////////////////////////////////////////////////////////////// // Modifications for Type VI Graph: Non-generic x^3 and x^4 // ////////////////////////////////////////////////////////////// // The following contains an example for the modified Type VI graph in R^3 (with one genus 1 component with a node). The curve can be visualized by means of projections. Our input is given by the file "TypeVIRefNonGenericx3x4Vertical.sing". We evaluation a at a random integer, so as to get a polynomial in Q(t) with the same valuation for all coefficients. LIB "all.lib"; LIB "poly.lib"; LIB "all.lib"; LIB "tropical.lib"; LIB "elim.lib"; ring rr = (0,t), (x,y,z),lp; // We start by writing the outputs: ring ra = (0,t),(a,x,y,z),lp; poly f2a = -x^5+(t^36+t^32+10*t^30+25*t^28+(2*a-2)*t^18-1)*x^4+(-t^68-10*t^66-25*t^64+(-2*a+2)*t^50+(-20*a+20)*t^48+(-50*a+50)*t^46+(-2*a+1)*t^36+t^32+10*t^30+25*t^28+(6*a+2)*t^18-4)*x^3+((2*a-1)*t^68+(20*a-10)*t^66+(50*a-25)*t^64+(-6*a-2)*t^50+(-60*a-20)*t^48+(-150*a-50)*t^46+(-2*a)*t^36+4*t^32+40*t^30+100*t^28+(4*a+4)*t^18-4)*x^2+y^2+((2*a)*t^68+(20*a)*t^66+(50*a)*t^64+(-4*a-4)*t^50+(-40*a-40)*t^48+(-100*a-100)*t^46+4*t^32+40*t^30+100*t^28)*x; ring r = (0,t),(x,y),dp; map newP2 = ra, 91,x,y,0; poly f2rat = newP2(f2a); // f2rat; // -x5+(t36+t32+10t30+25t28+180t18-1)*x4+(-t68-10t66-25t64-180t50-1800t48-4500t46-181t36+t32+10t30+25t28+548t18-4)*x3+(181t68+1810t66+4525t64-548t50-5480t48-13700t46-182t36+4t32+40t30+100t28+368t18-4)*x2+y2+(182t68+1820t66+4550t64-368t50-3680t48-9200t46+4t32+40t30+100t28)*x // drawTropicalCurve(f2rat,"max"); /////////////////// // XZ-projection // /////////////////// setring(ra); poly g2xz = -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18+t4+2*t2)*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(-2a+1)*t36+t32+10*t30+25*t28+(-2a-2)*t21+(-2a-2)*t20+(-2a-2)*t19+(4a)*t18+4*t3+4*t2+4*t)*x3+(-2*t2-2)*x2y+((2a-1)*t68+(20a-10)*t66+(50a-25)*t64+(-6a-2)*t50+(-60a-20)*t48+(-150a-50)*t46+(2a)*t38+(4a)*t37+4*t32+40*t30+100*t28+(-4a-4)*t20+(-8a-8)*t19+4*t2+8*t)*x2+((2a+2)*t19+(2a+2)*t18-4*t-4)*xy+y2+((2a)*t68+(20a)*t66+(50a)*t64+(-4a-4)*t50+(-40a-40)*t48+(-100a-100)*t46+4*t32+40*t30+100*t28)*x; // Replace y by z for drawing purposes: setring(r); // map newP2 = ra, 91,t,x,y,0; poly g2xzrat = newP2(g2xz); // g2xzrat; // -x5+(t36+t32+10t30+25t28+180t18+t4+2t2)*x4+(-t68-10t66-25t64-180t50-1800t48-4500t46-181t36+t32+10t30+25t28-184t21-184t20-184t19+364t18+4t3+4t2+4t)*x3+(-2t2-2)*x2y+(181t68+1810t66+4525t64-548t50-5480t48-13700t46+182t38+364t37+4t32+40t30+100t28-368t20-736t19+4t2+8t)*x2+(184t19+184t18-4t-4)*xy+y2+(182t68+1820t66+4550t64-368t50-3680t48-9200t46+4t32+40t30+100t28)*x // drawTropicalCurve(g2xzrat,"max"); ///////////////////// // Z_4Y-projection // ///////////////////// setring(ra); poly g2z4y = -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18+(-10a-1))*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(6a+1)*t36+(8a+1)*t32+(80a+10)*t30+(200a+25)*t28+(-10a-14)*t18+(-8a+36))*x3+((-4a-1)*t68+(-40a-10)*t66+(-100a-25)*t64+(6a+10)*t50+(60a+100)*t48+(150a+250)*t46+(4a-12)*t36+(6a-20)*t32+(60a-200)*t30+(150a-500)*t28+(-32a+16)*t18+(56a+20))*x2+y2+((-2a+4)*t68+(-20a+40)*t66+(-50a+100)*t64+(12a-4)*t50+(120a-40)*t48+(300a-100)*t46+(-8a-4)*t36+(-16a-8)*t32+(-160a-80)*t30+(-400a-200)*t28+(8a+24)*t18+(16a-32))*x; setring(r); // map newP2 = ra, 91,t,x,y,0; poly g2z4yrat = newP2(g2z4y); // g2z4yrat; // -x5+(t36+t32+10t30+25t28+180t18-911)*x4+(-t68-10t66-25t64-180t50-1800t48-4500t46+547t36+729t32+7290t30+18225t28-924t18-692)*x3+(-365t68-3650t66-9125t64+556t50+5560t48+13900t46+352t36+526t32+5260t30+13150t28-2896t18+5116)*x2+y2+(-178t68-1780t66-4450t64+1088t50+10880t48+27200t46-732t36-1464t32-14640t30-36600t28+752t18+1424)*x // drawTropicalCurve(g2z4yrat,"max"); ///////////////////// // Z_4Z-projection // ///////////////////// setring(ra); poly g2z4z = -x5+(t36+t32+10*t30+25*t28+(2a-2)*t18+t4+2*t2+(-10a))*x4+(-t68-10*t66-25*t64+(-2a+2)*t50+(-20a+20)*t48+(-50a+50)*t46+(6a+1)*t36+(8a+1)*t32+(80a+10)*t30+(200a+25)*t28+(-2a-2)*t21+(-2a-2)*t20+(-2a-2)*t19+(-12a-16)*t18+(8a)*t4+4*t3+(16a+4)*t2+4*t+40)*x3+(-2*t2-2)*x2y+((-4a-1)*t68+(-40a-10)*t66+(-100a-25)*t64+(6a+10)*t50+(60a+100)*t48+(150a+250)*t46+(2a)*t38+(4a)*t37+(6a-12)*t36+(6a-20)*t32+(60a-200)*t30+(150a-500)*t28+(-12a+12)*t21+(-16a+8)*t20+(-20a+4)*t19+(-48a+24)*t18-24*t4+(24a)*t3+(24a-44)*t2+(24a+8)*t+(80a))*x2+((2a+2)*t19+(2a+2)*t18+(-8a)*t2-4*t+(-8a-4))*xy+y2+((-2a+4)*t68+(-20a+40)*t66+(-50a+100)*t64+(12a-4)*t50+(120a-40)*t48+(300a-100)*t46-8*t38-16*t37+(-8a-12)*t36+(-16a-8)*t32+(-160a-80)*t30+(-400a-200)*t28+(24a+24)*t21+(8a+40)*t20+(-8a+56)*t19+(16a+64)*t18+(-32a)*t4-48*t3+(-48a-48)*t2+(32a-48)*t-80)*x+((4a-4)*t19+(4a-4)*t18+8*t2+(-8a)*t+(-8a+8))*y+((-8a)*t38+(-16a)*t37+(-8a)*t36+(16a-16)*t21+(32a)*t20+(48a+16)*t19+(32a)*t18+16*t4+(-32a)*t3+(-32a+16)*t2+(-32a-32)*t+(-32a)); setring(r); // map newP2 = ra, 