21840*x^20*y^32-120*x^4*y^48+125970*x^32*y^17-9100*x^16*y^33+10*y^49-77520*x^28*y^18+2800*x^12*y^34+38760*x^24*y^19-600*x^8*y^35-15504*x^20*y^20+80*x^4*y^36+4845*x^16*y^21-5*y^37-1140*x^12*y^22+190*x^8*y^23-20*x^4*y^24+y^25 m: 5 n: 5 k: 5 l: 2 niy_m_n_k_l: x^50*y^5-5*x^40*y^15+10*x^30*y^25-10*x^20*y^35+5*x^10*y^45-y^55-10*x^45*y^6+40*x^35*y^16-60*x^25*y^26+40*x^15*y^36-10*x^5*y^46+45*x^40*y^7-140*x^30*y^17+150*x^20*y^27-60*x^10*y^37+5*y^47-120*x^35*y^8+280*x^25*y^18-200*x^15*y^28+40*x^5*y^38+210*x^30*y^9-350*x^20*y^19+150*x^10*y^29-10*y^39-252*x^25*y^10+280*x^15*y^20-60*x^5*y^30+210*x^20*y^11-140*x^10*y^21+10*y^31-120*x^15*y^12+40*x^5*y^22+45*x^10*y^13-5*y^23-10*x^5*y^14+y^15 m: 5 n: 5 k: 5 l: 4 niy_m_n_k_l: x^100*y^5-5*x^80*y^25+10*x^60*y^45-10*x^40*y^65+5*x^20*y^85-y^105-20*x^95*y^6+80*x^75*y^26-120*x^55*y^46+80*x^35*y^66-20*x^15*y^86+190*x^90*y^7-600*x^70*y^27+660*x^50*y^47-280*x^30*y^67+30*x^10*y^87-1140*x^85*y^8+2800*x^65*y^28-2200*x^45*y^48+560*x^25*y^68-20*x^5*y^88+4845*x^80*y^9-9100*x^60*y^29+4950*x^40*y^49-700*x^20*y^69+5*y^89-15504*x^75*y^10+21840*x^55*y^30-7920*x^35*y^50+560*x^15*y^70+38760*x^70*y^11-40040*x^50*y^31+9240*x^30*y^51-280*x^10*y^71-77520*x^65*y^12+57200*x^45*y^32-7920*x^25*y^52+80*x^5*y^72+125970*x^60*y^13-64350*x^40*y^33+4950*x^20*y^53-10*y^73-167960*x^55*y^14+57200*x^35*y^34-2200*x^15*y^54+184756*x^50*y^15-40040*x^30*y^35+660*x^10*y^55-167960*x^45*y^16+21840*x^25*y^36-120*x^5*y^56+125970*x^40*y^17-9100*x^20*y^37+10*y^57-77520*x^35*y^18+2800*x^15*y^38+38760*x^30*y^19-600*x^10*y^39-15504*x^25*y^20+80*x^5*y^40+4845*x^20*y^21-5*y^41-1140*x^15*y^22+190*x^10*y^23-20*x^5*y^24+y^25 ---------------- Challenge 9 many isolated singularities ---------------- C_k_l: k: 2 l: 2 C_k_l: -x^4-2*x^2*y^2-y^4+2*x^2+3*y^2-1 k: 2 l: 3 C_k_l: -x^6-3*x^4*y^2-3*x^2*y^4-y^6+3*x^4+6*x^2*y^2+3*y^4-3*x^2-2*y^2+1 k: 2 l: 4 C_k_l: -x^8-4*x^6*y^2-6*x^4*y^4-4*x^2*y^6-y^8+4*x^6+12*x^4*y^2+12*x^2*y^4+4*y^6-6*x^4-11*x^2*y^2-6*y^4+4*x^2+4*y^2-1 k: 2 l: 5 C_k_l: -x^10-5*x^8*y^2-10*x^6*y^4-10*x^4*y^6-5*x^2*y^8-y^10+5*x^8+20*x^6*y^2+30*x^4*y^4+20*x^2*y^6+5*y^8-10*x^6-30*x^4*y^2-30*x^2*y^4-10*y^6+10*x^4+21*x^2*y^2+10*y^4-5*x^2-5*y^2+1 k: 2 l: 6 C_k_l: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+6*x^10+30*x^8*y^2+60*x^6*y^4+60*x^4*y^6+30*x^2*y^8+6*y^10-15*x^8-60*x^6*y^2-90*x^4*y^4-60*x^2*y^6-15*y^8+20*x^6+61*x^4*y^2+178/3*x^2*y^4+181/9*y^6-15*x^4-30*x^2*y^2-15*y^4+6*x^2+6*y^2-1 k: 2 l: 7 C_k_l: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+7*x^12+42*x^10*y^2+105*x^8*y^4+140*x^6*y^6+105*x^4*y^8+42*x^2*y^10+7*y^12-21*x^10-105*x^8*y^2-210*x^6*y^4-210*x^4*y^6-105*x^2*y^8-21*y^10+35*x^8+140*x^6*y^2+210*x^4*y^4+140*x^2*y^6+35*y^8-35*x^6-104*x^4*y^2-317/3*x^2*y^4-314/9*y^6+21*x^4+42*x^2*y^2+21*y^4-7*x^2-7*y^2+1 k: 2 l: 8 C_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+8*x^14+56*x^12*y^2+168*x^10*y^4+280*x^8*y^6+280*x^6*y^8+168*x^4*y^10+56*x^2*y^12+8*y^14-28*x^12-168*x^10*y^2-420*x^8*y^4-560*x^6*y^6-420*x^4*y^8-168*x^2*y^10-28*y^12+56*x^10+280*x^8*y^2+560*x^6*y^4+560*x^4*y^6+280*x^2*y^8+56*y^10-70*x^8-279*x^6*y^2-422*x^4*y^4-279*x^2*y^6-70*y^8+56*x^6+168*x^4*y^2+168*x^2*y^4+56*y^6-28*x^4-56*x^2*y^2-28*y^4+8*x^2+8*y^2-1 k: 2 l: 9 C_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+9*x^16+72*x^14*y^2+252*x^12*y^4+504*x^10*y^6+630*x^8*y^8+504*x^6*y^10+252*x^4*y^12+72*x^2*y^14+9*y^16-36*x^14-252*x^12*y^2-756*x^10*y^4-1260*x^8*y^6-1260*x^6*y^8-756*x^4*y^10-252*x^2*y^12-36*y^14+84*x^12+504*x^10*y^2+1260*x^8*y^4+1680*x^6*y^6+1260*x^4*y^8+504*x^2*y^10+84*y^12-126*x^10-630*x^8*y^2-1260*x^6*y^4-1260*x^4*y^6-630*x^2*y^8-126*y^10+126*x^8+505*x^6*y^2+754*x^4*y^4+505*x^2*y^6+126*y^8-84*x^6-252*x^4*y^2-252*x^2*y^4-84*y^6+36*x^4+72*x^2*y^2+36*y^4-9*x^2-9*y^2+1 k: 2 l: 10 C_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+10*x^18+90*x^16*y^2+360*x^14*y^4+840*x^12*y^6+1260*x^10*y^8+1260*x^8*y^10+840*x^6*y^12+360*x^4*y^14+90*x^2*y^16+10*y^18-45*x^16-360*x^14*y^2-1260*x^12*y^4-2520*x^10*y^6-3150*x^8*y^8-2520*x^6*y^10-1260*x^4*y^12-360*x^2*y^14-45*y^16+120*x^14+840*x^12*y^2+2520*x^10*y^4+4200*x^8*y^6+4200*x^6*y^8+2520*x^4*y^10+840*x^2*y^12+120*y^14-210*x^12-1260*x^10*y^2-3150*x^8*y^4-4200*x^6*y^6-3150*x^4*y^8-1260*x^2*y^10-210*y^12+252*x^10+1261*x^8*y^2+2516*x^6*y^4+12622/5*x^4*y^6+6296/5*x^2*y^8+6301/25*y^10-210*x^8-840*x^6*y^2-1260*x^4*y^4-840*x^2*y^6-210*y^8+120*x^6+360*x^4*y^2+360*x^2*y^4+120*y^6-45*x^4-90*x^2*y^2-45*y^4+10*x^2+10*y^2-1 ---------------- Challenge 10 many higher isolated singularities ---------------- F_k_l_m_m: k: 2 l: 2 m: 2 F_k_l_m_m: x^4-y^4-6*x^3-2*x^2*y+13*x^2+6*x*y+y^2-12*x-4*y+4 k: 3 l: 2 m: 2 F_k_l_m_m: -y^6+x^4-6*x^3-2*x^2*y+13*x^2+6*x*y+y^2-12*x-4*y+4 k: 3 l: 2 m: 3 F_k_l_m_m: x^6-y^6-12*x^5+58*x^4-2*x^3*y-144*x^3+12*x^2*y+193*x^2-22*x*y+y^2-132*x+12*y+36 k: 4 l: 2 m: 2 F_k_l_m_m: x^8-y^8-12*x^7+62*x^6-180*x^5-2*x^4*y+321*x^4+12*x^3*y-360*x^3-26*x^2*y+248*x^2+24*x*y+y^2-96*x-8*y+16 k: 4 l: 2 m: 3 F_k_l_m_m: -y^8+x^6-12*x^5+58*x^4-2*x^3*y-144*x^3+12*x^2*y+193*x^2-22*x*y+y^2-132*x+12*y+36 k: 4 l: 2 m: 4 F_k_l_m_m: x^8-y^8-20*x^7+170*x^6-800*x^5-2*x^4*y+2273*x^4+20*x^3*y-3980*x^3-70*x^2*y+4180*x^2+100*x*y+y^2-2400*x-48*y+576 k: 5 l: 2 m: 2 F_k_l_m_m: -y^10+x^8-12*x^7+62*x^6-180*x^5-2*x^4*y+321*x^4+12*x^3*y-360*x^3-26*x^2*y+248*x^2+24*x*y+y^2-96*x-8*y+16 k: 5 l: 2 m: 3 F_k_l_m_m: -y^10+x^6-12*x^5+58*x^4-2*x^3*y-144*x^3+12*x^2*y+193*x^2-22*x*y+y^2-132*x+12*y+36 k: 5 l: 2 m: 4 F_k_l_m_m: -y^10+x^8-20*x^7+170*x^6-800*x^5-2*x^4*y+2273*x^4+20*x^3*y-3980*x^3-70*x^2*y+4180*x^2+100*x*y+y^2-2400*x-48*y+576 k: 5 l: 2 m: 5 F_k_l_m_m: x^10-y^10-30*x^9+395*x^8-3000*x^7+14523*x^6-2*x^5*y-46710*x^5+30*x^4*y+100805*x^4-170*x^3*y-143700*x^3+450*x^2*y+129076*x^2-548*x*y+y^2-65760*x+240*y+14400 k: 6 l: 2 m: 2 F_k_l_m_m: x^12-y^12-18*x^11+147*x^10-720*x^9+2355*x^8-5418*x^7-2*x^6*y+8989*x^6+18*x^5*y-10836*x^5-66*x^4*y+9420*x^4+126*x^3*y-5760*x^3-132*x^2*y+2352*x^2+72*x*y+y^2-576*x-16*y+64 k: 6 l: 2 m: 3 F_k_l_m_m: x^12-y^12-24*x^11+260*x^10-1680*x^9+7206*x^8-21600*x^7-2*x^6*y+46364*x^6+24*x^5*y-71760*x^5-116*x^4*y+79441*x^4+288*x^3*y-61320*x^3-386*x^2*y+31320*x^2+264*x*y+y^2-9504*x-72*y+1296 k: 6 l: 2 m: 4 F_k_l_m_m: -y^12+x^8-20*x^7+170*x^6-800*x^5-2*x^4*y+2273*x^4+20*x^3*y-3980*x^3-70*x^2*y+4180*x^2+100*x*y+y^2-2400*x-48*y+576 k: 6 l: 2 m: 5 F_k_l_m_m: -y^12+x^10-30*x^9+395*x^8-3000*x^7+14523*x^6-2*x^5*y-46710*x^5+30*x^4*y+100805*x^4-170*x^3*y-143700*x^3+450*x^2*y+129076*x^2-548*x*y+y^2-65760*x+240*y+14400 k: 6 l: 2 m: 6 F_k_l_m_m: x^12-y^12-42*x^11+791*x^10-8820*x^9+64743*x^8-328986*x^7-2*x^6*y+1184153*x^6+42*x^5*y-3034920*x^5-350*x^4*y+5482456*x^4+1470*x^3*y-6787872*x^3-3248*x^2*y+5450256*x^2+3528*x*y+y^2-2540160*x-1440*y+518400 k: 7 l: 2 m: 2 F_k_l_m_m: -y^14+x^12-18*x^11+147*x^10-720*x^9+2355*x^8-5418*x^7-2*x^6*y+8989*x^6+18*x^5*y-10836*x^5-66*x^4*y+9420*x^4+126*x^3*y-5760*x^3-132*x^2*y+2352*x^2+72*x*y+y^2-576*x-16*y+64 k: 7 l: 2 m: 3 F_k_l_m_m: -y^14+x^12-24*x^11+260*x^10-1680*x^9+7206*x^8-21600*x^7-2*x^6*y+46364*x^6+24*x^5*y-71760*x^5-116*x^4*y+79441*x^4+288*x^3*y-61320*x^3-386*x^2*y+31320*x^2+264*x*y+y^2-9504*x-72*y+1296 k: 7 l: 2 m: 4 F_k_l_m_m: -y^14+x^8-20*x^7+170*x^6-800*x^5-2*x^4*y+2273*x^4+20*x^3*y-3980*x^3-70*x^2*y+4180*x^2+100*x*y+y^2-2400*x-48*y+576 k: 7 l: 2 m: 5 F_k_l_m_m: -y^14+x^10-30*x^9+395*x^8-3000*x^7+14523*x^6-2*x^5*y-46710*x^5+30*x^4*y+100805*x^4-170*x^3*y-143700*x^3+450*x^2*y+129076*x^2-548*x*y+y^2-65760*x+240*y+14400 k: 7 l: 2 m: 6 F_k_l_m_m: -y^14+x^12-42*x^11+791*x^10-8820*x^9+64743*x^8-328986*x^7-2*x^6*y+1184153*x^6+42*x^5*y-3034920*x^5-350*x^4*y+5482456*x^4+1470*x^3*y-6787872*x^3-3248*x^2*y+5450256*x^2+3528*x*y+y^2-2540160*x-1440*y+518400 k: 7 l: 2 m: 7 F_k_l_m_m: x^14-y^14-56*x^13+1428*x^12-21952*x^11+226982*x^10-1667568*x^9+8962364*x^8-2*x^7*y-35733376*x^7+56*x^6*y+105994833*x^6-644*x^5*y-232253336*x^5+3920*x^4*y+369120808*x^4-13538*x^3*y-411449472*x^3+26264*x^2*y+303143184*x^2-26136*x*y+y^2-131725440*x+10080*y+25401600 k: 8 l: 2 m: 2 F_k_l_m_m: x^16-y^16-24*x^15+268*x^14-1848*x^13+8806*x^12-30744*x^11+81340*x^10-166344*x^9-2*x^8*y+265729*x^8+24*x^7*y-332688*x^7-124*x^6*y+325360*x^6+360*x^5*y-245952*x^5-642*x^4*y+140896*x^4+720*x^3*y-59136*x^3-496*x^2*y+17152*x^2+192*x*y+y^2-3072*x-32*y+256 k: 8 l: 2 m: 3 F_k_l_m_m: -y^16+x^12-24*x^11+260*x^10-1680*x^9+7206*x^8-21600*x^7-2*x^6*y+46364*x^6+24*x^5*y-71760*x^5-116*x^4*y+79441*x^4+288*x^3*y-61320*x^3-386*x^2*y+31320*x^2+264*x*y+y^2-9504*x-72*y+1296 k: 8 l: 2 m: 4 F_k_l_m_m: x^16-y^16-40*x^15+740*x^14-8400*x^13+65446*x^12-370880*x^11+1580380*x^10-5162000*x^9-2*x^8*y+13052881*x^8+40*x^7*y-25620120*x^7-340*x^6*y+38878520*x^6+1600*x^5*y-45104800*x^5-4546*x^4*y+39194896*x^4+7960*x^3*y-24648960*x^3-8360*x^2*y+10575360*x^2+4800*x*y+y^2-2764800*x-1152*y+331776 k: 8 l: 2 m: 5 F_k_l_m_m: -y^16+x^10-30*x^9+395*x^8-3000*x^7+14523*x^6-2*x^5*y-46710*x^5+30*x^4*y+100805*x^4-170*x^3*y-143700*x^3+450*x^2*y+129076*x^2-548*x*y+y^2-65760*x+240*y+14400 k: 8 l: 2 m: 6 F_k_l_m_m: -y^16+x^12-42*x^11+791*x^10-8820*x^9+64743*x^8-328986*x^7-2*x^6*y+1184153*x^6+42*x^5*y-3034920*x^5-350*x^4*y+5482456*x^4+1470*x^3*y-6787872*x^3-3248*x^2*y+5450256*x^2+3528*x*y+y^2-2540160*x-1440*y+518400 k: 8 l: 2 m: 7 F_k_l_m_m: -y^16+x^14-56*x^13+1428*x^12-21952*x^11+226982*x^10-1667568*x^9+8962364*x^8-2*x^7*y-35733376*x^7+56*x^6*y+105994833*x^6-644*x^5*y-232253336*x^5+3920*x^4*y+369120808*x^4-13538*x^3*y-411449472*x^3+26264*x^2*y+303143184*x^2-26136*x*y+y^2-131725440*x+10080*y+25401600 k: 8 l: 2 m: 8 F_k_l_m_m: x^16-y^16-72*x^15+2388*x^14-48384*x^13+669606*x^12-6704208*x^11+50170300*x^10-285855552*x^9-2*x^8*y+1251320145*x^8+72*x^7*y-4215106728*x^7-1092*x^6*y+10868843496*x^6+9072*x^5*y-21181595904*x^5-44898*x^4*y+30510066448*x^4+134568*x^3*y-31314782592*x^3-236248*x^2*y+21534172416*x^2+219168*x*y+y^2-8836853760*x-80640*y+1625702400 k: 9 l: 2 m: 2 F_k_l_m_m: -y^18+x^16-24*x^15+268*x^14-1848*x^13+8806*x^12-30744*x^11+81340*x^10-166344*x^9-2*x^8*y+265729*x^8+24*x^7*y-332688*x^7-124*x^6*y+325360*x^6+360*x^5*y-245952*x^5-642*x^4*y+140896*x^4+720*x^3*y-59136*x^3-496*x^2*y+17152*x^2+192*x*y+y^2-3072*x-32*y+256 k: 9 l: 2 m: 3 F_k_l_m_m: x^18-y^18-36*x^17+606*x^16-6336*x^15+46095*x^14-247716*x^13+1018816*x^12-3278016*x^11+8361951*x^10-2*x^9*y-17033580*x^9+36*x^8*y+27767046*x^8-282*x^7*y-36128736*x^7+1260*x^6*y+37235521*x^6-3534*x^5*y-29981196*x^5+6444*x^4*y+18442620*x^4-7630*x^3*y-8362656*x^3+5652*x^2*y+2632176*x^2-2376*x*y+y^2-513216*x+432*y+46656 k: 9 l: 2 m: 4 F_k_l_m_m: -y^18+x^16-40*x^15+740*x^14-8400*x^13+65446*x^12-370880*x^11+1580380*x^10-5162000*x^9-2*x^8*y+13052881*x^8+40*x^7*y-25620120*x^7-340*x^6*y+38878520*x^6+1600*x^5*y-45104800*x^5-4546*x^4*y+39194896*x^4+7960*x^3*y-24648960*x^3-8360*x^2*y+10575360*x^2+4800*x*y+y^2-2764800*x-1152*y+331776 k: 9 l: 2 m: 5 F_k_l_m_m: -y^18+x^10-30*x^9+395*x^8-3000*x^7+14523*x^6-2*x^5*y-46710*x^5+30*x^4*y+100805*x^4-170*x^3*y-143700*x^3+450*x^2*y+129076*x^2-548*x*y+y^2-65760*x+240*y+14400 k: 9 l: 2 m: 6 F_k_l_m_m: -y^18+x^12-42*x^11+791*x^10-8820*x^9+64743*x^8-328986*x^7-2*x^6*y+1184153*x^6+42*x^5*y-3034920*x^5-350*x^4*y+5482456*x^4+1470*x^3*y-6787872*x^3-3248*x^2*y+5450256*x^2+3528*x*y+y^2-2540160*x-1440*y+518400 k: 9 l: 2 m: 7 F_k_l_m_m: -y^18+x^14-56*x^13+1428*x^12-21952*x^11+226982*x^10-1667568*x^9+8962364*x^8-2*x^7*y-35733376*x^7+56*x^6*y+105994833*x^6-644*x^5*y-232253336*x^5+3920*x^4*y+369120808*x^4-13538*x^3*y-411449472*x^3+26264*x^2*y+303143184*x^2-26136*x*y+y^2-131725440*x+10080*y+25401600 k: 9 l: 2 m: 8 F_k_l_m_m: -y^18+x^16-72*x^15+2388*x^14-48384*x^13+669606*x^12-6704208*x^11+50170300*x^10-285855552*x^9-2*x^8*y+1251320145*x^8+72*x^7*y-4215106728*x^7-1092*x^6*y+10868843496*x^6+9072*x^5*y-21181595904*x^5-44898*x^4*y+30510066448*x^4+134568*x^3*y-31314782592*x^3-236248*x^2*y+21534172416*x^2+219168*x*y+y^2-8836853760*x-80640*y+1625702400 k: 9 l: 2 m: 9 F_k_l_m_m: x^18-y^18-90*x^17+3765*x^16-97200*x^15+1733946*x^14-22676220*x^13+225084130*x^12-1731961800*x^11+10460514381*x^10-2*x^9*y-49893169050*x^9+90*x^8*y+188097696345*x^8-1740*x^7*y-558244423800*x^7+18900*x^6*y+1292155115896*x^6-126546*x^5*y-2296205246880*x^5+538650*x^4*y+3056515641360*x^4-1447360*x^3*y-2932949347200*x^3+2345400*x^2*y+1904957035776*x^2-2053152*x*y+y^2-745047797760*x+725760*y+131681894400 k: 10 l: 2 m: 2 F_k_l_m_m: x^20-y^20-30*x^19+425*x^18-3780*x^17+23670*x^16-110916*x^15+403530*x^14-1167120*x^13+2725365*x^12-5188590*x^11-2*x^10*y+8097453*x^10+30*x^9*y-10377180*x^9-200*x^8*y+10901460*x^8+780*x^7*y-9336960*x^7-1970*x^6*y+6456480*x^6+3366*x^5*y-3549312*x^5-3940*x^4*y+1514880*x^4+3120*x^3*y-483840*x^3-1600*x^2*y+108800*x^2+480*x*y+y^2-15360*x-64*y+1024 k: 10 l: 2 m: 3 F_k_l_m_m: -y^20+x^18-36*x^17+606*x^16-6336*x^15+46095*x^14-247716*x^13+1018816*x^12-3278016*x^11+8361951*x^10-2*x^9*y-17033580*x^9+36*x^8*y+27767046*x^8-282*x^7*y-36128736*x^7+1260*x^6*y+37235521*x^6-3534*x^5*y-29981196*x^5+6444*x^4*y+18442620*x^4-7630*x^3*y-8362656*x^3+5652*x^2*y+2632176*x^2-2376*x*y+y^2-513216*x+432*y+46656 k: 10 l: 2 m: 4 F_k_l_m_m: -y^20+x^16-40*x^15+740*x^14-8400*x^13+65446*x^12-370880*x^11+1580380*x^10-5162000*x^9-2*x^8*y+13052881*x^8+40*x^7*y-25620120*x^7-340*x^6*y+38878520*x^6+1600*x^5*y-45104800*x^5-4546*x^4*y+39194896*x^4+7960*x^3*y-24648960*x^3-8360*x^2*y+10575360*x^2+4800*x*y+y^2-2764800*x-1152*y+331776 k: 10 l: 2 m: 5 F_k_l_m_m: x^20-y^20-60*x^19+1690*x^18-29700*x^17+365071*x^16-3334800*x^15+23477380*x^14-130374600*x^13+579693631*x^12-2082967740*x^11-2*x^10*y+6077950570*x^10+60*x^9*y-14418383700*x^9-790*x^8*y+27741179521*x^8+6000*x^7*y-43026101880*x^7-29046*x^6*y+53234263960*x^6+93420*x^5*y-51699564000*x^5-201610*x^4*y+38463221776*x^4+287400*x^3*y-21114635520*x^3-258152*x^2*y+8041766400*x^2+131520*x*y+y^2-1893888000*x-28800*y+207360000 k: 10 l: 2 m: 6 F_k_l_m_m: -y^20+x^12-42*x^11+791*x^10-8820*x^9+64743*x^8-328986*x^7-2*x^6*y+1184153*x^6+42*x^5*y-3034920*x^5-350*x^4*y+5482456*x^4+1470*x^3*y-6787872*x^3-3248*x^2*y+5450256*x^2+3528*x*y+y^2-2540160*x-1440*y+518400 k: 10 l: 2 m: 7 F_k_l_m_m: -y^20+x^14-56*x^13+1428*x^12-21952*x^11+226982*x^10-1667568*x^9+8962364*x^8-2*x^7*y-35733376*x^7+56*x^6*y+105994833*x^6-644*x^5*y-232253336*x^5+3920*x^4*y+369120808*x^4-13538*x^3*y-411449472*x^3+26264*x^2*y+303143184*x^2-26136*x*y+y^2-131725440*x+10080*y+25401600 k: 10 l: 2 m: 8 F_k_l_m_m: -y^20+x^16-72*x^15+2388*x^14-48384*x^13+669606*x^12-6704208*x^11+50170300*x^10-285855552*x^9-2*x^8*y+1251320145*x^8+72*x^7*y-4215106728*x^7-1092*x^6*y+10868843496*x^6+9072*x^5*y-21181595904*x^5-44898*x^4*y+30510066448*x^4+134568*x^3*y-31314782592*x^3-236248*x^2*y+21534172416*x^2+219168*x*y+y^2-8836853760*x-80640*y+1625702400 k: 10 l: 2 m: 9 F_k_l_m_m: -y^20+x^18-90*x^17+3765*x^16-97200*x^15+1733946*x^14-22676220*x^13+225084130*x^12-1731961800*x^11+10460514381*x^10-2*x^9*y-49893169050*x^9+90*x^8*y+188097696345*x^8-1740*x^7*y-558244423800*x^7+18900*x^6*y+1292155115896*x^6-126546*x^5*y-2296205246880*x^5+538650*x^4*y+3056515641360*x^4-1447360*x^3*y-2932949347200*x^3+2345400*x^2*y+1904957035776*x^2-2053152*x*y+y^2-745047797760*x+725760*y+131681894400 k: 10 l: 2 m: 10 F_k_l_m_m: x^20-y^20-110*x^19+5665*x^18-181500*x^17+4054446*x^16-67075140*x^15+852003130*x^14-8501266400*x^13+67608163381*x^12-432299636670*x^11-2*x^10*y+2232012515445*x^10+110*x^9*y-9309515255700*x^9-2640*x^8*y+31266813226396*x^8+36300*x^7*y-83963749944800*x^7-315546*x^6*y+178196132168560*x^6+1804110*x^5*y-293683786862400*x^5-6833860*x^4*y+366215508115776*x^4+16819000*x^3*y-332139123233280*x^3-25507152*x^2*y+205528341427200*x^2+21257280*x*y+y^2-77138417664000*x-7257600*y+13168189440000 ---------------- Challenge 11 many higher isolated singularities, non-rational coordinates ---------------- FT_k_l_m_m: k: 2 l: 2 m: 2 FT_k_l_m_m: 4*x^4-y^4-4*x^2*y-4*x^2+y^2+2*y+1 k: 3 l: 2 m: 2 FT_k_l_m_m: -y^6+4*x^4-4*x^2*y-4*x^2+y^2+2*y+1 k: 3 l: 2 m: 3 FT_k_l_m_m: 16*x^6-y^6-24*x^4-8*x^3*y+9*x^2+6*x*y+y^2 k: 4 l: 2 m: 2 FT_k_l_m_m: 16*x^8-y^8-32*x^6-8*x^4*y+24*x^4+8*x^2*y-8*x^2+y^2-2*y+1 k: 4 l: 2 m: 3 FT_k_l_m_m: -y^8+16*x^6-24*x^4-8*x^3*y+9*x^2+6*x*y+y^2 k: 4 l: 2 m: 4 FT_k_l_m_m: 64*x^8-y^8-128*x^6-16*x^4*y+80*x^4+16*x^2*y-16*x^2+y^2-2*y+1 k: 5 l: 2 m: 2 FT_k_l_m_m: -y^10+16*x^8-32*x^6-8*x^4*y+24*x^4+8*x^2*y-8*x^2+y^2-2*y+1 k: 5 l: 2 m: 3 FT_k_l_m_m: -y^10+16*x^6-24*x^4-8*x^3*y+9*x^2+6*x*y+y^2 k: 5 l: 2 m: 4 FT_k_l_m_m: -y^10+64*x^8-128*x^6-16*x^4*y+80*x^4+16*x^2*y-16*x^2+y^2-2*y+1 k: 5 l: 2 m: 5 FT_k_l_m_m: 256*x^10-y^10-640*x^8+560*x^6-32*x^5*y-200*x^4+40*x^3*y+25*x^2-10*x*y+y^2 k: 6 l: 2 