91,t,x,y,0; poly g2z4zrat = newP2(g2z4z); // g2z4zrat; // -x5+(t36+t32+10t30+25t28+180t18+t4+2t2-910)*x4+(-t68-10t66-25t64-180t50-1800t48-4500t46+547t36+729t32+7290t30+18225t28-184t21-184t20-184t19-1108t18+728t4+4t3+1460t2+4t+40)*x3+(-2t2-2)*x2y+(-365t68-3650t66-9125t64+556t50+5560t48+13900t46+182t38+364t37+534t36+526t32+5260t30+13150t28-1080t21-1448t20-1816t19-4344t18-24t4+2184t3+2140t2+2192t+7280)*x2+(184t19+184t18-728t2-4t-732)*xy+y2+(-178t68-1780t66-4450t64+1088t50+10880t48+27200t46-8t38-16t37-740t36-1464t32-14640t30-36600t28+2208t21+768t20-672t19+1520t18-2912t4-48t3-4416t2+2864t-80)*x+(360t19+360t18+8t2-728t-720)*y+(-728t38-1456t37-728t36+1440t21+2912t20+4384t19+2912t18+16t4-2912t3-2896t2-2944t-2912) // drawTropicalCurve(g2z4zrat,"max"); ///////////////////// // Z_3Y-projection // ///////////////////// setring(ra); poly h2 = -x5+(-4*t36+t32+10*t30+25*t28+(-8a+8)*t18+(10a-1))*x4+(-6*t72+3*t68+30*t66+75*t64+(-24a+24)*t54+(6a-6)*t50+(60a-60)*t48+(150a-150)*t46+(78a-3)*t36+(-8a+1)*t32+(-80a+10)*t30+(-200a+25)*t28+(-66a-54)*t18+(8a+36))*x3+(-4*t108+3*t104+30*t102+75*t100+(-24a+24)*t90+(12a-12)*t86+(120a-120)*t84+(300a-300)*t82+(126a-3)*t72+(-40a+2)*t68+(-400a+20)*t66+(-1000a+50)*t64+(-196a-172)*t54+(36a+28)*t50+(360a+280)*t48+(900a+700)*t46+(40a+312)*t36+(-6a-20)*t32+(-60a-200)*t30+(-150a-500)*t28+(112a-176)*t18+(-56a+20))*x2+y2+(-t144+t140+10*t138+25*t136+(-8a+8)*t126+(6a-6)*t122+(60a-60)*t120+(150a-150)*t118+(58a-1)*t108+(-32a+1)*t104+(-320a+10)*t102+(-800a+25)*t100+(-130a-118)*t90+(52a+44)*t86+(520a+440)*t84+(1300a+1100)*t82+(32a+340)*t72+(-14a-84)*t68+(-140a-840)*t66+(-350a-2100)*t64+(256a-352)*t54+(-28a+52)*t50+(-280a+520)*t48+(-700a+1300)*t46+(-344a+84)*t36+(16a-8)*t32+(160a-80)*t30+(400a-200)*t28+(152a+72)*t18+(-16a-32))*x; setring(r); // map newP2 = ra, 91,t,x,y,0; poly h2rat = newP2(h2); // h2rat; // -x5+(-4t36+t32+10t30+25t28-720t18+909)*x4+(-6t72+3t68+30t66+75t64-2160t54+540t50+5400t48+13500t46+7095t36-727t32-7270t30-18175t28-6060t18+764)*x3+(-4t108+3t104+30t102+75t100-2160t90+1080t86+10800t84+27000t82+11463t72-3638t68-36380t66-90950t64-18008t54+3304t50+33040t48+82600t46+3952t36-566t32-5660t30-14150t28+10016t18-5076)*x2+y2+(-t144+t140+10t138+25t136-720t126+540t122+5400t120+13500t118+5277t108-2911t104-29110t102-72775t100-11948t90+4776t86+47760t84+119400t82+3252t72-1358t68-13580t66-33950t64+22944t54-2496t50-24960t48-62400t46-31220t36+1448t32+14480t30+36200t28+13904t18-1488)*x // drawTropicalCurve(h2rat,"max"); ///////////////////// // Z_3Z-projection // ///////////////////// setring(ra); poly gz3z = -x5+(-4*t36+t32+10*t30+25*t28+(-8a+8)*t18+t4+2*t2+(10a))*x4+(-6*t72+3*t68+30*t66+75*t64+(-24a+24)*t54+(6a-6)*t50+(60a-60)*t48+(150a-150)*t46+4*t40+8*t38+(78a+1)*t36+(-8a+1)*t32+(-80a+10)*t30+(-200a+25)*t28+(8a-8)*t22+(-2a-2)*t21+(14a-18)*t20+(-2a-2)*t19+(-60a-64)*t18+(-8a)*t4+4*t3+(-16a+4)*t2+4*t+40)*x3+(-2*t2-2)*x2y+(-4*t108+3*t104+30*t102+75*t100+(-24a+24)*t90+(12a-12)*t86+(120a-120)*t84+(300a-300)*t82+6*t76+12*t74+(126a+3)*t72+(-40a+2)*t68+(-400a+20)*t66+(-1000a+50)*t64+(24a-24)*t58+(-6a-6)*t57+(42a-54)*t56+(-6a-6)*t55+(-178a-202)*t54+(36a+28)*t50+(360a+280)*t48+(900a+700)*t46+(-72a)*t40+36*t39+(-142a+36)*t38+(4a+36)*t37+(-30a+348)*t36+(-6a-20)*t32+(-60a-200)*t30+(-150a-500)*t28+(48a+48)*t22+(36a-36)*t21+(128a+56)*t20+(28a-44)*t19+(192a-168)*t18-24*t4+(-24a)*t3+(-24a-44)*t2+(-24a+8)*t+(-80a))*x2+(-4*t38-4*t36+(-8a+8)*t20+(2a+2)*t19+(-6a+10)*t18+(8a)*t2-4*t+(8a-4))*xy+y2+(-t144+t140+10*t138+25*t136+(-8a+8)*t126+(6a-6)*t122+(60a-60)*t120+(150a-150)*t118+4*t112+8*t110+(58a+3)*t108+(-32a+1)*t104+(-320a+10)*t102+(-800a+25)*t100+(24a-24)*t94+(-6a-6)*t93+(42a-54)*t92+(-6a-6)*t91+(-112a-148)*t90+(52a+44)*t86+(520a+440)*t84+(1300a+1100)*t82+(-120a)*t76+60*t75+(-236a+60)*t74+(8a+60)*t73+(-84a+400)*t72+(-14a-84)*t68+(-140a-840)*t66+(-350a-2100)*t64+(160a+160)*t58+(120a-120)*t57+(424a+184)*t56+(88a-152)*t55+(520a-328)*t54+(-28a+52)*t50+(-280a+520)*t48+(-700a+1300)*t46-240*t40+(-240a)*t39+(-240a-432)*t38+(-240a+96)*t37+(-584a-108)*t36+(16a-8)*t32+(160a-80)*t30+(400a-200)*t28+(-96a+96)*t22+(120a+120)*t21+(-40a+280)*t20+(184a+56)*t19+(208a+256)*t18+(32a)*t4-48*t3+(48a-48)*t2+(-32a-48)*t-80)*x+(-2*t74-2*t72+(-8a+8)*t56+(2a+2)*t55+(-6a+10)*t54+(24a)*t38-12*t37+(24a-12)*t36+(-16a-16)*t20+(-12a+12)*t19+(-28a-4)*t18+8*t2+(8a)*t+(8a+8))*y+(t148+2*t146+t144+(8a-8)*t130+(-2a-2)*t129+(14a-18)*t128+(-2a-2)*t127+(6a-10)*t126+(-56a)*t112+28*t111+(-110a+28)*t110+(4a+28)*t109+(-54a+28)*t108+(112a+112)*t94+(84a-84)*t93+(296a+128)*t92+(60a-108)*t91+(184a+16)*t90-280*t76+(-280a)*t75+(-280a-500)*t74+(-280a+120)*t73+(-280a-220)*t72+(-224a+224)*t58+(280a+280)*t57+(-88a+648)*t56+(440a+120)*t55+(136a+424)*t54+(224a)*t40-336*t39+(328a-336)*t38+(-240a-336)*t37+(104a-336)*t36+(-64a-64)*t22+(-112a+112)*t21+(-192a+32)*t20+(-16a+208)*t19+(-128a+96)*t18+16*t4+(32a)*t3+(32a+16)*t2+(32a-32)*t+(32a)); setring(r); // map newP2 = ra, 91,t,x,y,0; poly gz3zrat = newP2(gz3z); // gz3zrat; // -x5+(-4t36+t32+10t30+25t28-720t18+t4+2t2+910)*x4+(-6t72+3t68+30t66+75t64-2160t54+540t50+5400t48+13500t46+4t40+8t38+7099t36-727t32-7270t30-18175t28+720t22-184t21+1256t20-184t19-5524t18-728t4+4t3-1452t2+4t+40)*x3+(-2t2-2)*x2y+(-4t108+3t104+30t102+75t100-2160t90+1080t86+10800t84+27000t82+6t76+12t74+11469t72-3638t68-36380t66-90950t64+2160t58-552t57+3768t56-552t55-16400t54+3304t50+33040t48+82600t46-6552t40+36t39-12886t38+400t37-2382t36-566t32-5660t30-14150t28+4416t22+3240t21+11704t20+2504t19+17304t18-24t4-2184t3-2228t2-2176t-7280)*x2+(-4t38-4t36-720t20+184t19-536t18+728t2-4t+724)*xy+y2+(-t144+t140+10t138+25t136-720t126+540t122+5400t120+13500t118+4t112+8t110+5281t108-2911t104-29110t102-72775t100+2160t94-552t93+3768t92-552t91-10340t90+4776t86+47760t84+119400t82-10920t76+60t75-21416t74+788t73-7244t72-1358t68-13580t66-33950t64+14720t58+10800t57+38768t56+7856t55+46992t54-2496t50-24960t48-62400t46-240t40-21840t39-22272t38-21744t37-53252t36+1448t32+14480t30+36200t28-8640t22+11040t21-3360t20+16800t19+19184t18+2912t4-48t3+4320t2-2960t-80)*x+(-2t74-2t72-720t56+184t55-536t54+2184t38-12t37+2172t36-1472t20-1080t19-2552t18+8t2+728t+736)*y+(t148+2t146+t144+720t130-184t129+1256t128-184t127+536t126-5096t112+28t111-9982t110+392t109-4886t108+10304t94+7560t93+27064t92+5352t91+16760t90-280t76-25480t75-25980t74-25360t73-25700t72-20160t58+25760t57-7360t56+40160t55+12800t54+20384t40-336t39+29512t38-22176t37+9128t36-5888t22-10080t21-17440t20-1248t19-11552t18+16t4+2912t3+2928t2+2880t+2912) // drawTropicalCurve(gz3zrat,"max"); /////////////////// // ZY-projection // /////////////////// setring(ra); ring rra = 0, (t, a,x,y), lp; // we take the coefficients from each monomial in the yz-elimination ideal (were we've replaced the variable y by x and z by y for visualization // We look at the above coefficients and keep the lowest t-term (after Singular reorders the coefficients). poly c50 = 1; setring(ra); poly cc50 = 1; setring(rra); poly c41 = -5; setring(ra); poly cc41 = -5; setring(rra); poly c32 = 10; setring(ra); poly cc32 = 10; setring(rra); poly c23 = -10; setring(ra); poly cc23 = -10; setring(rra); poly c14 = 5; setring(ra); poly cc14 = 5; setring(rra); poly c05 = -1; setring(ra); poly cc05 = -1; setring(rra); poly c40 = (4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+4t24-5t23+7t22-10t21+10t20+12t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+2t42+6t40+8t38+6t37+34t36+116t34+2t33+214t32+20t31+190t30+50t29+100t28-4t24-5t23-17t22-10t21-14t20-8t19-4t18+t10+5t8+8t6+10t5+14t4+20t3+12t2+8t); // c40; // t74+t72+t66+21t64+170t62+650t60+1125t58+4t56a+621t56-t55a-t55+3t54a-5t54-t51a-t51-t50a-t50-10t49a-10t49-10t48a-10t48-25t47a-25t47-25t46a-25t46+2t42+6t40-12t38a+8t38+6t37-12t36a+34t36+116t34+2t33+214t32+20t31+190t30+50t29+100t28+4t24a-4t24-5t23a-5t23+7t22a-17t22-10t21a-10t21+10t20a-14t20-8t19+12t18a-4t18+t10+5t8+8t6+10t5+14t4+20t3+12t2+8t setring(ra); poly cc40 = 8*t; setring(rra); poly c31 = (-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-8t24+10t23-14t22+20t21-36t20-10t19-50t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-4t42-12t40-16t38-24t37-80t36-232t34-8t33-432t32-80t31-420t30-200t29-300t28+8t24+10t23+34t22+20t21+12t20+22t19-2t18+4t6-20t5-8t4-40t3-12t+20); // c31; // -4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-16t56a-2484t56+4t55a+4t55-12t54a+20t54+4t51a+4t51+4t50a+4t50+40t49a+40t49+40t48a+40t48+100t47a+100t47+100t46a+100t46-4t42-12t40+48t38a-16t38-24t37+48t36a-80t36-232t34-8t33-432t32-80t31-420t30-200t29-300t28-8t24a+8t24+10t23a+10t23-14t22a+34t22+20t21a+20t21-36t20a+12t20-10t19a+22t19-50t18a-2t18+4t6-20t5-8t4-40t3-12t+20 setring(ra); poly cc31 = 20; setring(rra); poly c22 = (24t56-6t55+18t54-6t51-6t50-60t49-60t48-150t47-150t46-72t38-72t36+4t24-5t23+7t22-10t21+50t20+25t19+77t18)*a+(6t74+6t72+6t66+126t64+1020t62+3900t60+6750t58+3726t56-6t55-30t54-6t51-6t50-60t49-60t48-150t47-150t46+2t42+6t40+8t38+36t37+64t36+116t34+12t33+224t32+120t31+290t30+300t29+350t28-4t24-5t23-17t22-10t21+26t20-23t19+21t18-2t6+10t5+4t4+20t3-28t2-2t-46); // c22; // 6t74+6t72+6t66+126t64+1020t62+3900t60+6750t58+24t56a+3726t56-6t55a-6t55+18t54a-30t54-6t51a-6t51-6t50a-6t50-60t49a-60t49-60t48a-60t48-150t47a-150t47-150t46a-150t46+2t42+6t40-72t38a+8t38+36t37-72t36a+64t36+116t34+12t33+224t32+120t31+290t30+300t29+350t28+4t24a-4t24-5t23a-5t23+7t22a-17t22-10t21a-10t21+50t20a+26t20+25t19a-23t19+77t18a+21t18-2t6+10t5+4t4+20t3-28t2-2t-46 setring(ra); poly cc22 = -46; setring(rra); poly c13 = (-16t56+4t55-12t54+4t51+4t50+40t49+40t48+100t47+100t46+48t38+48t36-32t20-20t19-52t18)*a+(-4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-2484t56+4t55+20t54+4t51+4t50+40t49+40t48+100t47+100t46-24t37-24t36-8t33-8t32-80t31-80t30-200t29-200t28-32t20+12t19-20t18+28t2+8t+36); // c13; // -4t74-4t72-4t66-84t64-680t62-2600t60-4500t58-16t56a-2484t56+4t55a+4t55-12t54a+20t54+4t51a+4t51+4t50a+4t50+40t49a+40t49+40t48a+40t48+100t47a+100t47+100t46a+100t46+48t38a-24t37+48t36a-24t36-8t33-8t32-80t31-80t30-200t29-200t28-32t20a-32t20-20t19a+12t19-52t18a-20t18+28t2+8t+36 