m: 2 FT_k_l_m_m: 64*x^12-y^12-192*x^10+240*x^8-16*x^6*y-160*x^6+24*x^4*y+60*x^4-12*x^2*y-12*x^2+y^2+2*y+1 k: 6 l: 2 m: 3 FT_k_l_m_m: 256*x^12-y^12-768*x^10+864*x^8-32*x^6*y-432*x^6+48*x^4*y+81*x^4-18*x^2*y+y^2 k: 6 l: 2 m: 4 FT_k_l_m_m: -y^12+64*x^8-128*x^6-16*x^4*y+80*x^4+16*x^2*y-16*x^2+y^2-2*y+1 k: 6 l: 2 m: 5 FT_k_l_m_m: -y^12+256*x^10-640*x^8+560*x^6-32*x^5*y-200*x^4+40*x^3*y+25*x^2-10*x*y+y^2 k: 6 l: 2 m: 6 FT_k_l_m_m: 1024*x^12-y^12-3072*x^10+3456*x^8-64*x^6*y-1792*x^6+96*x^4*y+420*x^4-36*x^2*y-36*x^2+y^2+2*y+1 k: 7 l: 2 m: 2 FT_k_l_m_m: -y^14+64*x^12-192*x^10+240*x^8-16*x^6*y-160*x^6+24*x^4*y+60*x^4-12*x^2*y-12*x^2+y^2+2*y+1 k: 7 l: 2 m: 3 FT_k_l_m_m: -y^14+256*x^12-768*x^10+864*x^8-32*x^6*y-432*x^6+48*x^4*y+81*x^4-18*x^2*y+y^2 k: 7 l: 2 m: 4 FT_k_l_m_m: -y^14+64*x^8-128*x^6-16*x^4*y+80*x^4+16*x^2*y-16*x^2+y^2-2*y+1 k: 7 l: 2 m: 5 FT_k_l_m_m: -y^14+256*x^10-640*x^8+560*x^6-32*x^5*y-200*x^4+40*x^3*y+25*x^2-10*x*y+y^2 k: 7 l: 2 m: 6 FT_k_l_m_m: -y^14+1024*x^12-3072*x^10+3456*x^8-64*x^6*y-1792*x^6+96*x^4*y+420*x^4-36*x^2*y-36*x^2+y^2+2*y+1 k: 7 l: 2 m: 7 FT_k_l_m_m: 4096*x^14-y^14-14336*x^12+19712*x^10-13440*x^8-128*x^7*y+4704*x^6+224*x^5*y-784*x^4-112*x^3*y+49*x^2+14*x*y+y^2 k: 8 l: 2 m: 2 FT_k_l_m_m: 256*x^16-y^16-1024*x^14+1792*x^12-1792*x^10-32*x^8*y+1120*x^8+64*x^6*y-448*x^6-48*x^4*y+112*x^4+16*x^2*y-16*x^2+y^2-2*y+1 k: 8 l: 2 m: 3 FT_k_l_m_m: -y^16+256*x^12-768*x^10+864*x^8-32*x^6*y-432*x^6+48*x^4*y+81*x^4-18*x^2*y+y^2 k: 8 l: 2 m: 4 FT_k_l_m_m: 4096*x^16-y^16-16384*x^14+26624*x^12-22528*x^10-128*x^8*y+10624*x^8+256*x^6*y-2816*x^6-160*x^4*y+416*x^4+32*x^2*y-32*x^2+y^2-2*y+1 k: 8 l: 2 m: 5 FT_k_l_m_m: -y^16+256*x^10-640*x^8+560*x^6-32*x^5*y-200*x^4+40*x^3*y+25*x^2-10*x*y+y^2 k: 8 l: 2 m: 6 FT_k_l_m_m: -y^16+1024*x^12-3072*x^10+3456*x^8-64*x^6*y-1792*x^6+96*x^4*y+420*x^4-36*x^2*y-36*x^2+y^2+2*y+1 k: 8 l: 2 m: 7 FT_k_l_m_m: -y^16+4096*x^14-14336*x^12+19712*x^10-13440*x^8-128*x^7*y+4704*x^6+224*x^5*y-784*x^4-112*x^3*y+49*x^2+14*x*y+y^2 k: 8 l: 2 m: 8 FT_k_l_m_m: 16384*x^16-y^16-65536*x^14+106496*x^12-90112*x^10-256*x^8*y+42240*x^8+512*x^6*y-10752*x^6-320*x^4*y+1344*x^4+64*x^2*y-64*x^2+y^2-2*y+1 k: 9 l: 2 m: 2 FT_k_l_m_m: -y^18+256*x^16-1024*x^14+1792*x^12-1792*x^10-32*x^8*y+1120*x^8+64*x^6*y-448*x^6-48*x^4*y+112*x^4+16*x^2*y-16*x^2+y^2-2*y+1 k: 9 l: 2 m: 3 FT_k_l_m_m: 4096*x^18-y^18-18432*x^16+34560*x^14-34560*x^12+19440*x^10-128*x^9*y-5832*x^8+288*x^7*y+729*x^6-216*x^5*y+54*x^3*y+y^2 k: 9 l: 2 m: 4 FT_k_l_m_m: -y^18+4096*x^16-16384*x^14+26624*x^12-22528*x^10-128*x^8*y+10624*x^8+256*x^6*y-2816*x^6-160*x^4*y+416*x^4+32*x^2*y-32*x^2+y^2-2*y+1 k: 9 l: 2 m: 5 FT_k_l_m_m: -y^18+256*x^10-640*x^8+560*x^6-32*x^5*y-200*x^4+40*x^3*y+25*x^2-10*x*y+y^2 k: 9 l: 2 m: 6 FT_k_l_m_m: -y^18+1024*x^12-3072*x^10+3456*x^8-64*x^6*y-1792*x^6+96*x^4*y+420*x^4-36*x^2*y-36*x^2+y^2+2*y+1 k: 9 l: 2 m: 7 FT_k_l_m_m: -y^18+4096*x^14-14336*x^12+19712*x^10-13440*x^8-128*x^7*y+4704*x^6+224*x^5*y-784*x^4-112*x^3*y+49*x^2+14*x*y+y^2 k: 9 l: 2 m: 8 FT_k_l_m_m: -y^18+16384*x^16-65536*x^14+106496*x^12-90112*x^10-256*x^8*y+42240*x^8+512*x^6*y-10752*x^6-320*x^4*y+1344*x^4+64*x^2*y-64*x^2+y^2-2*y+1 k: 9 l: 2 m: 9 FT_k_l_m_m: 65536*x^18-y^18-294912*x^16+552960*x^14-559104*x^12+329472*x^10-512*x^9*y-114048*x^8+1152*x^7*y+22176*x^6-864*x^5*y-2160*x^4+240*x^3*y+81*x^2-18*x*y+y^2 k: 10 l: 2 m: 2 FT_k_l_m_m: 1024*x^20-y^20-5120*x^18+11520*x^16-15360*x^14+13440*x^12-64*x^10*y-8064*x^10+160*x^8*y+3360*x^8-160*x^6*y-960*x^6+80*x^4*y+180*x^4-20*x^2*y-20*x^2+y^2+2*y+1 k: 10 l: 2 m: 3 FT_k_l_m_m: -y^20+4096*x^18-18432*x^16+34560*x^14-34560*x^12+19440*x^10-128*x^9*y-5832*x^8+288*x^7*y+729*x^6-216*x^5*y+54*x^3*y+y^2 k: 10 l: 2 m: 4 FT_k_l_m_m: -y^20+4096*x^16-16384*x^14+26624*x^12-22528*x^10-128*x^8*y+10624*x^8+256*x^6*y-2816*x^6-160*x^4*y+416*x^4+32*x^2*y-32*x^2+y^2-2*y+1 k: 10 l: 2 m: 5 FT_k_l_m_m: 65536*x^20-y^20-327680*x^18+696320*x^16-819200*x^14+582400*x^12-512*x^10*y-256000*x^10+1280*x^8*y+68000*x^8-1120*x^6*y-10000*x^6+400*x^4*y+625*x^4-50*x^2*y+y^2 k: 10 l: 2 m: 6 FT_k_l_m_m: -y^20+1024*x^12-3072*x^10+3456*x^8-64*x^6*y-1792*x^6+96*x^4*y+420*x^4-36*x^2*y-36*x^2+y^2+2*y+1 k: 10 l: 2 m: 7 FT_k_l_m_m: -y^20+4096*x^14-14336*x^12+19712*x^10-13440*x^8-128*x^7*y+4704*x^6+224*x^5*y-784*x^4-112*x^3*y+49*x^2+14*x*y+y^2 k: 10 l: 2 m: 8 FT_k_l_m_m: -y^20+16384*x^16-65536*x^14+106496*x^12-90112*x^10-256*x^8*y+42240*x^8+512*x^6*y-10752*x^6-320*x^4*y+1344*x^4+64*x^2*y-64*x^2+y^2-2*y+1 k: 10 l: 2 m: 9 FT_k_l_m_m: -y^20+65536*x^18-294912*x^16+552960*x^14-559104*x^12+329472*x^10-512*x^9*y-114048*x^8+1152*x^7*y+22176*x^6-864*x^5*y-2160*x^4+240*x^3*y+81*x^2-18*x*y+y^2 k: 10 l: 2 m: 10 FT_k_l_m_m: 262144*x^20-y^20-1310720*x^18+2785280*x^16-3276800*x^14+2329600*x^12-1024*x^10*y-1025024*x^10+2560*x^8*y+274560*x^8-2240*x^6*y-42240*x^6+800*x^4*y+3300*x^4-100*x^2*y-100*x^2+y^2+2*y+1 k: 11 l: 2 m: 2 FT_k_l_m_m: -y^22+1024*x^20-5120*x^18+11520*x^16-15360*x^14+13440*x^12-64*x^10*y-8064*x^10+160*x^8*y+3360*x^8-160*x^6*y-960*x^6+80*x^4*y+180*x^4-20*x^2*y-20*x^2+y^2+2*y+1 k: 11 l: 2 m: 3 FT_k_l_m_m: -y^22+4096*x^18-18432*x^16+34560*x^14-34560*x^12+19440*x^10-128*x^9*y-5832*x^8+288*x^7*y+729*x^6-216*x^5*y+54*x^3*y+y^2 k: 11 l: 2 m: 4 FT_k_l_m_m: -y^22+4096*x^16-16384*x^14+26624*x^12-22528*x^10-128*x^8*y+10624*x^8+256*x^6*y-2816*x^6-160*x^4*y+416*x^4+32*x^2*y-32*x^2+y^2-2*y+1 k: 11 l: 2 m: 5 FT_k_l_m_m: -y^22+65536*x^20-327680*x^18+696320*x^16-819200*x^14+582400*x^12-512*x^10*y-256000*x^10+1280*x^8*y+68000*x^8-1120*x^6*y-10000*x^6+400*x^4*y+625*x^4-50*x^2*y+y^2 k: 11 l: 2 m: 6 FT_k_l_m_m: -y^22+1024*x^12-3072*x^10+3456*x^8-64*x^6*y-1792*x^6+96*x^4*y+420*x^4-36*x^2*y-36*x^2+y^2+2*y+1 k: 11 l: 2 m: 7 FT_k_l_m_m: -y^22+4096*x^14-14336*x^12+19712*x^10-13440*x^8-128*x^7*y+4704*x^6+224*x^5*y-784*x^4-112*x^3*y+49*x^2+14*x*y+y^2 k: 11 l: 2 m: 8 FT_k_l_m_m: -y^22+16384*x^16-65536*x^14+106496*x^12-90112*x^10-256*x^8*y+42240*x^8+512*x^6*y-10752*x^6-320*x^4*y+1344*x^4+64*x^2*y-64*x^2+y^2-2*y+1 k: 11 l: 2 m: 9 FT_k_l_m_m: -y^22+65536*x^18-294912*x^16+552960*x^14-559104*x^12+329472*x^10-512*x^9*y-114048*x^8+1152*x^7*y+22176*x^6-864*x^5*y-2160*x^4+240*x^3*y+81*x^2-18*x*y+y^2 k: 11 l: 2 m: 10 FT_k_l_m_m: -y^22+262144*x^20-1310720*x^18+2785280*x^16-3276800*x^14+2329600*x^12-1024*x^10*y-1025024*x^10+2560*x^8*y+274560*x^8-2240*x^6*y-42240*x^6+800*x^4*y+3300*x^4-100*x^2*y-100*x^2+y^2+2*y+1 k: 11 l: 2 m: 11 FT_k_l_m_m: 1048576*x^22-y^22-5767168*x^20+13697024*x^18-18382848*x^16+15319040*x^14-8200192*x^12-2048*x^11*y+2818816*x^10+5632*x^9*y-604032*x^8-5632*x^7*y+75504*x^6+2464*x^5*y-4840*x^4-440*x^3*y+121*x^2+22*x*y+y^2 k: 12 l: 2 m: 2 FT_k_l_m_m: 4096*x^24-y^24-24576*x^22+67584*x^20-112640*x^18+126720*x^16-101376*x^14-128*x^12*y+59136*x^12+384*x^10*y-25344*x^10-480*x^8*y+7920*x^8+320*x^6*y-1760*x^6-120*x^4*y+264*x^4+24*x^2*y-24*x^2+y^2-2*y+1 k: 12 l: 2 m: 3 FT_k_l_m_m: 65536*x^24-y^24-393216*x^22+1032192*x^20-1548288*x^18+1451520*x^16-870912*x^14-512*x^12*y+326592*x^12+1536*x^10*y-69984*x^10-1728*x^8*y+6561*x^8+864*x^6*y-162*x^4*y+y^2 k: 12 l: 2 m: 4 FT_k_l_m_m: 262144*x^24-y^24-1572864*x^22+4128768*x^20-6225920*x^18+5959680*x^16-3784704*x^14-1024*x^12*y+1624064*x^12+3072*x^10*y-473088*x^10-3456*x^8*y+93120*x^8+1792*x^6*y-12160*x^6-432*x^4*y+1008*x^4+48*x^2*y-48*x^2+y^2-2*y+1 k: 12 l: 2 m: 5 FT_k_l_m_m: -y^24+65536*x^20-327680*x^18+696320*x^16-819200*x^14+582400*x^12-512*x^10*y-256000*x^10+1280*x^8*y+68000*x^8-1120*x^6*y-10000*x^6+400*x^4*y+625*x^4-50*x^2*y+y^2 k: 12 l: 2 m: 6 FT_k_l_m_m: 1048576*x^24-y^24-6291456*x^22+16515072*x^20-24903680*x^18+23814144*x^16-15040512*x^14-2048*x^12*y+6337536*x^12+6144*x^10*y-1760256*x^10-6912*x^8*y+312336*x^8+3584*x^6*y-33824*x^6-840*x^4*y+2136*x^4+72*x^2*y-72*x^2+y^2-2*y+1 k: 12 l: 2 m: 7 FT_k_l_m_m: -y^24+4096*x^14-14336*x^12+19712*x^10-13440*x^8-128*x^7*y+4704*x^6+224*x^5*y-784*x^4-112*x^3*y+49*x^2+14*x*y+y^2 k: 12 l: 2 m: 8 FT_k_l_m_m: -y^24+16384*x^16-65536*x^14+106496*x^12-90112*x^10-256*x^8*y+42240*x^8+512*x^6*y-10752*x^6-320*x^4*y+1344*x^4+64*x^2*y-64*x^2+y^2-2*y+1 k: 12 l: 2 m: 9 FT_k_l_m_m: -y^24+65536*x^18-294912*x^16+552960*x^14-559104*x^12+329472*x^10-512*x^9*y-114048*x^8+1152*x^7*y+22176*x^6-864*x^5*y-2160*x^4+240*x^3*y+81*x^2-18*x*y+y^2 k: 12 l: 2 m: 10 FT_k_l_m_m: -y^24+262144*x^20-1310720*x^18+2785280*x^16-3276800*x^14+2329600*x^12-1024*x^10*y-1025024*x^10+2560*x^8*y+274560*x^8-2240*x^6*y-42240*x^6+800*x^4*y+3300*x^4-100*x^2*y-100*x^2+y^2+2*y+1 k: 12 l: 2 m: 11 FT_k_l_m_m: -y^24+1048576*x^22-5767168*x^20+13697024*x^18-18382848*x^16+15319040*x^14-8200192*x^12-2048*x^11*y+2818816*x^10+5632*x^9*y-604032*x^8-5632*x^7*y+75504*x^6+2464*x^5*y-4840*x^4-440*x^3*y+121*x^2+22*x*y+y^2 k: 12 l: 2 m: 12 FT_k_l_m_m: 4194304*x^24-y^24-25165824*x^22+66060288*x^20-99614720*x^18+95256576*x^16-60162048*x^14-4096*x^12*y+25346048*x^12+12288*x^10*y-7028736*x^10-13824*x^8*y+1235520*x^8+7168*x^6*y-128128*x^6-1680*x^4*y+6864*x^4+144*x^2*y-144*x^2+y^2-2*y+1 ---------------- Challenge 12 many higher isolated singularities, non-rational coordinates ---------------- k: 2 m: 2 FTT_k_m_m: 16*x^8-16*y^8-32*x^6-16*x^4*y^2+32*y^6+32*x^4+16*x^2*y^2-20*y^4-16*x^2+3 k: 2 m: 3 FTT_k_m_m: 256*x^12-256*y^12-768*x^10+768*y^10-128*x^6*y^3+864*x^8-864*y^8+96*x^6*y+192*x^4*y^3-432*x^6+448*y^6-144*x^4*y-72*x^2*y^3+81*x^4-105*y^4+54*x^2*y+9*y^2 k: 2 m: 4 FTT_k_m_m: 4096*x^16-4096*y^16-16384*x^14+16384*y^14+26624*x^12-1024*x^8*y^4-26624*y^12-22528*x^10+1024*x^8*y^2+2048*x^6*y^4+22528*y^10+10496*x^8-2048*x^6*y^2-1280*x^4*y^4-10560*y^8-2560*x^6+1280*x^4*y^2+256*x^2*y^4+2688*y^6+256*x^4-256*x^2*y^2-352*y^4+32*y^2-1 k: 2 m: 5 FTT_k_m_m: 65536*x^20-65536*y^20-327680*x^18+327680*y^18+696320*x^16-696320*y^16-8192*x^10*y^5-819200*x^14+819200*y^14+10240*x^10*y^3+20480*x^8*y^5+582400*x^12-582400*y^12-2560*x^10*y-25600*x^8*y^3-17920*x^6*y^5-256000*x^10+256256*y^10+6400*x^8*y+22400*x^6*y^3+6400*x^4*y^5+68000*x^8-68640*y^8-5600*x^6*y-8000*x^4*y^3-800*x^2*y^5-10000*x^6+10560*y^6+2000*x^4*y+1000*x^2*y^3+625*x^4-825*y^4-250*x^2*y+25*y^2 k: 3 m: 2 FTT_k_m_m: 64*x^12-64*y^12-192*x^10+192*y^10+240*x^8-32*x^6*y^2-240*y^8-144*x^6+48*x^4*y^2+160*y^6+36*x^4-24*x^2*y^2-56*y^4+12*y^2-1 k: 3 m: 3 FTT_k_m_m: 4096*x^18-4096*y^18-18432*x^16+18432*y^16+34560*x^14-34560*y^14-34560*x^12-512*x^9*y^3+34560*y^12+19440*x^10+384*x^9*y+1152*x^7*y^3-19440*y^10-5832*x^8-864*x^7*y-864*x^5*y^3+5832*y^8+729*x^6+648*x^5*y+216*x^3*y^3-713*y^6-162*x^3*y-24*y^4+9*y^2 k: 3 m: 4 FTT_k_m_m: 262144*x^24-262144*y^24-1572864*x^22+1572864*y^22+4128768*x^20-4128768*y^20-6225920*x^18+6225920*y^18+5959680*x^16-8192*x^12*y^4-5959680*y^16-3784704*x^14+8192*x^12*y^2+24576*x^10*y^4+3784704*y^14+1623040*x^12-24576*x^10*y^2-27648*x^8*y^4-1624064*y^12-470016*x^10+27648*x^8*y^2+14336*x^6*y^4+473088*y^10+89664*x^8-14336*x^6*y^2-3456*x^4*y^4-93056*y^8-10368*x^6+3456*x^4*y^2+384*x^2*y^4+12032*y^6+576*x^4-384*x^2*y^2-944*y^4+48*y^2-1 k: 3 m: 5 FTT_k_m_m: 16777216*x^30-16777216*y^30-125829120*x^28+125829120*y^28+424673280*x^26-424673280*y^26-851968000*x^24+851968000*y^24+1130496000*x^22-1130496000*y^22-1044480000*x^20-131072*x^15*y^5+1044480000*y^20+688640000*x^18+163840*x^15*y^3+491520*x^13*y^5-688640000*y^18-326400000*x^16-40960*x^15*y-614400*x^13*y^3-737280*x^11*y^5+326400000*y^16+110400000*x^14+153600*x^13*y+921600*x^11*y^3+563200*x^9*y^5-110400000*y^14-26000000*x^12-230400*x^11*y-704000*x^9*y^3-230400*x^7*y^5+26000000*y^12+4050000*x^10+176000*x^9*y+288000*x^7*y^3+48000*x^5*y^5-4049744*y^10-375000*x^8-72000*x^7*y-60000*x^5*y^3-4000*x^3*y^5+374360*y^8+15625*x^6+15000*x^5*y+5000*x^3*y^3-15065*y^6-1250*x^3*y-200*y^4+25*y^2 k: 4 m: 2 FTT_k_m_m: 256*x^16-256*y^16-1024*x^14+1024*y^14+1792*x^12-1792*y^12-1792*x^10-64*x^8*y^2+1792*y^10+1152*x^8+128*x^6*y^2-1120*y^8-512*x^6-96*x^4*y^2+448*y^6+160*x^4+32*x^2*y^2-108*y^4-32*x^2+8*y^2+3 k: 4 m: 3 FTT_k_m_m: 65536*x^24-65536*y^24-393216*x^22+393216*y^22+1032192*x^20-1032192*y^20-1548288*x^18+1548288*y^18+1451520*x^16-1451520*y^16-2048*x^12*y^3-870912*x^14+870912*y^14+1536*x^12*y+6144*x^10*y^3+326592*x^12-326592*y^12-4608*x^10*y-6912*x^8*y^3-69984*x^10+69984*y^10+5184*x^8*y+3456*x^6*y^3+6561*x^8-6561*y^8-2592*x^6*y-648*x^4*y^3+16*y^6+486*x^4*y-24*y^4+9*y^2 k: 4 m: 4 FTT_k_m_m: 16777216*x^32-16777216*y^32-134217728*x^30+134217728*y^30+486539264*x^28-486539264*y^28-1056964608*x^26+1056964608*y^26+1534066688*x^24-1534066688*y^24-1570766848*x^22+1570766848*y^22+1168900096*x^20-65536*x^16*y^4-1168900096*y^20-642514944*x^18+65536*x^16*y^2+262144*x^14*y^4+642514944*y^18+262946816*x^16-262144*x^14*y^2-425984*x^12*y^4-262955008*y^16-80281600*x^14+425984*x^12*y^2+360448*x^10*y^4+80314368*y^14+18210816*x^12-360448*x^10*y^2-169984*x^8*y^4-18264064*y^12-3022848*x^10+169984*x^8*y^2+45056*x^6*y^4+3067904*y^10+353280*x^8-45056*x^6*y^2-6656*x^4*y^4-374464*y^8-26624*x^6+6656*x^4*y^2+512*x^2*y^4+32128*y^6+1024*x^4-512*x^2*y^2-1792*y^4+64*y^2-1 k: 4 m: 5 FTT_k_m_m: 4294967296*x^40-4294967296*y^40-42949672960*x^38+42949672960*y^38+198642237440*x^36-198642237440*y^36-563714457600*x^34+563714457600*y^34+1098068787200*x^32-1098068787200*y^32-1556086784000*x^30+1556086784000*y^30+1658847232000*x^28-1658847232000*y^28-1356595200000*x^26+1356595200000*y^26-2097152*x^20*y^5+859955200000*x^24-859955200000*y^24+2621440*x^20*y^3+10485760*x^18*y^5-423936000000*x^22+423936000000*y^22-655360*x^20*y-13107200*x^18*y^3-22282240*x^16*y^5+161996800000*x^20-161996800000*y^20+3276800*x^18*y+27852800*x^16*y^3+26214400*x^14*y^5-47488000000*x^18+47488000000*y^18-6963200*x^16*y-32768000*x^14*y^3-18636800*x^12*y^5+10472000000*x^16-10472000000*y^16+8192000*x^14*y+23296000*x^12*y^3+8192000*x^10*y^5-1680000000*x^14+1680000000*y^14-5824000*x^12*y-10240000*x^10*y^3-2176000*x^8*y^5+185000000*x^12-185000000*y^12+2560000*x^10*y+2720000*x^8*y^3+320000*x^6*y^5-12500000*x^10+12500256*y^10-680000*x^8*y-400000*x^6*y^3-20000*x^4*y^5+390625*x^8-391265*y^8+100000*x^6*y+25000*x^4*y^3+560*y^6-6250*x^4*y-200*y^4+25*y^2 k: 5 m: 2 FTT_k_m_m: 1024*x^20-1024*y^20-5120*x^18+5120*y^18+11520*x^16-11520*y^16-15360*x^14+15360*y^14+13440*x^12-128*x^10*y^2-13440*y^12-8000*x^10+320*x^8*y^2+8064*y^10+3200*x^8-320*x^6*y^2-3360*y^8-800*x^6+160*x^4*y^2+960*y^6+100*x^4-40*x^2*y^2-176*y^4+20*y^2-1 k: 5 m: 3 FTT_k_m_m: 1048576*x^30-1048576*y^30-7864320*x^28+7864320*y^28+26542080*x^26-26542080*y^26-53084160*x^24+53084160*y^24+69672960*x^22-69672960*y^22-62705664*x^20+62705664*y^20+39191040*x^18-8192*x^15*y^3-39191040*y^18-16796160*x^16+6144*x^15*y+30720*x^13*y^3+16796160*y^16+4723920*x^14-23040*x^13*y-46080*x^11*y^3-4723920*y^14-787320*x^12+34560*x^11*y+34560*x^9*y^3+787320*y^12+59049*x^10-25920*x^9*y-12960*x^7*y^3-59049*y^10+9720*x^7*y+1944*x^5*y^3-1458*x^5*y+16*y^6-24*y^4+9*y^2 k: 5 m: 4 FTT_k_m_m: 1073741824*x^40-1073741824*y^40-10737418240*x^38+10737418240*y^38+49660559360*x^36-49660559360*y^36-140928614400*x^34+140928614400*y^34+274559139840*x^32-274559139840*y^32-389365628928*x^30+389365628928*y^30+415991070720*x^28-415991070720*y^28-342003548160*x^26+342003548160*y^26+219249377280*x^24-524288*x^20*y^4-219249377280*y^24-110472724480*x^22+524288*x^20*y^2+2621440*x^18*y^4+110472724480*y^22+43934613504*x^20-2621440*x^18*y^2-5570560*x^16*y^4-43934679040*y^20-13808762880*x^18+5570560*x^16*y^2+6553600*x^14*y^4+13809090560*y^18+3425075200*x^16-6553600*x^14*y^2-4669440*x^12*y^4-3425771520*y^16-667156480*x^14+4669440*x^12*y^2+2080768*x^10*y^4+667975680*y^14+100976640*x^12-2080768*x^10*y^2-583680*x^8*y^4-101560320*y^12-11622400*x^10+583680*x^8*y^2+102400*x^6*y^4+11882496*y^10+974400*x^8-102400*x^6*y^2-10880*x^4*y^4-1047296*y^8-54400*x^6+10880*x^4*y^2+640*x^2*y^4+67072*y^6+1600*x^4-640*x^2*y^2-2896*y^4+80*y^2-1 k: 5 m: 5 FTT_k_m_m: 1099511627776*x^50-1099511627776*y^50-13743895347200*x^48+13743895347200*y^48+80745385164800*x^46-80745385164800*y^46-296352743424000*x^44+296352743424000*y^44+761819824128000*x^42-761819824128000*y^42-1457604526080000*x^40+1457604526080000*y^40+2153187901440000*x^38-2153187901440000*y^38-2514065817600000*x^36+2514065817600000*y^36+2355992985600000*x^34-2355992985600000*y^34-1789263872000000*x^32+1789263872000000*y^32+1107155353600000*x^30-33554432*x^25*y^5-1107155353600000*y^30-559144960000000*x^28+41943040*x^25*y^3+209715200*x^23*y^5+559144960000000*y^28+230077440000000*x^26-10485760*x^25*y-262144000*x^23*y^3-576716800*x^21*y^5-230077440000000*y^26-76723200000000*x^24+65536000*x^23*y+720896000*x^21*y^3+917504000*x^19*y^5+76723200000000*y^24+20534400000000*x^22-180224000*x^21*y-1146880000*x^19*y^3-933888000*x^17*y^5-20534400000000*y^22-4344000000000*x^20+286720000*x^19*y+1167360000*x^17*y^3+634880000*x^15*y^5+4344000000000*y^20+709500000000*x^18-291840000*x^17*y-793600000*x^15*y^3-291840000*x^13*y^5-709500000000*y^18-86250000000*x^16+198400000*x^15*y+364800000*x^13*y^3+89600000*x^11*y^5+86250000000*y^16+7343750000*x^14-91200000*x^13*y-112000000*x^11*y^3-17600000*x^9*y^5-7343750000*y^14-390625000*x^12+28000000*x^11*y+22000000*x^9*y^3+2000000*x^7*y^5+390625000*y^12+9765625*x^10-5500000*x^9*y-2500000*x^7*y^3-100000*x^5*y^5-9765369*y^10+625000*x^7*y+125000*x^5*y^3-640*y^8-31250*x^5*y+560*y^6-200*y^4+25*y^2 ---------------- Challenge 12 many higher isolated singularities, non-rational coordinates ---------------- k: 2 m: 2 FTT_k_m_p: 16*x^8+16*y^8-32*x^6-16*x^4*y^2-32*y^6+32*x^4+16*x^2*y^2+28*y^4-16*x^2-16*y^2+5 k: 2 m: 3 FTT_k_m_p: 256*x^12+256*y^12-768*x^10-768*y^10-128*x^6*y^3+864*x^8+864*y^8+96*x^6*y+192*x^4*y^3-432*x^6-416*y^6-144*x^4*y-72*x^2*y^3+81*x^4+57*y^4+54*x^2*y+9*y^2 k: 2 m: 4 FTT_k_m_p: 4096*x^16+4096*y^16-16384*x^14-16384*y^14+26624*x^12-1024*x^8*y^4+26624*y^12-22528*x^10+1024*x^8*y^2+2048*x^6*y^4-22528*y^10+10496*x^8-2048*x^6*y^2-1280*x^4*y^4+10688*y^8-2560*x^6+1280*x^4*y^2+256*x^2*y^4-2944*y^6+256*x^4-256*x^2*y^2+480*y^4-32*y^2+1 k: 2 m: 5 FTT_k_m_p: 65536*x^20+65536*y^20-327680*x^18-327680*y^18+696320*x^16+696320*y^16-8192*x^10*y^5-819200*x^14-819200*y^14+10240*x^10*y^3+20480*x^8*y^5+582400*x^12+582400*y^12-2560*x^10*y-25600*x^8*y^3-17920*x^6*y^5-256000*x^10-255744*y^10+6400*x^8*y+22400*x^6*y^3+6400*x^4*y^5+68000*x^8+67360*y^8-5600*x^6*y-8000*x^4*y^3-800*x^2*y^5-10000*x^6-9440*y^6+2000*x^4*y+1000*x^2*y^3+625*x^4+425*y^4-250*x^2*y+25*y^2 k: 3 m: 2 FTT_k_m_p: 64*x^12+64*y^12-192*x^10-192*y^10+240*x^8-32*x^6*y^2+240*y^8-144*x^6+48*x^4*y^2-160*y^6+36*x^4-24*x^2*y^2+64*y^4-12*y^2+1 k: 3 m: 3 FTT_k_m_p: 4096*x^18+4096*y^18-18432*x^16-18432*y^16+34560*x^14+34560*y^14-34560*x^12-512*x^9*y^3-34560*y^12+19440*x^10+384*x^9*y+1152*x^7*y^3+19440*y^10-5832*x^8-864*x^7*y-864*x^5*y^3-5832*y^8+729*x^6+648*x^5*y+216*x^3*y^3+745*y^6-162*x^3*y-24*y^4+9*y^2 k: 3 m: 4 FTT_k_m_p: 262144*x^24+262144*y^24-1572864*x^22-1572864*y^22+4128768*x^20+4128768*y^20-6225920*x^18-6225920*y^18+5959680*x^16-8192*x^12*y^4+5959680*y^16-3784704*x^14+8192*x^12*y^2+24576*x^10*y^4-3784704*y^14+1623040*x^12-24576*x^10*y^2-27648*x^8*y^4+1624064*y^12-470016*x^10+27648*x^8*y^2+14336*x^6*y^4-473088*y^10+89664*x^8-14336*x^6*y^2-3456*x^4*y^4+93184*y^8-10368*x^6+3456*x^4*y^2+384*x^2*y^4-12288*y^6+576*x^4-384*x^2*y^2+1072*y^4-48*y^2+1 k: 3 m: 5 FTT_k_m_p: 16777216*x^30+16777216*y^30-125829120*x^28-125829120*y^28+424673280*x^26+424673280*y^26-851968000*x^24-851968000*y^24+1130496000*x^22+1130496000*y^22-1044480000*x^20-131072*x^15*y^5-1044480000*y^20+688640000*x^18+163840*x^15*y^3+491520*x^13*y^5+688640000*y^18-326400000*x^16-40960*x^15*y-614400*x^13*y^3-737280*x^11*y^5-326400000*y^16+110400000*x^14+153600*x^13*y+921600*x^11*y^3+563200*x^9*y^5+110400000*y^14-26000000*x^12-230400*x^11*y-704000*x^9*y^3-230400*x^7*y^5-26000000*y^12+4050000*x^10+176000*x^9*y+288000*x^7*y^3+48000*x^5*y^5+4050256*y^10-375000*x^8-72000*x^7*y-60000*x^5*y^3-4000*x^3*y^5-375640*y^8+15625*x^6+15000*x^5*y+5000*x^3*y^3+16185*y^6-1250*x^3*y-200*y^4+25*y^2 k: 4 m: 2 FTT_k_m_p: 256*x^16+256*y^16-1024*x^14-1024*y^14+1792*x^12+1792*y^12-1792*x^10-64*x^8*y^2-1792*y^10+1152*x^8+128*x^6*y^2+1120*y^8-512*x^6-96*x^4*y^2-448*y^6+160*x^4+32*x^2*y^2+116*y^4-32*x^2-24*y^2+5 k: 4 m: 3 FTT_k_m_p: 65536*x^24+65536*y^24-393216*x^22-393216*y^22+1032192*x^20+1032192*y^20-1548288*x^18-1548288*y^18+1451520*x^16+1451520*y^16-2048*x^12*y^3-870912*x^14-870912*y^14+1536*x^12*y+6144*x^10*y^3+326592*x^12+326592*y^12-4608*x^10*y-6912*x^8*y^3-69984*x^10-69984*y^10+5184*x^8*y+3456*x^6*y^3+6561*x^8+6561*y^8-2592*x^6*y-648*x^4*y^3+16*y^6+486*x^4*y-24*y^4+9*y^2 k: 4 m: 4 FTT_k_m_p: 16777216*x^32+16777216*y^32-134217728*x^30-134217728*y^30+486539264*x^28+486539264*y^28-1056964608*x^26-1056964608*y^26+1534066688*x^24+1534066688*y^24-1570766848*x^22-1570766848*y^22+1168900096*x^20-65536*x^16*y^4+1168900096*y^20-642514944*x^18+65536*x^16*y^2+262144*x^14*y^4-642514944*y^18+262946816*x^16-262144*x^14*y^2-425984*x^12*y^4+262955008*y^16-80281600*x^14+425984*x^12*y^2+360448*x^10*y^4-80314368*y^14+18210816*x^12-360448*x^10*y^2-169984*x^8*y^4+18264064*y^12-3022848*x^10+169984*x^8*y^2+45056*x^6*y^4-3067904*y^10+353280*x^8-45056*x^6*y^2-6656*x^4*y^4+374592*y^8-26624*x^6+6656*x^4*y^2+512*x^2*y^4-32384*y^6+1024*x^4-512*x^2*y^2+1920*y^4-64*y^2+1 k: 4 m: 5 FTT_k_m_p: 4294967296*x^40+4294967296*y^40-42949672960*x^38-42949672960*y^38+198642237440*x^36+198642237440*y^36-563714457600*x^34-563714457600*y^34+1098068787200*x^32+1098068787200*y^32-1556086784000*x^30-1556086784000*y^30+1658847232000*x^28+1658847232000*y^28-1356595200000*x^26-1356595200000*y^26-2097152*x^20*y^5+859955200000*x^24+859955200000*y^24+2621440*x^20*y^3+10485760*x^18*y^5-423936000000*x^22-423936000000*y^22-655360*x^20*y-13107200*x^18*y^3-22282240*x^16*y^5+161996800000*x^20+161996800000*y^20+3276800*x^18*y+27852800*x^16*y^3+26214400*x^14*y^5-47488000000*x^18-47488000000*y^18-6963200*x^16*y-32768000*x^14*y^3-18636800*x^12*y^5+10472000000*x^16+10472000000*y^16+8192000*x^14*y+23296000*x^12*y^3+8192000*x^10*y^5-1680000000*x^14-1680000000*y^14-5824000*x^12*y-10240000*x^10*y^3-2176000*x^8*y^5+185000000*x^12+185000000*y^12+2560000*x^10*y+2720000*x^8*y^3+320000*x^6*y^5-12500000*x^10-12499744*y^10-680000*x^8*y-400000*x^6*y^3-20000*x^4*y^5+390625*x^8+389985*y^8+100000*x^6*y+25000*x^4*y^3+560*y^6-6250*x^4*y-200*y^4+25*y^2 k: 5 m: 2 FTT_k_m_p: 1024*x^20+1024*y^20-5120*x^18-5120*y^18+11520*x^16+11520*y^16-15360*x^14-15360*y^14+13440*x^12-128*x^10*y^2+13440*y^12-8000*x^10+320*x^8*y^2-8064*y^10+3200*x^8-320*x^6*y^2+3360*y^8-800*x^6+160*x^4*y^2-960*y^6+100*x^4-40*x^2*y^2+184*y^4-20*y^2+1 k: 5 m: 3 FTT_k_m_p: 1048576*x^30+1048576*y^30-7864320*x^28-7864320*y^28+26542080*x^26+26542080*y^26-53084160*x^24-53084160*y^24+69672960*x^22+69672960*y^22-62705664*x^20-62705664*y^20+39191040*x^18-8192*x^15*y^3+39191040*y^18-16796160*x^16+6144*x^15*y+30720*x^13*y^3-16796160*y^16+4723920*x^14-23040*x^13*y-46080*x^11*y^3+4723920*y^14-787320*x^12+34560*x^11*y+34560*x^9*y^3-787320*y^12+59049*x^10-25920*x^9*y-12960*x^7*y^3+59049*y^10+9720*x^7*y+1944*x^5*y^3-1458*x^5*y+16*y^6-24*y^4+9*y^2 k: 5 m: 4 FTT_k_m_p: 1073741824*x^40+1073741824*y^40-10737418240*x^38-10737418240*y^38+49660559360*x^36+49660559360*y^36-140928614400*x^34-140928614400*y^34+274559139840*x^32+274559139840*y^32-389365628928*x^30-389365628928*y^30+415991070720*x^28+415991070720*y^28-342003548160*x^26-342003548160*y^26+219249377280*x^24-524288*x^20*y^4+219249377280*y^24-110472724480*x^22+524288*x^20*y^2+2621440*x^18*y^4-110472724480*y^22+43934613504*x^20-2621440*x^18*y^2-5570560*x^16*y^4+43934679040*y^20-13808762880*x^18+5570560*x^16*y^2+6553600*x^14*y^4-13809090560*y^18+3425075200*x^16-6553600*x^14*y^2-4669440*x^12*y^4+3425771520*y^16-667156480*x^14+4669440*x^12*y^2+2080768*x^10*y^4-667975680*y^14+100976640*x^12-2080768*x^10*y^2-583680*x^8*y^4+101560320*y^12-11622400*x^10+583680*x^8*y^2+102400*x^6*y^4-11882496*y^10+974400*x^8-102400*x^6*y^2-10880*x^4*y^4+1047424*y^8-54400*x^6+10880*x^4*y^2+640*x^2*y^4-67328*y^6+1600*x^4-640*x^2*y^2+3024*y^4-80*y^2+1 k: 5 m: 5 FTT_k_m_p: 1099511627776*x^50+1099511627776*y^50-13743895347200*x^48-13743895347200*y^48+80745385164800*x^46+80745385164800*y^46-296352743424000*x^44-296352743424000*y^44+761819824128000*x^42+761819824128000*y^42-1457604526080000*x^40-1457604526080000*y^40+2153187901440000*x^38+2153187901440000*y^38-2514065817600000*x^36-2514065817600000*y^36+2355992985600000*x^34+2355992985600000*y^34-1789263872000000*x^32-1789263872000000*y^32+1107155353600000*x^30-33554432*x^25*y^5+1107155353600000*y^30-559144960000000*x^28+41943040*x^25*y^3+209715200*x^23*y^5-559144960000000*y^28+230077440000000*x^26-10485760*x^25*y-262144000*x^23*y^3-576716800*x^21*y^5+230077440000000*y^26-76723200000000*x^24+65536000*x^23*y+720896000*x^21*y^3+917504000*x^19*y^5-76723200000000*y^24+20534400000000*x^22-180224000*x^21*y-1146880000*x^19*y^3-933888000*x^17*y^5+20534400000000*y^22-4344000000000*x^20+286720000*x^19*y+1167360000*x^17*y^3+634880000*x^15*y^5-4344000000000*y^20+709500000000*x^18-291840000*x^17*y-793600000*x^15*y^3-291840000*x^13*y^5+709500000000*y^18-86250000000*x^16+198400000*x^15*y+364800000*x^13*y^3+89600000*x^11*y^5-86250000000*y^16+7343750000*x^14-91200000*x^13*y-112000000*x^11*y^3-17600000*x^9*y^5+7343750000*y^14-390625000*x^12+28000000*x^11*y+22000000*x^9*y^3+2000000*x^7*y^5-390625000*y^12+9765625*x^10-5500000*x^9*y-2500000*x^7*y^3-100000*x^5*y^5+9765881*y^10+625000*x^7*y+125000*x^5*y^3-640*y^8-31250*x^5*y+560*y^6-200*y^4+25*y^2 ---------------- Challenge 13 ordinary d-tuple points ---------------- dfold_d: d: 2 dfold_d: 2*x*y d: 3 dfold_d: 3*x^2*y-y^3 d: 4 dfold_d: 4*x^3*y-4*x*y^3 d: 5 dfold_d: 5*x^4*y-10*x^2*y^3+y^5 d: 6 dfold_d: 6*x^5*y-20*x^3*y^3+6*x*y^5 d: 7 dfold_d: 7*x^6*y-35*x^4*y^3+21*x^2*y^5-y^7 d: 8 dfold_d: 8*x^7*y-56*x^5*y^3+56*x^3*y^5-8*x*y^7 d: 9 dfold_d: 9*x^8*y-84*x^6*y^3+126*x^4*y^5-36*x^2*y^7+y^9 d: 10 dfold_d: 10*x^9*y-120*x^7*y^3+252*x^5*y^5-120*x^3*y^7+10*x*y^9 d: 11 dfold_d: 11*x^10*y-165*x^8*y^3+462*x^6*y^5-330*x^4*y^7+55*x^2*y^9-y^11 d: 12 dfold_d: 12*x^11*y-220*x^9*y^3+792*x^7*y^5-792*x^5*y^7+220*x^3*y^9-12*x*y^11 dfold_fl_d: d: 2 dfold_fl_d: -x^4-2*x^2*y^2-y^4+2*x*y d: 3 dfold_fl_d: -x^4-2*x^2*y^2-y^4+3*x^2*y-y^3 d: 4 dfold_fl_d: -x^6-3*x^4*y^2-3*x^2*y^4-y^6+4*x^3*y-4*x*y^3 d: 5 dfold_fl_d: -x^6-3*x^4*y^2-3*x^2*y^4-y^6+5*x^4*y-10*x^2*y^3+y^5 d: 6 dfold_fl_d: -x^8-4*x^6*y^2-6*x^4*y^4-4*x^2*y^6-y^8+6*x^5*y-20*x^3*y^3+6*x*y^5 d: 7 dfold_fl_d: -x^8-4*x^6*y^2-6*x^4*y^4-4*x^2*y^6-y^8+7*x^6*y-35*x^4*y^3+21*x^2*y^5-y^7 d: 8 dfold_fl_d: -x^10-5*x^8*y^2-10*x^6*y^4-10*x^4*y^6-5*x^2*y^8-y^10+8*x^7*y-56*x^5*y^3+56*x^3*y^5-8*x*y^7 d: 9 dfold_fl_d: -x^10-5*x^8*y^2-10*x^6*y^4-10*x^4*y^6-5*x^2*y^8-y^10+9*x^8*y-84*x^6*y^3+126*x^4*y^5-36*x^2*y^7+y^9 d: 10 dfold_fl_d: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+10*x^9*y-120*x^7*y^3+252*x^5*y^5-120*x^3*y^7+10*x*y^9 d: 11 dfold_fl_d: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+11*x^10*y-165*x^8*y^3+462*x^6*y^5-330*x^4*y^7+55*x^2*y^9-y^11 d: 12 dfold_fl_d: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+12*x^11*y-220*x^9*y^3+792*x^7*y^5-792*x^5*y^7+220*x^3*y^9-12*x*y^11 ---------------- Challenge 14 singularities with high tangencies and many halfbranches ---------------- dfold_k_l: k: 2 l: 1 dfold_k_l: -x^6-3*x^4*y^2-3*x^2*y^4-y^6+4*x^2*y^2 k: 2 l: 2 dfold_k_l: -x^8-4*x^6*y^2-6*x^4*y^4-4*x^2*y^6-y^8+4*x^2*y^2 k: 2 l: 3 dfold_k_l: -x^10-5*x^8*y^2-10*x^6*y^4-10*x^4*y^6-5*x^2*y^8-y^10+4*x^2*y^2 k: 2 l: 4 dfold_k_l: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+4*x^2*y^2 k: 2 l: 5 dfold_k_l: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+4*x^2*y^2 k: 2 l: 6 dfold_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+4*x^2*y^2 k: 3 l: 1 dfold_k_l: -x^8-4*x^6*y^2-6*x^4*y^4-4*x^2*y^6-y^8+9*x^4*y^2-6*x^2*y^4+y^6 k: 3 l: 2 dfold_k_l: -x^10-5*x^8*y^2-10*x^6*y^4-10*x^4*y^6-5*x^2*y^8-y^10+9*x^4*y^2-6*x^2*y^4+y^6 k: 3 l: 3 dfold_k_l: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+9*x^4*y^2-6*x^2*y^4+y^6 k: 3 l: 4 dfold_k_l: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+9*x^4*y^2-6*x^2*y^4+y^6 k: 3 l: 5 dfold_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+9*x^4*y^2-6*x^2*y^4+y^6 k: 3 l: 6 dfold_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+9*x^4*y^2-6*x^2*y^4+y^6 k: 4 l: 1 dfold_k_l: -x^10-5*x^8*y^2-10*x^6*y^4-10*x^4*y^6-5*x^2*y^8-y^10+16*x^6*y^2-32*x^4*y^4+16*x^2*y^6 k: 4 l: 2 dfold_k_l: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+16*x^6*y^2-32*x^4*y^4+16*x^2*y^6 k: 4 l: 3 dfold_k_l: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+16*x^6*y^2-32*x^4*y^4+16*x^2*y^6 k: 4 l: 4 dfold_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+16*x^6*y^2-32*x^4*y^4+16*x^2*y^6 k: 4 l: 5 dfold_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+16*x^6*y^2-32*x^4*y^4+16*x^2*y^6 k: 4 l: 6 dfold_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+16*x^6*y^2-32*x^4*y^4+16*x^2*y^6 k: 5 l: 1 dfold_k_l: -x^12-6*x^10*y^2-15*x^8*y^4-20*x^6*y^6-15*x^4*y^8-6*x^2*y^10-y^12+25*x^8*y^2-100*x^6*y^4+110*x^4*y^6-20*x^2*y^8+y^10 k: 5 l: 2 dfold_k_l: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+25*x^8*y^2-100*x^6*y^4+110*x^4*y^6-20*x^2*y^8+y^10 k: 5 l: 3 dfold_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+25*x^8*y^2-100*x^6*y^4+110*x^4*y^6-20*x^2*y^8+y^10 k: 5 l: 4 dfold_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+25*x^8*y^2-100*x^6*y^4+110*x^4*y^6-20*x^2*y^8+y^10 k: 5 l: 5 dfold_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+25*x^8*y^2-100*x^6*y^4+110*x^4*y^6-20*x^2*y^8+y^10 k: 5 l: 6 dfold_k_l: -x^22-11*x^20*y^2-55*x^18*y^4-165*x^16*y^6-330*x^14*y^8-462*x^12*y^10-462*x^10*y^12-330*x^8*y^14-165*x^6*y^16-55*x^4*y^18-11*x^2*y^20-y^22+25*x^8*y^2-100*x^6*y^4+110*x^4*y^6-20*x^2*y^8+y^10 k: 6 l: 1 dfold_k_l: -x^14-7*x^12*y^2-21*x^10*y^4-35*x^8*y^6-35*x^6*y^8-21*x^4*y^10-7*x^2*y^12-y^14+36*x^10*y^2-240*x^8*y^4+472*x^6*y^6-240*x^4*y^8+36*x^2*y^10 k: 6 l: 2 dfold_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+36*x^10*y^2-240*x^8*y^4+472*x^6*y^6-240*x^4*y^8+36*x^2*y^10 k: 6 l: 3 dfold_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+36*x^10*y^2-240*x^8*y^4+472*x^6*y^6-240*x^4*y^8+36*x^2*y^10 k: 6 l: 4 dfold_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+36*x^10*y^2-240*x^8*y^4+472*x^6*y^6-240*x^4*y^8+36*x^2*y^10 k: 6 l: 5 dfold_k_l: -x^22-11*x^20*y^2-55*x^18*y^4-165*x^16*y^6-330*x^14*y^8-462*x^12*y^10-462*x^10*y^12-330*x^8*y^14-165*x^6*y^16-55*x^4*y^18-11*x^2*y^20-y^22+36*x^10*y^2-240*x^8*y^4+472*x^6*y^6-240*x^4*y^8+36*x^2*y^10 k: 6 l: 6 dfold_k_l: -x^24-12*x^22*y^2-66*x^20*y^4-220*x^18*y^6-495*x^16*y^8-792*x^14*y^10-924*x^12*y^12-792*x^10*y^14-495*x^8*y^16-220*x^6*y^18-66*x^4*y^20-12*x^2*y^22-y^24+36*x^10*y^2-240*x^8*y^4+472*x^6*y^6-240*x^4*y^8+36*x^2*y^10 k: 7 l: 1 dfold_k_l: -x^16-8*x^14*y^2-28*x^12*y^4-56*x^10*y^6-70*x^8*y^8-56*x^6*y^10-28*x^4*y^12-8*x^2*y^14-y^16+49*x^12*y^2-490*x^10*y^4+1519*x^8*y^6-1484*x^6*y^8+511*x^4*y^10-42*x^2*y^12+y^14 k: 7 l: 2 dfold_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+49*x^12*y^2-490*x^10*y^4+1519*x^8*y^6-1484*x^6*y^8+511*x^4*y^10-42*x^2*y^12+y^14 k: 7 l: 3 dfold_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+49*x^12*y^2-490*x^10*y^4+1519*x^8*y^6-1484*x^6*y^8+511*x^4*y^10-42*x^2*y^12+y^14 k: 7 l: 4 dfold_k_l: -x^22-11*x^20*y^2-55*x^18*y^4-165*x^16*y^6-330*x^14*y^8-462*x^12*y^10-462*x^10*y^12-330*x^8*y^14-165*x^6*y^16-55*x^4*y^18-11*x^2*y^20-y^22+49*x^12*y^2-490*x^10*y^4+1519*x^8*y^6-1484*x^6*y^8+511*x^4*y^10-42*x^2*y^12+y^14 k: 7 l: 5 dfold_k_l: -x^24-12*x^22*y^2-66*x^20*y^4-220*x^18*y^6-495*x^16*y^8-792*x^14*y^10-924*x^12*y^12-792*x^10*y^14-495*x^8*y^16-220*x^6*y^18-66*x^4*y^20-12*x^2*y^22-y^24+49*x^12*y^2-490*x^10*y^4+1519*x^8*y^6-1484*x^6*y^8+511*x^4*y^10-42*x^2*y^12+y^14 k: 7 l: 6 dfold_k_l: -x^26-13*x^24*y^2-78*x^22*y^4-286*x^20*y^6-715*x^18*y^8-1287*x^16*y^10-1716*x^14*y^12-1716*x^12*y^14-1287*x^10*y^16-715*x^8*y^18-286*x^6*y^20-78*x^4*y^22-13*x^2*y^24-y^26+49*x^12*y^2-490*x^10*y^4+1519*x^8*y^6-1484*x^6*y^8+511*x^4*y^10-42*x^2*y^12+y^14 k: 8 l: 1 dfold_k_l: -x^18-9*x^16*y^2-36*x^14*y^4-84*x^12*y^6-126*x^10*y^8-126*x^8*y^10-84*x^6*y^12-36*x^4*y^14-9*x^2*y^16-y^18+64*x^14*y^2-896*x^12*y^4+4032*x^10*y^6-6400*x^8*y^8+4032*x^6*y^10-896*x^4*y^12+64*x^2*y^14 k: 8 l: 2 dfold_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+64*x^14*y^2-896*x^12*y^4+4032*x^10*y^6-6400*x^8*y^8+4032*x^6*y^10-896*x^4*y^12+64*x^2*y^14 k: 8 l: 3 dfold_k_l: -x^22-11*x^20*y^2-55*x^18*y^4-165*x^16*y^6-330*x^14*y^8-462*x^12*y^10-462*x^10*y^12-330*x^8*y^14-165*x^6*y^16-55*x^4*y^18-11*x^2*y^20-y^22+64*x^14*y^2-896*x^12*y^4+4032*x^10*y^6-6400*x^8*y^8+4032*x^6*y^10-896*x^4*y^12+64*x^2*y^14 k: 8 l: 4 dfold_k_l: -x^24-12*x^22*y^2-66*x^20*y^4-220*x^18*y^6-495*x^16*y^8-792*x^14*y^10-924*x^12*y^12-792*x^10*y^14-495*x^8*y^16-220*x^6*y^18-66*x^4*y^20-12*x^2*y^22-y^24+64*x^14*y^2-896*x^12*y^4+4032*x^10*y^6-6400*x^8*y^8+4032*x^6*y^10-896*x^4*y^12+64*x^2*y^14 k: 8 l: 5 dfold_k_l: -x^26-13*x^24*y^2-78*x^22*y^4-286*x^20*y^6-715*x^18*y^8-1287*x^16*y^10-1716*x^14*y^12-1716*x^12*y^14-1287*x^10*y^16-715*x^8*y^18-286*x^6*y^20-78*x^4*y^22-13*x^2*y^24-y^26+64*x^14*y^2-896*x^12*y^4+4032*x^10*y^6-6400*x^8*y^8+4032*x^6*y^10-896*x^4*y^12+64*x^2*y^14 