setring(ra); poly cc13 = 36; setring(rra); poly c04 = (4t56-t55+3t54-t51-t50-10t49-10t48-25t47-25t46-12t38-12t36+8t20+5t19+13t18)*a+(t74+t72+t66+21t64+170t62+650t60+1125t58+621t56-t55-5t54-t51-t50-10t49-10t48-25t47-25t46+6t37+6t36+2t33+2t32+20t31+20t30+50t29+50t28+8t20-3t19+5t18-7t2-2t-9); // c04; // t74+t72+t66+21t64+170t62+650t60+1125t58+4t56a+621t56-t55a-t55+3t54a-5t54-t51a-t51-t50a-t50-10t49a-10t49-10t48a-10t48-25t47a-25t47-25t46a-25t46-12t38a+6t37-12t36a+6t36+2t33+2t32+20t31+20t30+50t29+50t28+8t20a+8t20+5t19a-3t19+13t18a+5t18-7t2-2t-9 setring(ra); poly cc04 = -9; setring(rra); poly c30 = (-t125-t124-11t123-7t122-36t121+52t120-46t119+718t118-170t117+3110t116-650t115+6450t114-1125t113+5875t112-625t111+1875t110+2t106+4t105+10t104+40t103-194t102+100t101-2242t100-9840t98-21300t96-21000t94+2t93-7498t92+38t91+38t90+194t89+186t88+522t87+458t86+800t85+856t84+280t83+2008t82+850t81+7410t80+3250t79+17442t78+5609t77+19597t76+3113t75+8055t74-16t73-378t72-232t71-1162t70-1180t69-2074t68-2400t67-2590t66-1500t65-1350t64+3t61+35t60+83t59+135t58+105t57+225t56-139t55+833t54-463t53+2061t52+159t51+2783t50+1690t49+2630t48+1600t47+1200t46+4t44-36t43-12t42-152t41-204t40-276t39-148t38-64t37+40t36-8t26+48t25-32t24+108t23+108t22+188t21+116t20+48t19-16t18)*a+(t140+22t138+191t136+820t134+1775t132+1750t130+625t128-t125-t124-11t123-15t122-36t121-124t120-46t119-810t118-170t117-3450t116-650t115-7750t114-1125t113-8125t112-625t111-3125t110+10t107+10t106+110t105+110t104+356t103+356t102+376t101+376t100+1020t99+1020t98+3900t97+3900t96+6750t95+6750t94+3756t93+3756t92+42t91+42t90+154t89+146t88+82t87+18t86-608t85-552t84-888t83+840t82-510t81+6050t80-1950t79+12250t78-3375t77+10624t76-1903t75+3115t74-252t73-109t72-1044t71-696t70-1868t69-1313t68-1132t67-766t66+508t65-1279t64-340t63-6080t62-1309t61-13702t60-2223t59-14445t58-1197t57-5484t56+205t55+641t54+929t53+2125t52+2671t51+3623t50+3410t49+3230t48+1400t47+1200t46+18t43-62t42-106t41-194t40-198t39-266t38-74t37-718t36-50t35-1910t34-998t33-2786t32-1980t31-2360t30-1200t29-900t28-8t26+24t25+8t24+164t23+228t22+332t21+212t20+144t19+8t8-24t7+24t6-80t5-88t4-152t3-104t2-64t); // c30; // t140+22t138+191t136+820t134+1775t132+1750t130+625t128-t125a-t125-t124a-t124-11t123a-11t123-7t122a-15t122-36t121a-36t121+52t120a-124t120-46t119a-46t119+718t118a-810t