k: 8 l: 6 dfold_k_l: -x^28-14*x^26*y^2-91*x^24*y^4-364*x^22*y^6-1001*x^20*y^8-2002*x^18*y^10-3003*x^16*y^12-3432*x^14*y^14-3003*x^12*y^16-2002*x^10*y^18-1001*x^8*y^20-364*x^6*y^22-91*x^4*y^24-14*x^2*y^26-y^28+64*x^14*y^2-896*x^12*y^4+4032*x^10*y^6-6400*x^8*y^8+4032*x^6*y^10-896*x^4*y^12+64*x^2*y^14 k: 9 l: 1 dfold_k_l: -x^20-10*x^18*y^2-45*x^16*y^4-120*x^14*y^6-210*x^12*y^8-252*x^10*y^10-210*x^8*y^12-120*x^6*y^14-45*x^4*y^16-10*x^2*y^18-y^20+81*x^16*y^2-1512*x^14*y^4+9324*x^12*y^6-21816*x^10*y^8+21942*x^8*y^10-9240*x^6*y^12+1548*x^4*y^14-72*x^2*y^16+y^18 k: 9 l: 2 dfold_k_l: -x^22-11*x^20*y^2-55*x^18*y^4-165*x^16*y^6-330*x^14*y^8-462*x^12*y^10-462*x^10*y^12-330*x^8*y^14-165*x^6*y^16-55*x^4*y^18-11*x^2*y^20-y^22+81*x^16*y^2-1512*x^14*y^4+9324*x^12*y^6-21816*x^10*y^8+21942*x^8*y^10-9240*x^6*y^12+1548*x^4*y^14-72*x^2*y^16+y^18 k: 9 l: 3 dfold_k_l: -x^24-12*x^22*y^2-66*x^20*y^4-220*x^18*y^6-495*x^16*y^8-792*x^14*y^10-924*x^12*y^12-792*x^10*y^14-495*x^8*y^16-220*x^6*y^18-66*x^4*y^20-12*x^2*y^22-y^24+81*x^16*y^2-1512*x^14*y^4+9324*x^12*y^6-21816*x^10*y^8+21942*x^8*y^10-9240*x^6*y^12+1548*x^4*y^14-72*x^2*y^16+y^18 k: 9 l: 4 dfold_k_l: -x^26-13*x^24*y^2-78*x^22*y^4-286*x^20*y^6-715*x^18*y^8-1287*x^16*y^10-1716*x^14*y^12-1716*x^12*y^14-1287*x^10*y^16-715*x^8*y^18-286*x^6*y^20-78*x^4*y^22-13*x^2*y^24-y^26+81*x^16*y^2-1512*x^14*y^4+9324*x^12*y^6-21816*x^10*y^8+21942*x^8*y^10-9240*x^6*y^12+1548*x^4*y^14-72*x^2*y^16+y^18 k: 9 l: 5 dfold_k_l: -x^28-14*x^26*y^2-91*x^24*y^4-364*x^22*y^6-1001*x^20*y^8-2002*x^18*y^10-3003*x^16*y^12-3432*x^14*y^14-3003*x^12*y^16-2002*x^10*y^18-1001*x^8*y^20-364*x^6*y^22-91*x^4*y^24-14*x^2*y^26-y^28+81*x^16*y^2-1512*x^14*y^4+9324*x^12*y^6-21816*x^10*y^8+21942*x^8*y^10-9240*x^6*y^12+1548*x^4*y^14-72*x^2*y^16+y^18 k: 9 l: 6 dfold_k_l: -x^30-15*x^28*y^2-105*x^26*y^4-455*x^24*y^6-1365*x^22*y^8-3003*x^20*y^10-5005*x^18*y^12-6435*x^16*y^14-6435*x^14*y^16-5005*x^12*y^18-3003*x^10*y^20-1365*x^8*y^22-455*x^6*y^24-105*x^4*y^26-15*x^2*y^28-y^30+81*x^16*y^2-1512*x^14*y^4+9324*x^12*y^6-21816*x^10*y^8+21942*x^8*y^10-9240*x^6*y^12+1548*x^4*y^14-72*x^2*y^16+y^18 k: 10 l: 1 dfold_k_l: -x^22-11*x^20*y^2-55*x^18*y^4-165*x^16*y^6-330*x^14*y^8-462*x^12*y^10-462*x^10*y^12-330*x^8*y^14-165*x^6*y^16-55*x^4*y^18-11*x^2*y^20-y^22+100*x^18*y^2-2400*x^16*y^4+19440*x^14*y^6-62880*x^12*y^8+92504*x^10*y^10-62880*x^8*y^12+19440*x^6*y^14-2400*x^4*y^16+100*x^2*y^18 k: 10 l: 2 dfold_k_l: -x^24-12*x^22*y^2-66*x^20*y^4-220*x^18*y^6-495*x^16*y^8-792*x^14*y^10-924*x^12*y^12-792*x^10*y^14-495*x^8*y^16-220*x^6*y^18-66*x^4*y^20-12*x^2*y^22-y^24+100*x^18*y^2-2400*x^16*y^4+19440*x^14*y^6-62880*x^12*y^8+92504*x^10*y^10-62880*x^8*y^12+19440*x^6*y^14-2400*x^4*y^16+100*x^2*y^18 k: 10 l: 3 dfold_k_l: -x^26-13*x^24*y^2-78*x^22*y^4-286*x^20*y^6-715*x^18*y^8-1287*x^16*y^10-1716*x^14*y^12-1716*x^12*y^14-1287*x^10*y^16-715*x^8*y^18-286*x^6*y^20-78*x^4*y^22-13*x^2*y^24-y^26+100*x^18*y^2-2400*x^16*y^4+19440*x^14*y^6-62880*x^12*y^8+92504*x^10*y^10-62880*x^8*y^12+19440*x^6*y^14-2400*x^4*y^16+100*x^2*y^18 k: 10 l: 4 dfold_k_l: -x^28-14*x^26*y^2-91*x^24*y^4-364*x^22*y^6-1001*x^20*y^8-2002*x^18*y^10-3003*x^16*y^12-3432*x^14*y^14-3003*x^12*y^16-2002*x^10*y^18-1001*x^8*y^20-364*x^6*y^22-91*x^4*y^24-14*x^2*y^26-y^28+100*x^18*y^2-2400*x^16*y^4+19440*x^14*y^6-62880*x^12*y^8+92504*x^10*y^10-62880*x^8*y^12+19440*x^6*y^14-2400*x^4*y^16+100*x^2*y^18 k: 10 l: 5 dfold_k_l: -x^30-15*x^28*y^2-105*x^26*y^4-455*x^24*y^6-1365*x^22*y^8-3003*x^20*y^10-5005*x^18*y^12-6435*x^16*y^14-6435*x^14*y^16-5005*x^12*y^18-3003*x^10*y^20-1365*x^8*y^22-455*x^6*y^24-105*x^4*y^26-15*x^2*y^28-y^30+100*x^18*y^2-2400*x^16*y^4+19440*x^14*y^6-62880*x^12*y^8+92504*x^10*y^10-62880*x^8*y^12+19440*x^6*y^14-2400*x^4*y^16+100*x^2*y^18 k: 10 l: 6 dfold_k_l: -x^32-16*x^30*y^2-120*x^28*y^4-560*x^26*y^6-1820*x^24*y^8-4368*x^22*y^10-8008*x^20*y^12-11440*x^18*y^14-12870*x^16*y^16-11440*x^14*y^18-8008*x^12*y^20-4368*x^10*y^22-1820*x^8*y^24-560*x^6*y^26-120*x^4*y^28-16*x^2*y^30-y^32+100*x^18*y^2-2400*x^16*y^4+19440*x^14*y^6-62880*x^12*y^8+92504*x^10*y^10-62880*x^8*y^12+19440*x^6*y^14-2400*x^4*y^16+100*x^2*y^18 ---------------- Challenge 15 normal forms of some unimodal singularities ---------------- J_10_k_pm: k: 1 a: 5/7 J_10_k_p: 5/7*y^7+x^2*y^2+x^3 J_10_k_m: 5/7*y^7-x^2*y^2+x^3 k: 1 a: 9/7 J_10_k_p: 9/7*y^7+x^2*y^2+x^3 J_10_k_m: 9/7*y^7-x^2*y^2+x^3 k: 1 a: 13/7 J_10_k_p: 13/7*y^7+x^2*y^2+x^3 J_10_k_m: 13/7*y^7-x^2*y^2+x^3 k: 2 a: 5/7 J_10_k_p: 5/7*y^8+x^2*y^2+x^3 J_10_k_m: 5/7*y^8-x^2*y^2+x^3 k: 2 a: 9/7 J_10_k_p: 9/7*y^8+x^2*y^2+x^3 J_10_k_m: 9/7*y^8-x^2*y^2+x^3 k: 2 a: 13/7 J_10_k_p: 13/7*y^8+x^2*y^2+x^3 J_10_k_m: 13/7*y^8-x^2*y^2+x^3 k: 3 a: 5/7 J_10_k_p: 5/7*y^9+x^2*y^2+x^3 J_10_k_m: 5/7*y^9-x^2*y^2+x^3 k: 3 a: 9/7 J_10_k_p: 9/7*y^9+x^2*y^2+x^3 J_10_k_m: 9/7*y^9-x^2*y^2+x^3 k: 3 a: 13/7 J_10_k_p: 13/7*y^9+x^2*y^2+x^3 J_10_k_m: 13/7*y^9-x^2*y^2+x^3 k: 4 a: 5/7 J_10_k_p: 5/7*y^10+x^2*y^2+x^3 J_10_k_m: 5/7*y^10-x^2*y^2+x^3 k: 4 a: 9/7 J_10_k_p: 9/7*y^10+x^2*y^2+x^3 J_10_k_m: 9/7*y^10-x^2*y^2+x^3 k: 4 a: 13/7 J_10_k_p: 13/7*y^10+x^2*y^2+x^3 J_10_k_m: 13/7*y^10-x^2*y^2+x^3 k: 5 a: 5/7 J_10_k_p: 5/7*y^11+x^2*y^2+x^3 J_10_k_m: 5/7*y^11-x^2*y^2+x^3 k: 5 a: 9/7 J_10_k_p: 9/7*y^11+x^2*y^2+x^3 J_10_k_m: 9/7*y^11-x^2*y^2+x^3 k: 5 a: 13/7 J_10_k_p: 13/7*y^11+x^2*y^2+x^3 J_10_k_m: 13/7*y^11-x^2*y^2+x^3 k: 6 a: 5/7 J_10_k_p: 5/7*y^12+x^2*y^2+x^3 J_10_k_m: 5/7*y^12-x^2*y^2+x^3 k: 6 a: 9/7 J_10_k_p: 9/7*y^12+x^2*y^2+x^3 J_10_k_m: 9/7*y^12-x^2*y^2+x^3 k: 6 a: 13/7 J_10_k_p: 13/7*y^12+x^2*y^2+x^3 J_10_k_m: 13/7*y^12-x^2*y^2+x^3 k: 7 a: 5/7 J_10_k_p: 5/7*y^13+x^2*y^2+x^3 J_10_k_m: 5/7*y^13-x^2*y^2+x^3 k: 7 a: 9/7 J_10_k_p: 9/7*y^13+x^2*y^2+x^3 J_10_k_m: 9/7*y^13-x^2*y^2+x^3 k: 7 a: 13/7 J_10_k_p: 13/7*y^13+x^2*y^2+x^3 J_10_k_m: 13/7*y^13-x^2*y^2+x^3 k: 8 a: 5/7 J_10_k_p: 5/7*y^14+x^2*y^2+x^3 J_10_k_m: 5/7*y^14-x^2*y^2+x^3 k: 8 a: 9/7 J_10_k_p: 9/7*y^14+x^2*y^2+x^3 J_10_k_m: 9/7*y^14-x^2*y^2+x^3 k: 8 a: 13/7 J_10_k_p: 13/7*y^14+x^2*y^2+x^3 J_10_k_m: 13/7*y^14-x^2*y^2+x^3 k: 9 a: 5/7 J_10_k_p: 5/7*y^15+x^2*y^2+x^3 J_10_k_m: 5/7*y^15-x^2*y^2+x^3 k: 9 a: 9/7 J_10_k_p: 9/7*y^15+x^2*y^2+x^3 J_10_k_m: 9/7*y^15-x^2*y^2+x^3 k: 9 a: 13/7 J_10_k_p: 13/7*y^15+x^2*y^2+x^3 J_10_k_m: 13/7*y^15-x^2*y^2+x^3 k: 10 a: 5/7 J_10_k_p: 5/7*y^16+x^2*y^2+x^3 J_10_k_m: 5/7*y^16-x^2*y^2+x^3 k: 10 a: 9/7 J_10_k_p: 9/7*y^16+x^2*y^2+x^3 J_10_k_m: 9/7*y^16-x^2*y^2+x^3 k: 10 a: 13/7 J_10_k_p: 13/7*y^16+x^2*y^2+x^3 J_10_k_m: 13/7*y^16-x^2*y^2+x^3 k: 11 a: 5/7 J_10_k_p: 5/7*y^17+x^2*y^2+x^3 J_10_k_m: 5/7*y^17-x^2*y^2+x^3 k: 11 a: 9/7 J_10_k_p: 9/7*y^17+x^2*y^2+x^3 J_10_k_m: 9/7*y^17-x^2*y^2+x^3 k: 11 a: 13/7 J_10_k_p: 13/7*y^17+x^2*y^2+x^3 J_10_k_m: 13/7*y^17-x^2*y^2+x^3 k: 12 a: 5/7 J_10_k_p: 5/7*y^18+x^2*y^2+x^3 J_10_k_m: 5/7*y^18-x^2*y^2+x^3 k: 12 a: 9/7 J_10_k_p: 9/7*y^18+x^2*y^2+x^3 J_10_k_m: 9/7*y^18-x^2*y^2+x^3 k: 12 a: 13/7 J_10_k_p: 13/7*y^18+x^2*y^2+x^3 J_10_k_m: 13/7*y^18-x^2*y^2+x^3 X_9_k_pmpm: k: 1 a: 5/7 X_9_k_p_p: 5/7*y^5+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^5+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^5-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^5-x^4+x^2*y^2 k: 1 a: 9/7 X_9_k_p_p: 9/7*y^5+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^5+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^5-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^5-x^4+x^2*y^2 k: 1 a: 13/7 X_9_k_p_p: 13/7*y^5+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^5+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^5-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^5-x^4+x^2*y^2 k: 2 a: 5/7 X_9_k_p_p: 5/7*y^6+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^6+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^6-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^6-x^4+x^2*y^2 k: 2 a: 9/7 X_9_k_p_p: 9/7*y^6+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^6+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^6-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^6-x^4+x^2*y^2 k: 2 a: 13/7 X_9_k_p_p: 13/7*y^6+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^6+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^6-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^6-x^4+x^2*y^2 k: 3 a: 5/7 X_9_k_p_p: 5/7*y^7+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^7+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^7-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^7-x^4+x^2*y^2 k: 3 a: 9/7 X_9_k_p_p: 9/7*y^7+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^7+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^7-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^7-x^4+x^2*y^2 k: 3 a: 13/7 X_9_k_p_p: 13/7*y^7+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^7+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^7-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^7-x^4+x^2*y^2 k: 4 a: 5/7 X_9_k_p_p: 5/7*y^8+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^8+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^8-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^8-x^4+x^2*y^2 k: 4 a: 9/7 X_9_k_p_p: 9/7*y^8+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^8+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^8-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^8-x^4+x^2*y^2 k: 4 a: 13/7 X_9_k_p_p: 13/7*y^8+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^8+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^8-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^8-x^4+x^2*y^2 k: 5 a: 5/7 X_9_k_p_p: 5/7*y^9+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^9+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^9-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^9-x^4+x^2*y^2 k: 5 a: 9/7 X_9_k_p_p: 9/7*y^9+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^9+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^9-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^9-x^4+x^2*y^2 k: 5 a: 13/7 X_9_k_p_p: 13/7*y^9+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^9+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^9-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^9-x^4+x^2*y^2 k: 6 a: 5/7 X_9_k_p_p: 5/7*y^10+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^10+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^10-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^10-x^4+x^2*y^2 k: 6 a: 9/7 X_9_k_p_p: 9/7*y^10+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^10+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^10-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^10-x^4+x^2*y^2 k: 6 a: 13/7 X_9_k_p_p: 13/7*y^10+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^10+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^10-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^10-x^4+x^2*y^2 k: 7 a: 5/7 X_9_k_p_p: 5/7*y^11+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^11+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^11-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^11-x^4+x^2*y^2 k: 7 a: 9/7 X_9_k_p_p: 9/7*y^11+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^11+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^11-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^11-x^4+x^2*y^2 k: 7 a: 13/7 X_9_k_p_p: 13/7*y^11+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^11+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^11-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^11-x^4+x^2*y^2 k: 8 a: 5/7 X_9_k_p_p: 5/7*y^12+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^12+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^12-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^12-x^4+x^2*y^2 k: 8 a: 9/7 X_9_k_p_p: 9/7*y^12+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^12+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^12-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^12-x^4+x^2*y^2 k: 8 a: 13/7 X_9_k_p_p: 13/7*y^12+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^12+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^12-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^12-x^4+x^2*y^2 k: 9 a: 5/7 X_9_k_p_p: 5/7*y^13+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^13+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^13-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^13-x^4+x^2*y^2 k: 9 a: 9/7 X_9_k_p_p: 9/7*y^13+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^13+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^13-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^13-x^4+x^2*y^2 k: 9 a: 13/7 X_9_k_p_p: 13/7*y^13+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^13+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^13-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^13-x^4+x^2*y^2 k: 10 a: 5/7 X_9_k_p_p: 5/7*y^14+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^14+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^14-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^14-x^4+x^2*y^2 k: 10 a: 9/7 X_9_k_p_p: 9/7*y^14+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^14+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^14-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^14-x^4+x^2*y^2 k: 10 a: 13/7 X_9_k_p_p: 13/7*y^14+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^14+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^14-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^14-x^4+x^2*y^2 k: 11 a: 5/7 X_9_k_p_p: 5/7*y^15+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^15+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^15-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^15-x^4+x^2*y^2 k: 11 a: 9/7 X_9_k_p_p: 9/7*y^15+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^15+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^15-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^15-x^4+x^2*y^2 k: 11 a: 13/7 X_9_k_p_p: 13/7*y^15+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^15+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^15-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^15-x^4+x^2*y^2 k: 12 a: 5/7 X_9_k_p_p: 5/7*y^16+x^4+x^2*y^2 X_9_k_p_m: -5/7*y^16+x^4+x^2*y^2 X_9_k_m_p: 5/7*y^16-x^4+x^2*y^2 X_9_k_m_m: -5/7*y^16-x^4+x^2*y^2 k: 12 a: 9/7 X_9_k_p_p: 9/7*y^16+x^4+x^2*y^2 X_9_k_p_m: -9/7*y^16+x^4+x^2*y^2 X_9_k_m_p: 9/7*y^16-x^4+x^2*y^2 X_9_k_m_m: -9/7*y^16-x^4+x^2*y^2 k: 12 a: 13/7 X_9_k_p_p: 13/7*y^16+x^4+x^2*y^2 X_9_k_p_m: -13/7*y^16+x^4+x^2*y^2 X_9_k_m_p: 13/7*y^16-x^4+x^2*y^2 X_9_k_m_m: -13/7*y^16-x^4+x^2*y^2 Y_r_s_pmpm: // ** redefining a ** r: 5 s: 5 a: 5/7 Y_r_s_p_p: x^5+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^5+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^5+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^5+5/7*y^5-x^2*y^2 r: 5 s: 5 a: 9/7 Y_r_s_p_p: x^5+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^5+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^5+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^5+9/7*y^5-x^2*y^2 r: 5 s: 5 a: 13/7 Y_r_s_p_p: x^5+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^5+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^5+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^5+13/7*y^5-x^2*y^2 r: 5 s: 6 a: 5/7 Y_r_s_p_p: 5/7*y^6+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^6-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^6+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^6-x^5-x^2*y^2 r: 5 s: 6 a: 9/7 Y_r_s_p_p: 9/7*y^6+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^6-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^6+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^6-x^5-x^2*y^2 r: 5 s: 6 a: 13/7 Y_r_s_p_p: 13/7*y^6+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^6-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^6+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^6-x^5-x^2*y^2 r: 5 s: 7 a: 5/7 Y_r_s_p_p: 5/7*y^7+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^7-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^7+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^7-x^5-x^2*y^2 r: 5 s: 7 a: 9/7 Y_r_s_p_p: 9/7*y^7+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^7-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^7+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^7-x^5-x^2*y^2 r: 5 s: 7 a: 13/7 Y_r_s_p_p: 13/7*y^7+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^7-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^7+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^7-x^5-x^2*y^2 r: 5 s: 8 a: 5/7 Y_r_s_p_p: 5/7*y^8+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^8-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^8+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^8-x^5-x^2*y^2 r: 5 s: 8 a: 9/7 Y_r_s_p_p: 9/7*y^8+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^8-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^8+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^8-x^5-x^2*y^2 r: 5 s: 8 a: 13/7 Y_r_s_p_p: 13/7*y^8+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^8-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^8+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^8-x^5-x^2*y^2 r: 5 s: 9 a: 5/7 Y_r_s_p_p: 5/7*y^9+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^9-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^9+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^9-x^5-x^2*y^2 r: 5 s: 9 a: 9/7 Y_r_s_p_p: 9/7*y^9+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^9-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^9+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^9-x^5-x^2*y^2 r: 5 s: 9 a: 13/7 Y_r_s_p_p: 13/7*y^9+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^9-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^9+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^9-x^5-x^2*y^2 r: 5 s: 10 a: 5/7 Y_r_s_p_p: 5/7*y^10+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^10-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^10+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^10-x^5-x^2*y^2 r: 5 s: 10 a: 9/7 Y_r_s_p_p: 9/7*y^10+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^10-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^10+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^10-x^5-x^2*y^2 r: 5 s: 10 a: 13/7 Y_r_s_p_p: 13/7*y^10+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^10-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^10+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^10-x^5-x^2*y^2 r: 5 s: 11 a: 5/7 Y_r_s_p_p: 5/7*y^11+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^11-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^11+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^11-x^5-x^2*y^2 r: 5 s: 11 a: 9/7 Y_r_s_p_p: 9/7*y^11+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^11-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^11+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^11-x^5-x^2*y^2 r: 5 s: 11 a: 13/7 Y_r_s_p_p: 13/7*y^11+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^11-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^11+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^11-x^5-x^2*y^2 r: 5 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^5+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^5+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^5-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^5-x^2*y^2 r: 5 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^5+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^5+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^5-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^5-x^2*y^2 r: 5 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^5+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^5+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^5-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^5-x^2*y^2 r: 6 s: 5 a: 5/7 Y_r_s_p_p: x^6+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^6+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^6+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^6+5/7*y^5-x^2*y^2 r: 6 s: 5 a: 9/7 Y_r_s_p_p: x^6+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^6+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^6+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^6+9/7*y^5-x^2*y^2 r: 6 s: 5 a: 13/7 Y_r_s_p_p: x^6+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^6+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^6+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^6+13/7*y^5-x^2*y^2 r: 6 s: 6 a: 5/7 Y_r_s_p_p: x^6+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^6+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^6+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^6+5/7*y^6-x^2*y^2 r: 6 s: 6 a: 9/7 Y_r_s_p_p: x^6+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^6+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^6+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^6+9/7*y^6-x^2*y^2 r: 6 s: 6 a: 13/7 Y_r_s_p_p: x^6+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^6+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^6+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^6+13/7*y^6-x^2*y^2 r: 6 s: 7 a: 5/7 Y_r_s_p_p: 5/7*y^7+x^6+x^2*y^2 Y_r_s_p_m: 5/7*y^7-x^6+x^2*y^2 Y_r_s_m_p: 5/7*y^7+x^6-x^2*y^2 Y_r_s_m_m: 5/7*y^7-x^6-x^2*y^2 r: 6 s: 7 a: 9/7 Y_r_s_p_p: 9/7*y^7+x^6+x^2*y^2 Y_r_s_p_m: 9/7*y^7-x^6+x^2*y^2 Y_r_s_m_p: 9/7*y^7+x^6-x^2*y^2 Y_r_s_m_m: 9/7*y^7-x^6-x^2*y^2 r: 6 s: 7 a: 13/7 Y_r_s_p_p: 13/7*y^7+x^6+x^2*y^2 Y_r_s_p_m: 13/7*y^7-x^6+x^2*y^2 Y_r_s_m_p: 13/7*y^7+x^6-x^2*y^2 Y_r_s_m_m: 13/7*y^7-x^6-x^2*y^2 r: 6 s: 8 a: 5/7 Y_r_s_p_p: 5/7*y^8+x^6+x^2*y^2 Y_r_s_p_m: 5/7*y^8-x^6+x^2*y^2 Y_r_s_m_p: 5/7*y^8+x^6-x^2*y^2 Y_r_s_m_m: 5/7*y^8-x^6-x^2*y^2 r: 6 s: 8 a: 9/7 Y_r_s_p_p: 9/7*y^8+x^6+x^2*y^2 Y_r_s_p_m: 9/7*y^8-x^6+x^2*y^2 Y_r_s_m_p: 9/7*y^8+x^6-x^2*y^2 Y_r_s_m_m: 9/7*y^8-x^6-x^2*y^2 r: 6 s: 8 a: 13/7 Y_r_s_p_p: 13/7*y^8+x^6+x^2*y^2 Y_r_s_p_m: 13/7*y^8-x^6+x^2*y^2 Y_r_s_m_p: 13/7*y^8+x^6-x^2*y^2 Y_r_s_m_m: 13/7*y^8-x^6-x^2*y^2 r: 6 s: 9 a: 5/7 Y_r_s_p_p: 5/7*y^9+x^6+x^2*y^2 Y_r_s_p_m: 5/7*y^9-x^6+x^2*y^2 Y_r_s_m_p: 5/7*y^9+x^6-x^2*y^2 Y_r_s_m_m: 5/7*y^9-x^6-x^2*y^2 r: 6 s: 9 a: 9/7 Y_r_s_p_p: 9/7*y^9+x^6+x^2*y^2 Y_r_s_p_m: 9/7*y^9-x^6+x^2*y^2 Y_r_s_m_p: 9/7*y^9+x^6-x^2*y^2 Y_r_s_m_m: 9/7*y^9-x^6-x^2*y^2 r: 6 s: 9 a: 13/7 Y_r_s_p_p: 13/7*y^9+x^6+x^2*y^2 Y_r_s_p_m: 13/7*y^9-x^6+x^2*y^2 Y_r_s_m_p: 13/7*y^9+x^6-x^2*y^2 Y_r_s_m_m: 13/7*y^9-x^6-x^2*y^2 r: 6 s: 10 a: 5/7 Y_r_s_p_p: 5/7*y^10+x^6+x^2*y^2 Y_r_s_p_m: 5/7*y^10-x^6+x^2*y^2 Y_r_s_m_p: 5/7*y^10+x^6-x^2*y^2 Y_r_s_m_m: 5/7*y^10-x^6-x^2*y^2 r: 6 s: 10 a: 9/7 Y_r_s_p_p: 9/7*y^10+x^6+x^2*y^2 Y_r_s_p_m: 9/7*y^10-x^6+x^2*y^2 Y_r_s_m_p: 9/7*y^10+x^6-x^2*y^2 Y_r_s_m_m: 9/7*y^10-x^6-x^2*y^2 r: 6 s: 10 a: 13/7 Y_r_s_p_p: 13/7*y^10+x^6+x^2*y^2 Y_r_s_p_m: 13/7*y^10-x^6+x^2*y^2 Y_r_s_m_p: 13/7*y^10+x^6-x^2*y^2 Y_r_s_m_m: 13/7*y^10-x^6-x^2*y^2 r: 6 s: 11 a: 5/7 Y_r_s_p_p: 5/7*y^11+x^6+x^2*y^2 Y_r_s_p_m: 5/7*y^11-x^6+x^2*y^2 Y_r_s_m_p: 5/7*y^11+x^6-x^2*y^2 Y_r_s_m_m: 5/7*y^11-x^6-x^2*y^2 r: 6 s: 11 a: 9/7 Y_r_s_p_p: 9/7*y^11+x^6+x^2*y^2 Y_r_s_p_m: 9/7*y^11-x^6+x^2*y^2 Y_r_s_m_p: 9/7*y^11+x^6-x^2*y^2 Y_r_s_m_m: 9/7*y^11-x^6-x^2*y^2 r: 6 s: 11 a: 13/7 Y_r_s_p_p: 13/7*y^11+x^6+x^2*y^2 Y_r_s_p_m: 13/7*y^11-x^6+x^2*y^2 Y_r_s_m_p: 13/7*y^11+x^6-x^2*y^2 Y_r_s_m_m: 13/7*y^11-x^6-x^2*y^2 r: 6 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^6+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^6+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^6-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^6-x^2*y^2 r: 6 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^6+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^6+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^6-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^6-x^2*y^2 r: 6 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^6+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^6+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^6-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^6-x^2*y^2 r: 7 s: 5 a: 5/7 Y_r_s_p_p: x^7+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^7+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^7+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^7+5/7*y^5-x^2*y^2 r: 7 s: 5 a: 9/7 Y_r_s_p_p: x^7+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^7+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^7+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^7+9/7*y^5-x^2*y^2 r: 7 s: 5 a: 13/7 Y_r_s_p_p: x^7+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^7+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^7+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^7+13/7*y^5-x^2*y^2 r: 7 s: 6 a: 5/7 Y_r_s_p_p: x^7+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^7+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^7+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^7+5/7*y^6-x^2*y^2 r: 7 s: 6 a: 9/7 Y_r_s_p_p: x^7+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^7+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^7+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^7+9/7*y^6-x^2*y^2 r: 7 s: 6 a: 13/7 Y_r_s_p_p: x^7+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^7+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^7+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^7+13/7*y^6-x^2*y^2 r: 7 s: 7 a: 5/7 Y_r_s_p_p: x^7+5/7*y^7+x^2*y^2 Y_r_s_p_m: -x^7+5/7*y^7+x^2*y^2 Y_r_s_m_p: x^7+5/7*y^7-x^2*y^2 Y_r_s_m_m: -x^7+5/7*y^7-x^2*y^2 r: 7 s: 7 a: 9/7 Y_r_s_p_p: x^7+9/7*y^7+x^2*y^2 Y_r_s_p_m: -x^7+9/7*y^7+x^2*y^2 Y_r_s_m_p: x^7+9/7*y^7-x^2*y^2 Y_r_s_m_m: -x^7+9/7*y^7-x^2*y^2 r: 7 s: 7 a: 13/7 Y_r_s_p_p: x^7+13/7*y^7+x^2*y^2 Y_r_s_p_m: -x^7+13/7*y^7+x^2*y^2 Y_r_s_m_p: x^7+13/7*y^7-x^2*y^2 Y_r_s_m_m: -x^7+13/7*y^7-x^2*y^2 r: 7 s: 8 a: 5/7 Y_r_s_p_p: 5/7*y^8+x^7+x^2*y^2 Y_r_s_p_m: 5/7*y^8-x^7+x^2*y^2 Y_r_s_m_p: 5/7*y^8+x^7-x^2*y^2 Y_r_s_m_m: 5/7*y^8-x^7-x^2*y^2 r: 7 s: 8 a: 9/7 Y_r_s_p_p: 9/7*y^8+x^7+x^2*y^2 Y_r_s_p_m: 9/7*y^8-x^7+x^2*y^2 Y_r_s_m_p: 9/7*y^8+x^7-x^2*y^2 Y_r_s_m_m: 9/7*y^8-x^7-x^2*y^2 r: 7 s: 8 a: 13/7 Y_r_s_p_p: 13/7*y^8+x^7+x^2*y^2 Y_r_s_p_m: 13/7*y^8-x^7+x^2*y^2 Y_r_s_m_p: 13/7*y^8+x^7-x^2*y^2 Y_r_s_m_m: 13/7*y^8-x^7-x^2*y^2 r: 7 s: 9 a: 5/7 Y_r_s_p_p: 5/7*y^9+x^7+x^2*y^2 Y_r_s_p_m: 5/7*y^9-x^7+x^2*y^2 Y_r_s_m_p: 5/7*y^9+x^7-x^2*y^2 Y_r_s_m_m: 5/7*y^9-x^7-x^2*y^2 r: 7 s: 9 a: 9/7 Y_r_s_p_p: 9/7*y^9+x^7+x^2*y^2 Y_r_s_p_m: 9/7*y^9-x^7+x^2*y^2 Y_r_s_m_p: 9/7*y^9+x^7-x^2*y^2 Y_r_s_m_m: 9/7*y^9-x^7-x^2*y^2 r: 7 s: 9 a: 13/7 Y_r_s_p_p: 13/7*y^9+x^7+x^2*y^2 Y_r_s_p_m: 13/7*y^9-x^7+x^2*y^2 Y_r_s_m_p: 13/7*y^9+x^7-x^2*y^2 Y_r_s_m_m: 13/7*y^9-x^7-x^2*y^2 r: 7 s: 10 a: 5/7 Y_r_s_p_p: 5/7*y^10+x^7+x^2*y^2 Y_r_s_p_m: 5/7*y^10-x^7+x^2*y^2 Y_r_s_m_p: 5/7*y^10+x^7-x^2*y^2 Y_r_s_m_m: 5/7*y^10-x^7-x^2*y^2 r: 7 s: 10 a: 9/7 Y_r_s_p_p: 9/7*y^10+x^7+x^2*y^2 Y_r_s_p_m: 9/7*y^10-x^7+x^2*y^2 Y_r_s_m_p: 9/7*y^10+x^7-x^2*y^2 Y_r_s_m_m: 9/7*y^10-x^7-x^2*y^2 r: 7 s: 10 a: 13/7 Y_r_s_p_p: 13/7*y^10+x^7+x^2*y^2 Y_r_s_p_m: 13/7*y^10-x^7+x^2*y^2 Y_r_s_m_p: 13/7*y^10+x^7-x^2*y^2 Y_r_s_m_m: 13/7*y^10-x^7-x^2*y^2 r: 7 s: 11 a: 5/7 Y_r_s_p_p: 5/7*y^11+x^7+x^2*y^2 Y_r_s_p_m: 5/7*y^11-x^7+x^2*y^2 Y_r_s_m_p: 5/7*y^11+x^7-x^2*y^2 Y_r_s_m_m: 5/7*y^11-x^7-x^2*y^2 r: 7 s: 11 a: 9/7 Y_r_s_p_p: 9/7*y^11+x^7+x^2*y^2 Y_r_s_p_m: 9/7*y^11-x^7+x^2*y^2 Y_r_s_m_p: 9/7*y^11+x^7-x^2*y^2 Y_r_s_m_m: 9/7*y^11-x^7-x^2*y^2 r: 7 s: 11 a: 13/7 Y_r_s_p_p: 13/7*y^11+x^7+x^2*y^2 Y_r_s_p_m: 13/7*y^11-x^7+x^2*y^2 Y_r_s_m_p: 13/7*y^11+x^7-x^2*y^2 Y_r_s_m_m: 13/7*y^11-x^7-x^2*y^2 r: 7 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^7+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^7+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^7-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^7-x^2*y^2 r: 7 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^7+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^7+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^7-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^7-x^2*y^2 r: 7 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^7+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^7+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^7-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^7-x^2*y^2 r: 8 s: 5 a: 5/7 Y_r_s_p_p: x^8+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^8+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^8+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^8+5/7*y^5-x^2*y^2 r: 8 s: 5 a: 9/7 Y_r_s_p_p: x^8+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^8+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^8+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^8+9/7*y^5-x^2*y^2 r: 8 s: 5 a: 13/7 Y_r_s_p_p: x^8+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^8+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^8+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^8+13/7*y^5-x^2*y^2 r: 8 s: 6 a: 5/7 Y_r_s_p_p: x^8+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^8+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^8+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^8+5/7*y^6-x^2*y^2 r: 8 s: 6 a: 9/7 Y_r_s_p_p: x^8+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^8+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^8+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^8+9/7*y^6-x^2*y^2 r: 8 s: 6 a: 13/7 Y_r_s_p_p: x^8+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^8+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^8+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^8+13/7*y^6-x^2*y^2 r: 8 s: 7 a: 5/7 Y_r_s_p_p: x^8+5/7*y^7+x^2*y^2 Y_r_s_p_m: -x^8+5/7*y^7+x^2*y^2 Y_r_s_m_p: x^8+5/7*y^7-x^2*y^2 Y_r_s_m_m: -x^8+5/7*y^7-x^2*y^2 r: 8 s: 7 a: 9/7 Y_r_s_p_p: x^8+9/7*y^7+x^2*y^2 Y_r_s_p_m: -x^8+9/7*y^7+x^2*y^2 Y_r_s_m_p: x^8+9/7*y^7-x^2*y^2 Y_r_s_m_m: -x^8+9/7*y^7-x^2*y^2 r: 8 s: 7 a: 13/7 Y_r_s_p_p: x^8+13/7*y^7+x^2*y^2 Y_r_s_p_m: -x^8+13/7*y^7+x^2*y^2 Y_r_s_m_p: x^8+13/7*y^7-x^2*y^2 Y_r_s_m_m: -x^8+13/7*y^7-x^2*y^2 r: 8 s: 8 a: 5/7 Y_r_s_p_p: x^8+5/7*y^8+x^2*y^2 Y_r_s_p_m: -x^8+5/7*y^8+x^2*y^2 Y_r_s_m_p: x^8+5/7*y^8-x^2*y^2 Y_r_s_m_m: -x^8+5/7*y^8-x^2*y^2 r: 8 s: 8 a: 9/7 Y_r_s_p_p: x^8+9/7*y^8+x^2*y^2 Y_r_s_p_m: -x^8+9/7*y^8+x^2*y^2 Y_r_s_m_p: x^8+9/7*y^8-x^2*y^2 Y_r_s_m_m: -x^8+9/7*y^8-x^2*y^2 r: 8 s: 8 a: 13/7 Y_r_s_p_p: x^8+13/7*y^8+x^2*y^2 Y_r_s_p_m: -x^8+13/7*y^8+x^2*y^2 Y_r_s_m_p: x^8+13/7*y^8-x^2*y^2 Y_r_s_m_m: -x^8+13/7*y^8-x^2*y^2 r: 8 s: 9 a: 5/7 Y_r_s_p_p: 5/7*y^9+x^8+x^2*y^2 Y_r_s_p_m: 5/7*y^9-x^8+x^2*y^2 Y_r_s_m_p: 5/7*y^9+x^8-x^2*y^2 Y_r_s_m_m: 5/7*y^9-x^8-x^2*y^2 r: 8 s: 9 a: 9/7 Y_r_s_p_p: 9/7*y^9+x^8+x^2*y^2 Y_r_s_p_m: 9/7*y^9-x^8+x^2*y^2 Y_r_s_m_p: 9/7*y^9+x^8-x^2*y^2 Y_r_s_m_m: 9/7*y^9-x^8-x^2*y^2 r: 8 s: 9 a: 13/7 Y_r_s_p_p: 13/7*y^9+x^8+x^2*y^2 Y_r_s_p_m: 13/7*y^9-x^8+x^2*y^2 Y_r_s_m_p: 13/7*y^9+x^8-x^2*y^2 Y_r_s_m_m: 13/7*y^9-x^8-x^2*y^2 r: 8 s: 10 a: 5/7 Y_r_s_p_p: 5/7*y^10+x^8+x^2*y^2 Y_r_s_p_m: 5/7*y^10-x^8+x^2*y^2 Y_r_s_m_p: 5/7*y^10+x^8-x^2*y^2 Y_r_s_m_m: 5/7*y^10-x^8-x^2*y^2 r: 8 s: 10 a: 9/7 Y_r_s_p_p: 9/7*y^10+x^8+x^2*y^2 Y_r_s_p_m: 9/7*y^10-x^8+x^2*y^2 Y_r_s_m_p: 9/7*y^10+x^8-x^2*y^2 Y_r_s_m_m: 9/7*y^10-x^8-x^2*y^2 r: 8 s: 10 a: 13/7 Y_r_s_p_p: 13/7*y^10+x^8+x^2*y^2 Y_r_s_p_m: 13/7*y^10-x^8+x^2*y^2 Y_r_s_m_p: 13/7*y^10+x^8-x^2*y^2 Y_r_s_m_m: 13/7*y^10-x^8-x^2*y^2 r: 8 s: 11 a: 5/7 Y_r_s_p_p: 5/7*y^11+x^8+x^2*y^2 Y_r_s_p_m: 5/7*y^11-x^8+x^2*y^2 Y_r_s_m_p: 5/7*y^11+x^8-x^2*y^2 Y_r_s_m_m: 5/7*y^11-x^8-x^2*y^2 r: 8 s: 11 a: 9/7 Y_r_s_p_p: 9/7*y^11+x^8+x^2*y^2 Y_r_s_p_m: 9/7*y^11-x^8+x^2*y^2 Y_r_s_m_p: 9/7*y^11+x^8-x^2*y^2 Y_r_s_m_m: 9/7*y^11-x^8-x^2*y^2 r: 8 s: 11 a: 13/7 Y_r_s_p_p: 13/7*y^11+x^8+x^2*y^2 Y_r_s_p_m: 13/7*y^11-x^8+x^2*y^2 Y_r_s_m_p: 13/7*y^11+x^8-x^2*y^2 Y_r_s_m_m: 13/7*y^11-x^8-x^2*y^2 r: 8 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^8+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^8+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^8-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^8-x^2*y^2 r: 8 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^8+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^8+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^8-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^8-x^2*y^2 r: 8 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^8+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^8+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^8-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^8-x^2*y^2 r: 9 s: 5 a: 5/7 Y_r_s_p_p: x^9+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^9+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^9+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^9+5/7*y^5-x^2*y^2 r: 9 s: 5 a: 9/7 Y_r_s_p_p: x^9+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^9+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^9+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^9+9/7*y^5-x^2*y^2 r: 9 s: 5 a: 13/7 Y_r_s_p_p: x^9+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^9+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^9+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^9+13/7*y^5-x^2*y^2 r: 9 s: 6 a: 5/7 Y_r_s_p_p: x^9+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^9+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^9+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^9+5/7*y^6-x^2*y^2 r: 9 s: 6 a: 9/7 Y_r_s_p_p: x^9+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^9+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^9+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^9+9/7*y^6-x^2*y^2 r: 9 s: 6 a: 13/7 Y_r_s_p_p: x^9+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^9+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^9+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^9+13/7*y^6-x^2*y^2 r: 9 s: 7 a: 5/7 Y_r_s_p_p: x^9+5/7*y^7+x^2*y^2 Y_r_s_p_m: -x^9+5/7*y^7+x^2*y^2 Y_r_s_m_p: x^9+5/7*y^7-x^2*y^2 Y_r_s_m_m: -x^9+5/7*y^7-x^2*y^2 r: 9 s: 7 a: 9/7 Y_r_s_p_p: x^9+9/7*y^7+x^2*y^2 Y_r_s_p_m: -x^9+9/7*y^7+x^2*y^2 Y_r_s_m_p: x^9+9/7*y^7-x^2*y^2 Y_r_s_m_m: -x^9+9/7*y^7-x^2*y^2 r: 9 s: 7 a: 13/7 Y_r_s_p_p: x^9+13/7*y^7+x^2*y^2 Y_r_s_p_m: -x^9+13/7*y^7+x^2*y^2 Y_r_s_m_p: x^9+13/7*y^7-x^2*y^2 Y_r_s_m_m: -x^9+13/7*y^7-x^2*y^2 r: 9 s: 8 a: 5/7 Y_r_s_p_p: x^9+5/7*y^8+x^2*y^2 Y_r_s_p_m: -x^9+5/7*y^8+x^2*y^2 Y_r_s_m_p: x^9+5/7*y^8-x^2*y^2 Y_r_s_m_m: -x^9+5/7*y^8-x^2*y^2 r: 9 s: 8 a: 9/7 Y_r_s_p_p: x^9+9/7*y^8+x^2*y^2 Y_r_s_p_m: -x^9+9/7*y^8+x^2*y^2 Y_r_s_m_p: x^9+9/7*y^8-x^2*y^2 Y_r_s_m_m: -x^9+9/7*y^8-x^2*y^2 r: 9 s: 8 a: 13/7 Y_r_s_p_p: x^9+13/7*y^8+x^2*y^2 Y_r_s_p_m: -x^9+13/7*y^8+x^2*y^2 Y_r_s_m_p: x^9+13/7*y^8-x^2*y^2 Y_r_s_m_m: -x^9+13/7*y^8-x^2*y^2 r: 9 s: 9 a: 5/7 Y_r_s_p_p: x^9+5/7*y^9+x^2*y^2 Y_r_s_p_m: -x^9+5/7*y^9+x^2*y^2 Y_r_s_m_p: x^9+5/7*y^9-x^2*y^2 Y_r_s_m_m: -x^9+5/7*y^9-x^2*y^2 r: 9 s: 9 a: 9/7 Y_r_s_p_p: x^9+9/7*y^9+x^2*y^2 Y_r_s_p_m: -x^9+9/7*y^9+x^2*y^2 Y_r_s_m_p: x^9+9/7*y^9-x^2*y^2 Y_r_s_m_m: -x^9+9/7*y^9-x^2*y^2 r: 9 s: 9 a: 13/7 Y_r_s_p_p: x^9+13/7*y^9+x^2*y^2 Y_r_s_p_m: -x^9+13/7*y^9+x^2*y^2 Y_r_s_m_p: x^9+13/7*y^9-x^2*y^2 Y_r_s_m_m: -x^9+13/7*y^9-x^2*y^2 r: 9 s: 10 a: 5/7 Y_r_s_p_p: 5/7*y^10+x^9+x^2*y^2 Y_r_s_p_m: 5/7*y^10-x^9+x^2*y^2 Y_r_s_m_p: 5/7*y^10+x^9-x^2*y^2 Y_r_s_m_m: 5/7*y^10-x^9-x^2*y^2 r: 9 s: 10 a: 9/7 Y_r_s_p_p: 9/7*y^10+x^9+x^2*y^2 Y_r_s_p_m: 9/7*y^10-x^9+x^2*y^2 Y_r_s_m_p: 9/7*y^10+x^9-x^2*y^2 Y_r_s_m_m: 9/7*y^10-x^9-x^2*y^2 r: 9 s: 10 a: 13/7 Y_r_s_p_p: 13/7*y^10+x^9+x^2*y^2 Y_r_s_p_m: 13/7*y^10-x^9+x^2*y^2 Y_r_s_m_p: 13/7*y^10+x^9-x^2*y^2 Y_r_s_m_m: 13/7*y^10-x^9-x^2*y^2 r: 9 s: 11 a: 5/7 Y_r_s_p_p: 5/7*y^11+x^9+x^2*y^2 Y_r_s_p_m: 5/7*y^11-x^9+x^2*y^2 Y_r_s_m_p: 5/7*y^11+x^9-x^2*y^2 Y_r_s_m_m: 5/7*y^11-x^9-x^2*y^2 r: 9 s: 11 a: 9/7 Y_r_s_p_p: 9/7*y^11+x^9+x^2*y^2 Y_r_s_p_m: 9/7*y^11-x^9+x^2*y^2 Y_r_s_m_p: 9/7*y^11+x^9-x^2*y^2 Y_r_s_m_m: 9/7*y^11-x^9-x^2*y^2 r: 9 s: 11 a: 13/7 Y_r_s_p_p: 13/7*y^11+x^9+x^2*y^2 Y_r_s_p_m: 13/7*y^11-x^9+x^2*y^2 Y_r_s_m_p: 13/7*y^11+x^9-x^2*y^2 Y_r_s_m_m: 13/7*y^11-x^9-x^2*y^2 r: 9 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^9+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^9+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^9-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^9-x^2*y^2 r: 9 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^9+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^9+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^9-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^9-x^2*y^2 r: 9 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^9+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^9+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^9-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^9-x^2*y^2 r: 10 s: 5 a: 5/7 Y_r_s_p_p: x^10+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^10+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^10+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^10+5/7*y^5-x^2*y^2 r: 10 s: 5 a: 9/7 Y_r_s_p_p: x^10+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^10+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^10+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^10+9/7*y^5-x^2*y^2 r: 10 s: 5 a: 13/7 Y_r_s_p_p: x^10+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^10+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^10+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^10+13/7*y^5-x^2*y^2 r: 10 s: 6 a: 5/7 Y_r_s_p_p: x^10+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^10+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^10+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^10+5/7*y^6-x^2*y^2 r: 10 s: 6 a: 9/7 Y_r_s_p_p: x^10+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^10+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^10+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^10+9/7*y^6-x^2*y^2 r: 10 s: 6 a: 13/7 Y_r_s_p_p: x^10+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^10+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^10+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^10+13/7*y^6-x^2*y^2 r: 10 s: 7 a: 5/7 Y_r_s_p_p: x^10+5/7*y^7+x^2*y^2 Y_r_s_p_m: -x^10+5/7*y^7+x^2*y^2 Y_r_s_m_p: x^10+5/7*y^7-x^2*y^2 Y_r_s_m_m: -x^10+5/7*y^7-x^2*y^2 r: 10 s: 7 a: 9/7 Y_r_s_p_p: x^10+9/7*y^7+x^2*y^2 Y_r_s_p_m: -x^10+9/7*y^7+x^2*y^2 Y_r_s_m_p: x^10+9/7*y^7-x^2*y^2 Y_r_s_m_m: -x^10+9/7*y^7-x^2*y^2 r: 10 s: 7 a: 13/7 Y_r_s_p_p: x^10+13/7*y^7+x^2*y^2 Y_r_s_p_m: -x^10+13/7*y^7+x^2*y^2 Y_r_s_m_p: x^10+13/7*y^7-x^2*y^2 Y_r_s_m_m: -x^10+13/7*y^7-x^2*y^2 r: 10 s: 8 a: 5/7 Y_r_s_p_p: x^10+5/7*y^8+x^2*y^2 Y_r_s_p_m: -x^10+5/7*y^8+x^2*y^2 Y_r_s_m_p: x^10+5/7*y^8-x^2*y^2 Y_r_s_m_m: -x^10+5/7*y^8-x^2*y^2 r: 10 s: 8 a: 9/7 Y_r_s_p_p: x^10+9/7*y^8+x^2*y^2 Y_r_s_p_m: -x^10+9/7*y^8+x^2*y^2 Y_r_s_m_p: x^10+9/7*y^8-x^2*y^2 Y_r_s_m_m: -x^10+9/7*y^8-x^2*y^2 r: 10 s: 8 a: 13/7 Y_r_s_p_p: x^10+13/7*y^8+x^2*y^2 Y_r_s_p_m: -x^10+13/7*y^8+x^2*y^2 Y_r_s_m_p: x^10+13/7*y^8-x^2*y^2 Y_r_s_m_m: -x^10+13/7*y^8-x^2*y^2 r: 10 s: 9 a: 5/7 Y_r_s_p_p: x^10+5/7*y^9+x^2*y^2 Y_r_s_p_m: -x^10+5/7*y^9+x^2*y^2 Y_r_s_m_p: x^10+5/7*y^9-x^2*y^2 Y_r_s_m_m: -x^10+5/7*y^9-x^2*y^2 r: 10 s: 9 a: 9/7 Y_r_s_p_p: x^10+9/7*y^9+x^2*y^2 Y_r_s_p_m: -x^10+9/7*y^9+x^2*y^2 Y_r_s_m_p: x^10+9/7*y^9-x^2*y^2 Y_r_s_m_m: -x^10+9/7*y^9-x^2*y^2 r: 10 s: 9 a: 13/7 Y_r_s_p_p: x^10+13/7*y^9+x^2*y^2 Y_r_s_p_m: -x^10+13/7*y^9+x^2*y^2 Y_r_s_m_p: x^10+13/7*y^9-x^2*y^2 Y_r_s_m_m: -x^10+13/7*y^9-x^2*y^2 r: 10 s: 10 a: 5/7 Y_r_s_p_p: x^10+5/7*y^10+x^2*y^2 Y_r_s_p_m: -x^10+5/7*y^10+x^2*y^2 Y_r_s_m_p: x^10+5/7*y^10-x^2*y^2 Y_r_s_m_m: -x^10+5/7*y^10-x^2*y^2 r: 10 s: 10 a: 9/7 Y_r_s_p_p: x^10+9/7*y^10+x^2*y^2 Y_r_s_p_m: -x^10+9/7*y^10+x^2*y^2 Y_r_s_m_p: x^10+9/7*y^10-x^2*y^2 Y_r_s_m_m: -x^10+9/7*y^10-x^2*y^2 r: 10 s: 10 a: 13/7 Y_r_s_p_p: x^10+13/7*y^10+x^2*y^2 Y_r_s_p_m: -x^10+13/7*y^10+x^2*y^2 Y_r_s_m_p: x^10+13/7*y^10-x^2*y^2 Y_r_s_m_m: -x^10+13/7*y^10-x^2*y^2 r: 10 s: 11 a: 5/7 Y_r_s_p_p: 5/7*y^11+x^10+x^2*y^2 Y_r_s_p_m: 5/7*y^11-x^10+x^2*y^2 Y_r_s_m_p: 5/7*y^11+x^10-x^2*y^2 Y_r_s_m_m: 5/7*y^11-x^10-x^2*y^2 r: 10 s: 11 a: 9/7 Y_r_s_p_p: 9/7*y^11+x^10+x^2*y^2 Y_r_s_p_m: 9/7*y^11-x^10+x^2*y^2 Y_r_s_m_p: 9/7*y^11+x^10-x^2*y^2 Y_r_s_m_m: 9/7*y^11-x^10-x^2*y^2 r: 10 s: 11 a: 13/7 Y_r_s_p_p: 13/7*y^11+x^10+x^2*y^2 Y_r_s_p_m: 13/7*y^11-x^10+x^2*y^2 Y_r_s_m_p: 13/7*y^11+x^10-x^2*y^2 Y_r_s_m_m: 13/7*y^11-x^10-x^2*y^2 r: 10 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^10+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^10+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^10-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^10-x^2*y^2 r: 10 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^10+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^10+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^10-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^10-x^2*y^2 r: 10 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^10+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^10+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^10-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^10-x^2*y^2 r: 11 s: 5 a: 5/7 Y_r_s_p_p: x^11+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^5-x^2*y^2 r: 11 s: 5 a: 9/7 Y_r_s_p_p: x^11+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^5-x^2*y^2 r: 11 s: 5 a: 13/7 Y_r_s_p_p: x^11+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^5-x^2*y^2 r: 11 s: 6 a: 5/7 Y_r_s_p_p: x^11+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^6-x^2*y^2 r: 11 s: 6 a: 9/7 Y_r_s_p_p: x^11+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^6-x^2*y^2 r: 11 s: 6 a: 13/7 Y_r_s_p_p: x^11+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^6-x^2*y^2 r: 11 s: 7 a: 5/7 Y_r_s_p_p: x^11+5/7*y^7+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^7+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^7-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^7-x^2*y^2 r: 11 s: 7 a: 9/7 Y_r_s_p_p: x^11+9/7*y^7+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^7+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^7-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^7-x^2*y^2 r: 11 s: 7 a: 13/7 Y_r_s_p_p: x^11+13/7*y^7+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^7+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^7-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^7-x^2*y^2 r: 11 s: 8 a: 5/7 Y_r_s_p_p: x^11+5/7*y^8+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^8+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^8-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^8-x^2*y^2 r: 11 s: 8 a: 9/7 Y_r_s_p_p: x^11+9/7*y^8+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^8+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^8-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^8-x^2*y^2 r: 11 s: 8 a: 13/7 Y_r_s_p_p: x^11+13/7*y^8+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^8+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^8-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^8-x^2*y^2 r: 11 s: 9 a: 5/7 Y_r_s_p_p: x^11+5/7*y^9+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^9+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^9-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^9-x^2*y^2 r: 11 s: 9 a: 9/7 Y_r_s_p_p: x^11+9/7*y^9+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^9+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^9-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^9-x^2*y^2 r: 11 s: 9 a: 13/7 Y_r_s_p_p: x^11+13/7*y^9+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^9+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^9-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^9-x^2*y^2 r: 11 s: 10 a: 5/7 Y_r_s_p_p: x^11+5/7*y^10+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^10+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^10-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^10-x^2*y^2 r: 11 s: 10 a: 9/7 Y_r_s_p_p: x^11+9/7*y^10+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^10+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^10-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^10-x^2*y^2 r: 11 s: 10 a: 13/7 Y_r_s_p_p: x^11+13/7*y^10+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^10+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^10-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^10-x^2*y^2 r: 11 s: 11 a: 5/7 Y_r_s_p_p: x^11+5/7*y^11+x^2*y^2 Y_r_s_p_m: -x^11+5/7*y^11+x^2*y^2 Y_r_s_m_p: x^11+5/7*y^11-x^2*y^2 Y_r_s_m_m: -x^11+5/7*y^11-x^2*y^2 r: 11 s: 11 a: 9/7 Y_r_s_p_p: x^11+9/7*y^11+x^2*y^2 Y_r_s_p_m: -x^11+9/7*y^11+x^2*y^2 Y_r_s_m_p: x^11+9/7*y^11-x^2*y^2 Y_r_s_m_m: -x^11+9/7*y^11-x^2*y^2 r: 11 s: 11 a: 13/7 Y_r_s_p_p: x^11+13/7*y^11+x^2*y^2 Y_r_s_p_m: -x^11+13/7*y^11+x^2*y^2 Y_r_s_m_p: x^11+13/7*y^11-x^2*y^2 Y_r_s_m_m: -x^11+13/7*y^11-x^2*y^2 r: 11 s: 12 a: 5/7 Y_r_s_p_p: 5/7*y^12+x^11+x^2*y^2 Y_r_s_p_m: 5/7*y^12-x^11+x^2*y^2 Y_r_s_m_p: 5/7*y^12+x^11-x^2*y^2 Y_r_s_m_m: 5/7*y^12-x^11-x^2*y^2 r: 11 s: 12 a: 9/7 Y_r_s_p_p: 9/7*y^12+x^11+x^2*y^2 Y_r_s_p_m: 9/7*y^12-x^11+x^2*y^2 Y_r_s_m_p: 9/7*y^12+x^11-x^2*y^2 Y_r_s_m_m: 9/7*y^12-x^11-x^2*y^2 r: 11 s: 12 a: 13/7 Y_r_s_p_p: 13/7*y^12+x^11+x^2*y^2 Y_r_s_p_m: 13/7*y^12-x^11+x^2*y^2 Y_r_s_m_p: 13/7*y^12+x^11-x^2*y^2 Y_r_s_m_m: 13/7*y^12-x^11-x^2*y^2 r: 12 s: 5 a: 5/7 Y_r_s_p_p: x^12+5/7*y^5+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^5+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^5-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^5-x^2*y^2 r: 12 s: 5 a: 9/7 Y_r_s_p_p: x^12+9/7*y^5+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^5+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^5-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^5-x^2*y^2 r: 12 s: 5 a: 13/7 Y_r_s_p_p: x^12+13/7*y^5+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^5+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^5-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^5-x^2*y^2 r: 12 s: 6 a: 5/7 Y_r_s_p_p: x^12+5/7*y^6+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^6+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^6-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^6-x^2*y^2 r: 12 s: 6 a: 9/7 Y_r_s_p_p: x^12+9/7*y^6+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^6+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^6-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^6-x^2*y^2 r: 12 s: 6 a: 13/7 Y_r_s_p_p: x^12+13/7*y^6+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^6+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^6-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^6-x^2*y^2 r: 12 s: 7 a: 5/7 Y_r_s_p_p: x^12+5/7*y^7+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^7+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^7-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^7-x^2*y^2 r: 12 s: 7 a: 9/7 Y_r_s_p_p: x^12+9/7*y^7+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^7+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^7-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^7-x^2*y^2 r: 12 s: 7 a: 13/7 Y_r_s_p_p: x^12+13/7*y^7+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^7+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^7-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^7-x^2*y^2 r: 12 s: 8 a: 5/7 Y_r_s_p_p: x^12+5/7*y^8+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^8+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^8-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^8-x^2*y^2 r: 12 s: 8 a: 9/7 Y_r_s_p_p: x^12+9/7*y^8+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^8+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^8-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^8-x^2*y^2 r: 12 s: 8 a: 13/7 Y_r_s_p_p: x^12+13/7*y^8+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^8+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^8-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^8-x^2*y^2 r: 12 s: 9 a: 5/7 Y_r_s_p_p: x^12+5/7*y^9+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^9+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^9-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^9-x^2*y^2 r: 12 s: 9 a: 9/7 Y_r_s_p_p: x^12+9/7*y^9+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^9+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^9-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^9-x^2*y^2 r: 12 s: 9 a: 13/7 Y_r_s_p_p: x^12+13/7*y^9+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^9+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^9-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^9-x^2*y^2 r: 12 s: 10 a: 5/7 Y_r_s_p_p: x^12+5/7*y^10+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^10+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^10-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^10-x^2*y^2 r: 12 s: 10 a: 9/7 Y_r_s_p_p: x^12+9/7*y^10+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^10+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^10-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^10-x^2*y^2 r: 12 s: 10 a: 13/7 Y_r_s_p_p: x^12+13/7*y^10+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^10+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^10-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^10-x^2*y^2 r: 12 s: 11 a: 5/7 Y_r_s_p_p: x^12+5/7*y^11+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^11+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^11-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^11-x^2*y^2 r: 12 s: 11 a: 9/7 Y_r_s_p_p: x^12+9/7*y^11+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^11+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^11-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^11-x^2*y^2 r: 12 s: 11 a: 13/7 Y_r_s_p_p: x^12+13/7*y^11+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^11+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^11-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^11-x^2*y^2 r: 12 s: 12 a: 5/7 Y_r_s_p_p: x^12+5/7*y^12+x^2*y^2 Y_r_s_p_m: -x^12+5/7*y^12+x^2*y^2 Y_r_s_m_p: x^12+5/7*y^12-x^2*y^2 Y_r_s_m_m: -x^12+5/7*y^12-x^2*y^2 r: 12 s: 12 a: 9/7 Y_r_s_p_p: x^12+9/7*y^12+x^2*y^2 Y_r_s_p_m: -x^12+9/7*y^12+x^2*y^2 Y_r_s_m_p: x^12+9/7*y^12-x^2*y^2 Y_r_s_m_m: -x^12+9/7*y^12-x^2*y^2 r: 12 s: 12 a: 13/7 Y_r_s_p_p: x^12+13/7*y^12+x^2*y^2 Y_r_s_p_m: -x^12+13/7*y^12+x^2*y^2 Y_r_s_m_p: x^12+13/7*y^12-x^2*y^2 Y_r_s_m_m: -x^12+13/7*y^12-x^2*y^2 Y_tilde_r_pmpm: // ** redefining a ** k: 1 a: 5/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+5/7*x Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+5/7*x Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+5/7*x Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+5/7*x k: 1 a: 9/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+9/7*x Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+9/7*x Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+9/7*x Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+9/7*x k: 1 a: 13/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+13/7*x Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+13/7*x Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+13/7*x Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+13/7*x k: 2 a: 5/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+5/7*x^2 Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+5/7*x^2 Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+5/7*x^2 Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+5/7*x^2 k: 2 a: 9/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+9/7*x^2 Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+9/7*x^2 Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+9/7*x^2 Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+9/7*x^2 k: 2 a: 13/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+13/7*x^2 Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+13/7*x^2 Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+13/7*x^2 Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+13/7*x^2 k: 3 a: 5/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+5/7*x^3 Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+5/7*x^3 Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+5/7*x^3 Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+5/7*x^3 k: 3 a: 9/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+9/7*x^3 Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+9/7*x^3 Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+9/7*x^3 Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+9/7*x^3 k: 3 a: 13/7 Y_tilde_r_p_p: x^4+2*x^2*y^2+y^4+13/7*x^3 Y_tilde_r_p_m: x^4-2*x^2*y^2+y^4+13/7*x^3 Y_tilde_r_m_p: -x^4-2*x^2*y^2-y^4+13/7*x^3 Y_tilde_r_m_m: -x^4+2*x^2*y^2-y^4+13/7*x^3 k: 4 a: 5/7 Y_tilde_r_p_p: 12/7*x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 12/7*x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: -2/7*x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: -2/7*x^4+2*x^2*y^2-y^4 k: 4 a: 9/7 Y_tilde_r_p_p: 16/7*x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 16/7*x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 2/7*x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 2/7*x^4+2*x^2*y^2-y^4 k: 4 a: 13/7 Y_tilde_r_p_p: 20/7*x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 20/7*x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 6/7*x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 6/7*x^4+2*x^2*y^2-y^4 k: 5 a: 5/7 Y_tilde_r_p_p: 5/7*x^5+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^5+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^5-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^5-x^4+2*x^2*y^2-y^4 k: 5 a: 9/7 Y_tilde_r_p_p: 9/7*x^5+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^5+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^5-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^5-x^4+2*x^2*y^2-y^4 k: 5 a: 13/7 Y_tilde_r_p_p: 13/7*x^5+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^5+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^5-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^5-x^4+2*x^2*y^2-y^4 k: 6 a: 5/7 Y_tilde_r_p_p: 5/7*x^6+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^6+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^6-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^6-x^4+2*x^2*y^2-y^4 k: 6 a: 9/7 Y_tilde_r_p_p: 9/7*x^6+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^6+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^6-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^6-x^4+2*x^2*y^2-y^4 k: 6 a: 13/7 Y_tilde_r_p_p: 13/7*x^6+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^6+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^6-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^6-x^4+2*x^2*y^2-y^4 k: 7 a: 5/7 Y_tilde_r_p_p: 5/7*x^7+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^7+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^7-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^7-x^4+2*x^2*y^2-y^4 k: 7 a: 9/7 Y_tilde_r_p_p: 9/7*x^7+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^7+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^7-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^7-x^4+2*x^2*y^2-y^4 k: 7 a: 13/7 Y_tilde_r_p_p: 13/7*x^7+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^7+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^7-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^7-x^4+2*x^2*y^2-y^4 k: 8 a: 5/7 Y_tilde_r_p_p: 5/7*x^8+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^8+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^8-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^8-x^4+2*x^2*y^2-y^4 k: 8 a: 9/7 Y_tilde_r_p_p: 9/7*x^8+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^8+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^8-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^8-x^4+2*x^2*y^2-y^4 k: 8 a: 13/7 Y_tilde_r_p_p: 13/7*x^8+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^8+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^8-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^8-x^4+2*x^2*y^2-y^4 k: 9 a: 5/7 Y_tilde_r_p_p: 5/7*x^9+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^9+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^9-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^9-x^4+2*x^2*y^2-y^4 k: 9 a: 9/7 Y_tilde_r_p_p: 9/7*x^9+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^9+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^9-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^9-x^4+2*x^2*y^2-y^4 k: 9 a: 13/7 Y_tilde_r_p_p: 13/7*x^9+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^9+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^9-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^9-x^4+2*x^2*y^2-y^4 k: 10 a: 5/7 Y_tilde_r_p_p: 5/7*x^10+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^10+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^10-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^10-x^4+2*x^2*y^2-y^4 k: 10 a: 9/7 Y_tilde_r_p_p: 9/7*x^10+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^10+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^10-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^10-x^4+2*x^2*y^2-y^4 k: 10 a: 13/7 Y_tilde_r_p_p: 13/7*x^10+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^10+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^10-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^10-x^4+2*x^2*y^2-y^4 k: 11 a: 5/7 Y_tilde_r_p_p: 5/7*x^11+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^11+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^11-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^11-x^4+2*x^2*y^2-y^4 k: 11 a: 9/7 Y_tilde_r_p_p: 9/7*x^11+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^11+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^11-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^11-x^4+2*x^2*y^2-y^4 k: 11 a: 13/7 Y_tilde_r_p_p: 13/7*x^11+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^11+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^11-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^11-x^4+2*x^2*y^2-y^4 k: 12 a: 5/7 Y_tilde_r_p_p: 5/7*x^12+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 5/7*x^12+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 5/7*x^12-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 5/7*x^12-x^4+2*x^2*y^2-y^4 k: 12 a: 9/7 Y_tilde_r_p_p: 9/7*x^12+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 9/7*x^12+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 9/7*x^12-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 9/7*x^12-x^4+2*x^2*y^2-y^4 k: 12 a: 13/7 Y_tilde_r_p_p: 13/7*x^12+x^4+2*x^2*y^2+y^4 Y_tilde_r_p_m: 13/7*x^12+x^4-2*x^2*y^2+y^4 Y_tilde_r_m_p: 13/7*x^12-x^4-2*x^2*y^2-y^4 Y_tilde_r_m_m: 13/7*x^12-x^4+2*x^2*y^2-y^4 ---------------- Challenge 16 the discriminant D of a system of 2 equations ---------------- D: D: 1816274895843482705708030487016037960921088*x^45*y^45+24519711093887016527058411574716512472434688*x^46*y^39+24519711093887016527058411574716512472434688*x^39*y^46+82754024941868680778822139064668229594467072*x^47*y^33-1382857482588991594621856281744153452803994624*x^40*y^40+82754024941868680778822139064668229594467072*x^33*y^47-21034640556603101797073088972187333790660436864*x^41*y^34-21034640556603101797073088972187333790660436864*x^34*y^41-64692524354845875214754581881148274484815004672*x^42*y^28-7262663129907778310522865630114322908083751120*x^35*y^35-64692524354845875214754581881148274484815004672*x^28*y^42+45707486651439559266284202160587828803602159296*x^43*y^22+3748225467651453229201948457758388644676161761600*x^36*y^29+3748225467651453229201948457758388644676161761600*x^29*y^36+45707486651439559266284202160587828803602159296*x^22*y^43+24941314853111247935885131129664284932525713375712*x^37*y^23+74268630326294559239611631031564286630254733223424*x^30*y^30+24941314853111247935885131129664284932525713375712*x^23*y^37+41207664199903653076991000690234985094533094566144*x^38*y^17+412135181350390183442816324226955474457329028451840*x^31*y^24+412135181350390183442816324226955474457329028451840*x^24*y^31+41207664199903653076991000690234985094533094566144*x^17*y^38+8415197276745089043520547466937512136683223717776*x^39*y^11+702895423288031690919605187889043797831187902752768*x^32*y^18+2218314692460666836925542429565491177644708007287488*x^25*y^25+702895423288031690919605187889043797831187902752768*x^18*y^32+8415197276745089043520547466937512136683223717776*x^11*y^39+143179068880953778932665444119482631585536972924672*x^33*y^12+3868355234950754259360595357692756784447296591507264*x^26*y^19+3868355234950754259360595357692756784447296591507264*x^19*y^26+143179068880953778932665444119482631585536972924672*x^12*y^33+17458752420081093875109627316025221604311252224096*x^34*y^6+785145092246909876150591435521602332059258264670112*x^27*y^13+6928958745160627098972661174706927675938439861357568*x^20*y^20+785145092246909876150591435521602332059258264670112*x^13*y^27+17458752420081093875109627316025221604311252224096*x^6*y^34+516440160351044111358464119738658142157348733522052*x^35+236627403090264575474785219707184968001345670463360*x^28*y^7+1398733594760368236093256811269504896377517856840320*x^21*y^14+1398733594760368236093256811269504896377517856840320*x^14*y^21+236627403090264575474785219707184968001345670463360*x^7*y^28+516440160351044111358464119738658142157348733522052*y^35+8821163670466338815738170064779601944777780404750000*x^29*y+818616116909248137227768928071007988989779492250000*x^22*y^8+282899832910494363044397530137205019165966367950000*x^15*y^15+818616116909248137227768928071007988989779492250000*x^8*y^22+8821163670466338815738170064779601944777780404750000*x*y^29+48642180526070778429206216629487443546990203515625000*x^23*y^2+142726890361303135859187972744481872248100000000000*x^16*y^9+142726890361303135859187972744481872248100000000000*x^9*y^16+48642180526070778429206216629487443546990203515625000*x^2*y^23+87388579975718405520742649542672056483735351562500000*x^17*y^3+82727507188427789157427030752395750250000000000000*x^10*y^10+87388579975718405520742649542672056483735351562500000*x^3*y^17+17631004810327637966335552676449435712814331054687500*x^11*y^4+17631004810327637966335552676449435712814331054687500*x^4*y^11+9160055037139324605994754035171051025390625000000000*x^5*y^5+1102507499354148695951786433413508348166942596435546875 ---------------- Challenge 17 high solitary point and singularities with high tangencies ---------------- SA_k_l: k: 2 l: 2 SA_k_l: y^9+x^8-5*y^8-4*x^6*y+10*y^7+2*x^6+6*x^4*y^2-10*y^6-6*x^4*y-4*x^2*y^3+5*y^5+x^4+6*x^2*y^2-2*x^2*y-2*y^3+y^2 k: 2 l: 4 SA_k_l: y^17+x^16-9*y^16-8*x^14*y+36*y^15+4*x^14+28*x^12*y^2-84*y^14-28*x^12*y-56*x^10*y^3+126*y^13+6*x^12+84*x^10*y^2+70*x^8*y^4-126*y^12-36*x^10*y-140*x^8*y^3-56*x^6*y^5+84*y^11+4*x^10+90*x^8*y^2+140*x^6*y^4+28*x^4*y^6-36*y^10-20*x^8*y-120*x^6*y^3-84*x^4*y^5-8*x^2*y^7+9*y^9+x^8+40*x^6*y^2+90*x^4*y^4+28*x^2*y^6-4*x^6*y-40*x^4*y^3-36*x^2*y^5-4*y^7+6*x^4*y^2+20*x^2*y^4+6*y^6-4*x^2*y^3-4*y^5+y^4 k: 2 l: 6 SA_k_l: y^25+x^24-13*y^24-12*x^22*y+78*y^23+6*x^22+66*x^20*y^2-286*y^22-66*x^20*y-220*x^18*y^3+715*y^21+15*x^20+330*x^18*y^2+495*x^16*y^4-1287*y^20-150*x^18*y-990*x^16*y^3-792*x^14*y^5+1716*y^19+20*x^18+675*x^16*y^2+1980*x^14*y^4+924*x^12*y^6-1716*y^18-180*x^16*y-1800*x^14*y^3-2772*x^12*y^5-792*x^10*y^7+1287*y^17+15*x^16+720*x^14*y^2+3150*x^12*y^4+2772*x^10*y^6+495*x^8*y^8-715*y^16-120*x^14*y-1680*x^12*y^3-3780*x^10*y^5-1980*x^8*y^7-220*x^6*y^9+286*y^15+6*x^14+420*x^12*y^2+2520*x^10*y^4+3150*x^8*y^6+990*x^6*y^8+66*x^4*y^10-78*y^14-42*x^12*y-840*x^10*y^3-2520*x^8*y^5-1800*x^6*y^7-330*x^4*y^9-12*x^2*y^11+13*y^13+x^12+126*x^10*y^2+1050*x^8*y^4+1680*x^6*y^6+675*x^4*y^8+66*x^2*y^10-6*x^10*y-210*x^8*y^3-840*x^6*y^5-720*x^4*y^7-150*x^2*y^9-6*y^11+15*x^8*y^2+210*x^6*y^4+420*x^4*y^6+180*x^2*y^8+15*y^10-20*x^6*y^3-126*x^4*y^5-120*x^2*y^7-20*y^9+15*x^4*y^4+42*x^2*y^6+15*y^8-6*x^2*y^5-6*y^7+y^6 k: 4 l: 2 SA_k_l: y^17+x^16-9*y^16+36*y^15-84*y^14-4*x^12*y+126*y^13+2*x^12-126*y^12+84*y^11+6*x^8*y^2-36*y^10-6*x^8*y+9*y^9+x^8-y^8-4*x^4*y^3+6*x^4*y^2-2*x^4*y+y^4-2*y^3+y^2 k: 4 l: 4 SA_k_l: y^33+x^32-17*y^32+136*y^31-680*y^30-8*x^28*y+2380*y^29+4*x^28-6188*y^28+12376*y^27+28*x^24*y^2-19448*y^26-28*x^24*y+24310*y^25+6*x^24-24310*y^24-56*x^20*y^3+19448*y^23+84*x^20*y^2-12376*y^22-36*x^20*y+6188*y^21+4*x^20+70*x^16*y^4-2380*y^20-140*x^16*y^3+680*y^19+90*x^16*y^2-136*y^18-20*x^16*y-56*x^12*y^5+17*y^17+x^16+140*x^12*y^4-y^16-120*x^12*y^3+40*x^12*y^2+28*x^8*y^6-4*x^12*y-84*x^8*y^5+90*x^8*y^4-40*x^8*y^3-8*x^4*y^7+6*x^8*y^2+28*x^4*y^6-36*x^4*y^5+20*x^4*y^4+y^8-4*x^4*y^3-4*y^7+6*y^6-4*y^5+y^4 k: 4 l: 6 SA_k_l: y^49+x^48-25*y^48+300*y^47-2300*y^46-12*x^44*y+12650*y^45+6*x^44-53130*y^44+177100*y^43+66*x^40*y^2-480700*y^42-66*x^40*y+1081575*y^41+15*x^40-2042975*y^40-220*x^36*y^3+3268760*y^39+330*x^36*y^2-4457400*y^38-150*x^36*y+5200300*y^37+20*x^36+495*x^32*y^4-5200300*y^36-990*x^32*y^3+4457400*y^35+675*x^32*y^2-3268760*y^34-180*x^32*y-792*x^28*y^5+2042975*y^33+15*x^32+1980*x^28*y^4-1081575*y^32-1800*x^28*y^3+480700*y^31+720*x^28*y^2+924*x^24*y^6-177100*y^30-120*x^28*y-2772*x^24*y^5+53130*y^29+6*x^28+3150*x^24*y^4-12650*y^28-1680*x^24*y^3-792*x^20*y^7+2300*y^27+420*x^24*y^2+2772*x^20*y^6-300*y^26-42*x^24*y-3780*x^20*y^5+25*y^25+x^24+2520*x^20*y^4+495*x^16*y^8-y^24-840*x^20*y^3-1980*x^16*y^7+126*x^20*y^2+3150*x^16*y^6-6*x^20*y-2520*x^16*y^5-220*x^12*y^9+1050*x^16*y^4+990*x^12*y^8-210*x^16*y^3-1800*x^12*y^7+15*x^16*y^2+1680*x^12*y^6+66*x^8*y^10-840*x^12*y^5-330*x^8*y^9+210*x^12*y^4+675*x^8*y^8-20*x^12*y^3-720*x^8*y^7-12*x^4*y^11+420*x^8*y^6+66*x^4*y^10-126*x^8*y^5-150*x^4*y^9+15*x^8*y^4+180*x^4*y^8+y^12-120*x^4*y^7-6*y^11+42*x^4*y^6+15*y^10-6*x^4*y^5-20*y^9+15*y^8-6*y^7+y^6 k: 6 l: 2 SA_k_l: y^25+x^24-13*y^24+78*y^23-286*y^22+715*y^21-1287*y^20-4*x^18*y+1716*y^19+2*x^18-1716*y^18+1287*y^17-715*y^16+286*y^15+6*x^12*y^2-78*y^14-6*x^12*y+13*y^13+x^12-y^12-4*x^6*y^3+6*x^6*y^2-2*x^6*y+y^4-2*y^3+y^2 k: 6 l: 4 SA_k_l: y^49+x^48-25*y^48+300*y^47-2300*y^46+12650*y^45-53130*y^44-8*x^42*y+177100*y^43+4*x^42-480700*y^42+1081575*y^41-2042975*y^40+3268760*y^39+28*x^36*y^2-4457400*y^38-28*x^36*y+5200300*y^37+6*x^36-5200300*y^36+4457400*y^35-3268760*y^34-56*x^30*y^3+2042975*y^33+84*x^30*y^2-1081575*y^32-36*x^30*y+480700*y^31+4*x^30-177100*y^30+53130*y^29+70*x^24*y^4-12650*y^28-140*x^24*y^3+2300*y^27+90*x^24*y^2-300*y^26-20*x^24*y+25*y^25+x^24-y^24-56*x^18*y^5+140*x^18*y^4-120*x^18*y^3+40*x^18*y^2-4*x^18*y+28*x^12*y^6-84*x^12*y^5+90*x^12*y^4-40*x^12*y^3+6*x^12*y^2-8*x^6*y^7+28*x^6*y^6-36*x^6*y^5+20*x^6*y^4-4*x^6*y^3+y^8-4*y^7+6*y^6-4*y^5+y^4 k: 6 l: 6 SA_k_l: 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---------------- Challenge 18 singularities with high tangencies and small non-real ovals ---------------- SA_k_l_eps: k: 2 l: 2 eps: -1/10 SA_k_l_eps: y^9+x^8-5*y^8-4*x^6*y+10*y^7+12/5*x^6+6*x^4*y^2-10*y^6-36/5*x^4*y-4*x^2*y^3+5*y^5+83/50*x^4+36/5*x^2*y^2-83/25*x^2*y-12/5*y^3+33/125*x^2+83/50*y^2-33/125*y+121/10000 k: 2 l: 2 eps: -1/100 SA_k_l_eps: y^9+x^8-5*y^8-4*x^6*y+10*y^7+51/25*x^6+6*x^4*y^2-10*y^6-153/25*x^4*y-4*x^2*y^3+5*y^5+5303/5000*x^4+153/25*x^2*y^2-5303/2500*x^2*y-51/25*y^3+5151/250000*x^2+5303/5000*y^2-5151/250000*y+10201/100000000 k: 2 l: 2 eps: -1/1000 SA_k_l_eps: y^9+x^8-5*y^8-4*x^6*y+10*y^7+501/250*x^6+6*x^4*y^2-10*y^6-1503/250*x^4*y-4*x^2*y^3+5*y^5+503003/500000*x^4+1503/250*x^2*y^2-503003/250000*x^2*y-501/250*y^3+501501/250000000*x^2+503003/500000*y^2-501501/250000000*y+1002001/1000000000000 k: 2 l: 2 eps: -1/10000 SA_k_l_eps: 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k: 4 l: 4 eps: 1/1000000 SA_k_l_eps: 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k: 4 l: 4 eps: 1/10000000 SA_k_l_eps: 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k: 4 l: 4 eps: 1/100000000 SA_k_l_eps: 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---------------- Challenge 19 a high solitary point close to a one-dimensional component ---------------- SCA_k_l_eps: k: 2 l: 2 eps: 1/10 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/10*x^4-x^2*y^2+11/10*y^4-1/5*x^2*y+1/10*y^2 k: 2 l: 2 eps: 1/100 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/100*x^4-x^2*y^2+101/100*y^4-1/50*x^2*y+1/100*y^2 k: 2 l: 2 eps: 1/1000 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/1000*x^4-x^2*y^2+1001/1000*y^4-1/500*x^2*y+1/1000*y^2 k: 2 l: 2 eps: 1/10000 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/10000*x^4-x^2*y^2+10001/10000*y^4-1/5000*x^2*y+1/10000*y^2 k: 2 l: 2 eps: 1/100000 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/100000*x^4-x^2*y^2+100001/100000*y^4-1/50000*x^2*y+1/100000*y^2 k: 2 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/1000000*x^4-x^2*y^2+1000001/1000000*y^4-1/500000*x^2*y+1/1000000*y^2 k: 2 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/10000000*x^4-x^2*y^2+10000001/10000000*y^4-1/5000000*x^2*y+1/10000000*y^2 k: 2 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^6+x^4*y^2-x^2*y^4+2*y^6+2*x^4*y-2*x^2*y^3+1/100000000*x^4-x^2*y^2+100000001/100000000*y^4-1/50000000*x^2*y+1/100000000*y^2 k: 3 l: 2 eps: 1/10 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/10*x^6+2*x^5*y-2*x^3*y^3+1/10*y^6-1/5*x^3*y-x^2*y^2+y^4+1/10*y^2 k: 3 l: 2 eps: 1/100 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/100*x^6+2*x^5*y-2*x^3*y^3+1/100*y^6-1/50*x^3*y-x^2*y^2+y^4+1/100*y^2 k: 3 l: 2 eps: 1/1000 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/1000*x^6+2*x^5*y-2*x^3*y^3+1/1000*y^6-1/500*x^3*y-x^2*y^2+y^4+1/1000*y^2 k: 3 l: 2 eps: 1/10000 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/10000*x^6+2*x^5*y-2*x^3*y^3+1/10000*y^6-1/5000*x^3*y-x^2*y^2+y^4+1/10000*y^2 k: 3 l: 2 eps: 1/100000 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/100000*x^6+2*x^5*y-2*x^3*y^3+1/100000*y^6-1/50000*x^3*y-x^2*y^2+y^4+1/100000*y^2 k: 3 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/1000000*x^6+2*x^5*y-2*x^3*y^3+1/1000000*y^6-1/500000*x^3*y-x^2*y^2+y^4+1/1000000*y^2 k: 3 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/10000000*x^6+2*x^5*y-2*x^3*y^3+1/10000000*y^6-1/5000000*x^3*y-x^2*y^2+y^4+1/10000000*y^2 k: 3 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^8+x^6*y^2-x^2*y^6+2*y^8+1/100000000*x^6+2*x^5*y-2*x^3*y^3+1/100000000*y^6-1/50000000*x^3*y-x^2*y^2+y^4+1/100000000*y^2 k: 4 l: 2 eps: 1/10 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/10*x^8+1/10*y^8+2*x^6*y-2*x^4*y^3-1/5*x^4*y-x^2*y^2+y^4+1/10*y^2 k: 4 l: 2 eps: 1/100 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/100*x^8+1/100*y^8+2*x^6*y-2*x^4*y^3-1/50*x^4*y-x^2*y^2+y^4+1/100*y^2 k: 4 l: 2 eps: 1/1000 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/1000*x^8+1/1000*y^8+2*x^6*y-2*x^4*y^3-1/500*x^4*y-x^2*y^2+y^4+1/1000*y^2 k: 4 l: 2 eps: 1/10000 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/10000*x^8+1/10000*y^8+2*x^6*y-2*x^4*y^3-1/5000*x^4*y-x^2*y^2+y^4+1/10000*y^2 k: 4 l: 2 eps: 1/100000 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/100000*x^8+1/100000*y^8+2*x^6*y-2*x^4*y^3-1/50000*x^4*y-x^2*y^2+y^4+1/100000*y^2 k: 4 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/1000000*x^8+1/1000000*y^8+2*x^6*y-2*x^4*y^3-1/500000*x^4*y-x^2*y^2+y^4+1/1000000*y^2 k: 4 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/10000000*x^8+1/10000000*y^8+2*x^6*y-2*x^4*y^3-1/5000000*x^4*y-x^2*y^2+y^4+1/10000000*y^2 k: 4 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^10+x^8*y^2-x^2*y^8+2*y^10+1/100000000*x^8+1/100000000*y^8+2*x^6*y-2*x^4*y^3-1/50000000*x^4*y-x^2*y^2+y^4+1/100000000*y^2 k: 5 l: 2 eps: 1/10 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/10*x^10+1/10*y^10+2*x^7*y-2*x^5*y^3-1/5*x^5*y-x^2*y^2+y^4+1/10*y^2 k: 5 l: 2 eps: 1/100 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/100*x^10+1/100*y^10+2*x^7*y-2*x^5*y^3-1/50*x^5*y-x^2*y^2+y^4+1/100*y^2 k: 5 l: 2 eps: 1/1000 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/1000*x^10+1/1000*y^10+2*x^7*y-2*x^5*y^3-1/500*x^5*y-x^2*y^2+y^4+1/1000*y^2 k: 5 l: 2 eps: 1/10000 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/10000*x^10+1/10000*y^10+2*x^7*y-2*x^5*y^3-1/5000*x^5*y-x^2*y^2+y^4+1/10000*y^2 k: 5 l: 2 eps: 1/100000 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/100000*x^10+1/100000*y^10+2*x^7*y-2*x^5*y^3-1/50000*x^5*y-x^2*y^2+y^4+1/100000*y^2 k: 5 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/1000000*x^10+1/1000000*y^10+2*x^7*y-2*x^5*y^3-1/500000*x^5*y-x^2*y^2+y^4+1/1000000*y^2 k: 5 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/10000000*x^10+1/10000000*y^10+2*x^7*y-2*x^5*y^3-1/5000000*x^5*y-x^2*y^2+y^4+1/10000000*y^2 k: 5 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^12+x^10*y^2-x^2*y^10+2*y^12+1/100000000*x^10+1/100000000*y^10+2*x^7*y-2*x^5*y^3-1/50000000*x^5*y-x^2*y^2+y^4+1/100000000*y^2 k: 6 l: 2 eps: 1/10 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/10*x^12+1/10*y^12+2*x^8*y-2*x^6*y^3-1/5*x^6*y-x^2*y^2+y^4+1/10*y^2 k: 6 l: 2 eps: 1/100 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/100*x^12+1/100*y^12+2*x^8*y-2*x^6*y^3-1/50*x^6*y-x^2*y^2+y^4+1/100*y^2 k: 6 l: 2 eps: 1/1000 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/1000*x^12+1/1000*y^12+2*x^8*y-2*x^6*y^3-1/500*x^6*y-x^2*y^2+y^4+1/1000*y^2 k: 6 l: 2 eps: 1/10000 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/10000*x^12+1/10000*y^12+2*x^8*y-2*x^6*y^3-1/5000*x^6*y-x^2*y^2+y^4+1/10000*y^2 k: 6 l: 2 eps: 1/100000 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/100000*x^12+1/100000*y^12+2*x^8*y-2*x^6*y^3-1/50000*x^6*y-x^2*y^2+y^4+1/100000*y^2 k: 6 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/1000000*x^12+1/1000000*y^12+2*x^8*y-2*x^6*y^3-1/500000*x^6*y-x^2*y^2+y^4+1/1000000*y^2 k: 6 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/10000000*x^12+1/10000000*y^12+2*x^8*y-2*x^6*y^3-1/5000000*x^6*y-x^2*y^2+y^4+1/10000000*y^2 k: 6 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^14+x^12*y^2-x^2*y^12+2*y^14+1/100000000*x^12+1/100000000*y^12+2*x^8*y-2*x^6*y^3-1/50000000*x^6*y-x^2*y^2+y^4+1/100000000*y^2 k: 7 l: 2 eps: 1/10 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/10*x^14+1/10*y^14+2*x^9*y-2*x^7*y^3-1/5*x^7*y-x^2*y^2+y^4+1/10*y^2 k: 7 l: 2 eps: 1/100 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/100*x^14+1/100*y^14+2*x^9*y-2*x^7*y^3-1/50*x^7*y-x^2*y^2+y^4+1/100*y^2 k: 7 l: 2 eps: 1/1000 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/1000*x^14+1/1000*y^14+2*x^9*y-2*x^7*y^3-1/500*x^7*y-x^2*y^2+y^4+1/1000*y^2 k: 7 l: 2 eps: 1/10000 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/10000*x^14+1/10000*y^14+2*x^9*y-2*x^7*y^3-1/5000*x^7*y-x^2*y^2+y^4+1/10000*y^2 k: 7 l: 2 eps: 1/100000 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/100000*x^14+1/100000*y^14+2*x^9*y-2*x^7*y^3-1/50000*x^7*y-x^2*y^2+y^4+1/100000*y^2 k: 7 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/1000000*x^14+1/1000000*y^14+2*x^9*y-2*x^7*y^3-1/500000*x^7*y-x^2*y^2+y^4+1/1000000*y^2 k: 7 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/10000000*x^14+1/10000000*y^14+2*x^9*y-2*x^7*y^3-1/5000000*x^7*y-x^2*y^2+y^4+1/10000000*y^2 k: 7 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^16+x^14*y^2-x^2*y^14+2*y^16+1/100000000*x^14+1/100000000*y^14+2*x^9*y-2*x^7*y^3-1/50000000*x^7*y-x^2*y^2+y^4+1/100000000*y^2 k: 8 l: 2 eps: 1/10 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/10*x^16+1/10*y^16+2*x^10*y-2*x^8*y^3-1/5*x^8*y-x^2*y^2+y^4+1/10*y^2 k: 8 l: 2 eps: 1/100 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/100*x^16+1/100*y^16+2*x^10*y-2*x^8*y^3-1/50*x^8*y-x^2*y^2+y^4+1/100*y^2 k: 8 l: 2 eps: 1/1000 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/1000*x^16+1/1000*y^16+2*x^10*y-2*x^8*y^3-1/500*x^8*y-x^2*y^2+y^4+1/1000*y^2 k: 8 l: 2 eps: 1/10000 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/10000*x^16+1/10000*y^16+2*x^10*y-2*x^8*y^3-1/5000*x^8*y-x^2*y^2+y^4+1/10000*y^2 k: 8 l: 2 eps: 1/100000 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/100000*x^16+1/100000*y^16+2*x^10*y-2*x^8*y^3-1/50000*x^8*y-x^2*y^2+y^4+1/100000*y^2 k: 8 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/1000000*x^16+1/1000000*y^16+2*x^10*y-2*x^8*y^3-1/500000*x^8*y-x^2*y^2+y^4+1/1000000*y^2 k: 8 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/10000000*x^16+1/10000000*y^16+2*x^10*y-2*x^8*y^3-1/5000000*x^8*y-x^2*y^2+y^4+1/10000000*y^2 k: 8 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^18+x^16*y^2-x^2*y^16+2*y^18+1/100000000*x^16+1/100000000*y^16+2*x^10*y-2*x^8*y^3-1/50000000*x^8*y-x^2*y^2+y^4+1/100000000*y^2 k: 9 l: 2 eps: 1/10 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/10*x^18+1/10*y^18+2*x^11*y-2*x^9*y^3-1/5*x^9*y-x^2*y^2+y^4+1/10*y^2 k: 9 l: 2 eps: 1/100 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/100*x^18+1/100*y^18+2*x^11*y-2*x^9*y^3-1/50*x^9*y-x^2*y^2+y^4+1/100*y^2 k: 9 l: 2 eps: 1/1000 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/1000*x^18+1/1000*y^18+2*x^11*y-2*x^9*y^3-1/500*x^9*y-x^2*y^2+y^4+1/1000*y^2 k: 9 l: 2 eps: 1/10000 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/10000*x^18+1/10000*y^18+2*x^11*y-2*x^9*y^3-1/5000*x^9*y-x^2*y^2+y^4+1/10000*y^2 k: 9 l: 2 eps: 1/100000 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/100000*x^18+1/100000*y^18+2*x^11*y-2*x^9*y^3-1/50000*x^9*y-x^2*y^2+y^4+1/100000*y^2 k: 9 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/1000000*x^18+1/1000000*y^18+2*x^11*y-2*x^9*y^3-1/500000*x^9*y-x^2*y^2+y^4+1/1000000*y^2 k: 9 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/10000000*x^18+1/10000000*y^18+2*x^11*y-2*x^9*y^3-1/5000000*x^9*y-x^2*y^2+y^4+1/10000000*y^2 k: 9 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^20+x^18*y^2-x^2*y^18+2*y^20+1/100000000*x^18+1/100000000*y^18+2*x^11*y-2*x^9*y^3-1/50000000*x^9*y-x^2*y^2+y^4+1/100000000*y^2 k: 10 l: 2 eps: 1/10 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/10*x^20+1/10*y^20+2*x^12*y-2*x^10*y^3-1/5*x^10*y-x^2*y^2+y^4+1/10*y^2 k: 10 l: 2 eps: 1/100 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/100*x^20+1/100*y^20+2*x^12*y-2*x^10*y^3-1/50*x^10*y-x^2*y^2+y^4+1/100*y^2 k: 10 l: 2 eps: 1/1000 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/1000*x^20+1/1000*y^20+2*x^12*y-2*x^10*y^3-1/500*x^10*y-x^2*y^2+y^4+1/1000*y^2 k: 10 l: 2 eps: 1/10000 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/10000*x^20+1/10000*y^20+2*x^12*y-2*x^10*y^3-1/5000*x^10*y-x^2*y^2+y^4+1/10000*y^2 k: 10 l: 2 eps: 1/100000 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/100000*x^20+1/100000*y^20+2*x^12*y-2*x^10*y^3-1/50000*x^10*y-x^2*y^2+y^4+1/100000*y^2 k: 10 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/1000000*x^20+1/1000000*y^20+2*x^12*y-2*x^10*y^3-1/500000*x^10*y-x^2*y^2+y^4+1/1000000*y^2 k: 10 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/10000000*x^20+1/10000000*y^20+2*x^12*y-2*x^10*y^3-1/5000000*x^10*y-x^2*y^2+y^4+1/10000000*y^2 k: 10 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^22+x^20*y^2-x^2*y^20+2*y^22+1/100000000*x^20+1/100000000*y^20+2*x^12*y-2*x^10*y^3-1/50000000*x^10*y-x^2*y^2+y^4+1/100000000*y^2 k: 11 l: 2 eps: 1/10 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/10*x^22+1/10*y^22+2*x^13*y-2*x^11*y^3-1/5*x^11*y-x^2*y^2+y^4+1/10*y^2 k: 11 l: 2 eps: 1/100 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/100*x^22+1/100*y^22+2*x^13*y-2*x^11*y^3-1/50*x^11*y-x^2*y^2+y^4+1/100*y^2 k: 11 l: 2 eps: 1/1000 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/1000*x^22+1/1000*y^22+2*x^13*y-2*x^11*y^3-1/500*x^11*y-x^2*y^2+y^4+1/1000*y^2 k: 11 l: 2 eps: 1/10000 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/10000*x^22+1/10000*y^22+2*x^13*y-2*x^11*y^3-1/5000*x^11*y-x^2*y^2+y^4+1/10000*y^2 k: 11 l: 2 eps: 1/100000 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/100000*x^22+1/100000*y^22+2*x^13*y-2*x^11*y^3-1/50000*x^11*y-x^2*y^2+y^4+1/100000*y^2 k: 11 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/1000000*x^22+1/1000000*y^22+2*x^13*y-2*x^11*y^3-1/500000*x^11*y-x^2*y^2+y^4+1/1000000*y^2 k: 11 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/10000000*x^22+1/10000000*y^22+2*x^13*y-2*x^11*y^3-1/5000000*x^11*y-x^2*y^2+y^4+1/10000000*y^2 k: 11 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^24+x^22*y^2-x^2*y^22+2*y^24+1/100000000*x^22+1/100000000*y^22+2*x^13*y-2*x^11*y^3-1/50000000*x^11*y-x^2*y^2+y^4+1/100000000*y^2 k: 12 l: 2 eps: 1/10 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/10*x^24+1/10*y^24+2*x^14*y-2*x^12*y^3-1/5*x^12*y-x^2*y^2+y^4+1/10*y^2 k: 12 l: 2 eps: 1/100 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/100*x^24+1/100*y^24+2*x^14*y-2*x^12*y^3-1/50*x^12*y-x^2*y^2+y^4+1/100*y^2 k: 12 l: 2 eps: 1/1000 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/1000*x^24+1/1000*y^24+2*x^14*y-2*x^12*y^3-1/500*x^12*y-x^2*y^2+y^4+1/1000*y^2 k: 12 l: 2 eps: 1/10000 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/10000*x^24+1/10000*y^24+2*x^14*y-2*x^12*y^3-1/5000*x^12*y-x^2*y^2+y^4+1/10000*y^2 k: 12 l: 2 eps: 1/100000 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/100000*x^24+1/100000*y^24+2*x^14*y-2*x^12*y^3-1/50000*x^12*y-x^2*y^2+y^4+1/100000*y^2 k: 12 l: 2 eps: 1/1000000 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/1000000*x^24+1/1000000*y^24+2*x^14*y-2*x^12*y^3-1/500000*x^12*y-x^2*y^2+y^4+1/1000000*y^2 k: 12 l: 2 eps: 1/10000000 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/10000000*x^24+1/10000000*y^24+2*x^14*y-2*x^12*y^3-1/5000000*x^12*y-x^2*y^2+y^4+1/10000000*y^2 k: 12 l: 2 eps: 1/100000000 SCA_k_l_eps: -x^26+x^24*y^2-x^2*y^24+2*y^26+1/100000000*x^24+1/100000000*y^24+2*x^14*y-2*x^12*y^3-1/50000000*x^12*y-x^2*y^2+y^4+1/100000000*y^2 ---------------- Challenge 20 a high solitary point close to a one-dimensional component ---------------- SAA_k_l_eps: k: 2 l: 2 eps: 1/10 SAA_k_l_eps: -x^8+x^4*y^4+y^8+2*x^6*y-2*x^5*y^2-2*x^2*y^5-2*x*y^6+x^6-x^4*y^2+4*x^3*y^3+x^2*y^4+y^6-2*x^4*y-2*x*y^4-1/10*x^4+x^2*y^2-1/10*y^4+1/5*x^2*y-1/10*y^2 k: 2 l: 2 eps: 1/100 SAA_k_l_eps: -x^8+x^4*y^4+y^8+2*x^6*y-2*x^5*y^2-2*x^2*y^5-2*x*y^6+x^6-x^4*y^2+4*x^3*y^3+x^2*y^4+y^6-2*x^4*y-2*x*y^4-1/100*x^4+x^2*y^2-1/100*y^4+1/50*x^2*y-1/100*y^2 k: 2 l: 2 eps: 1/1000 SAA_k_l_eps: -x^8+x^4*y^4+y^8+2*x^6*y-2*x^5*y^2-2*x^2*y^5-2*x*y^6+x^6-x^4*y^2+4*x^3*y^3+x^2*y^4+y^6-2*x^4*y-2*x*y^4-1/1000*x^4+x^2*y^2-1/1000*y^4+1/500*x^2*y-1/1000*y^2