118-170t117a-170t117+3110t116a-3450t116-650t115a-650t115+6450t114a-7750t114-1125t113a-1125t113+5875t112a-8125t112-625t111a-625t111+1875t110a-3125t110+10t107+2t106a+10t106+4t105a+110t105+10t104a+110t104+40t103a+356t103-194t102a+356t102+100t101a+376t101-2242t100a+376t100+1020t99-9840t98a+1020t98+3900t97-21300t96a+3900t96+6750t95-21000t94a+6750t94+2t93a+3756t93-7498t92a+3756t92+38t91a+42t91+38t90a+42t90+194t89a+154t89+186t88a+146t88+522t87a+82t87+458t86a+18t86+800t85a-608t85+856t84a-552t84+280t83a-888t83+2008t82a+840t82+850t81a-510t81+7410t80a+6050t80+3250t79a-1950t79+17442t78a+12250t78+5609t77a-3375t77+19597t76a+10624t76+3113t75a-1903t75+8055t74a+3115t74-16t73a-252t73-378t72a-109t72-232t71a-1044t71-1162t70a-696t70-1180t69a-1868t69-2074t68a-1313t68-2400t67a-1132t67-2590t66a-766t66-1500t65a+508t65-1350t64a-1279t64-340t63-6080t62+3t61a-1309t61+35t60a-13702t60+83t59a-2223t59+135t58a-14445t58+105t57a-1197t57+225t56a-5484t56-139t55a+205t55+833t54a+641t54-463t53a+929t53+2061t52a+2125t52+159t51a+2671t51+2783t50a+3623t50+1690t49a+3410t49+2630t48a+3230t48+1600t47a+1400t47+1200t46a+1200t46+4t44a-36t43a+18t43-12t42a-62t42-152t41a-106t41-204t40a-194t40-276t39a-198t39-148t38a-266t38-64t37a-74t37+40t36a-718t36-50t35-1910t34-998t33-2786t32-1980t31-2360t30-1200t29-900t28-8t26a-8t26+48t25a+24t25-32t24a+8t24+108t23a+164t23+108t22a+228t22+188t21a+332t21+116t20a+212t20+48t19a+144t19-16t18a+8t8-24t7+24t6-80t5-88t4-152t3-104t2-64t setring(ra); poly cc30 = -64*t; setring(rra); poly c21 = (3t125+3t124+33t123+21t122+108t121-156t120+138t119-2154t118+510t117-9330t116+1950t115-19350t114+3375t113-17625t112+1875t111-5625t110-6t106-12t105-30t104-120t103+582t102-300t101+6726t100+29520t98+63900t96+63000t94+22500t92-36t91-36t90-234t89-210t88-930t87-738t86-1890t85-2058t84-690t83-5874t82-2550t81-22230t80-9750t79-52342t78-16859t77-58847t76-9403t75-24341t74-16t73+342t72+312t71+1246t70+2068t69+2998t68+5280t67+5530t66+3700t65+3450t64-3t61-35t60-83t59-111t58+9t57-47t56+285t55-679t54+417t53-2131t52-713t51-3553t50-3780t49-5080t48-3950t47-2950t46-4t44+36t43+12t42+152t41+132t40+196t39-172t38-208t37-288t36+8t26-48t25+32t24-108t23-60t22-180t21+68t20+120t19+152t18)*a+(-3t140-66t138-573t136-2460t134-5325t132-5250t130-1875t128+3t125+3t124+33t123+45t122+108t121+372t120+138t119+2430t118+510t117+10350t116+1950t115+23250t114+3375t113+24375t112+1875t111+9375t110-30t107-30t106-330t105-330t104-1068t103-1068t102-1128t101-1128t100-3060t99-3060t98-11700t97-11700t96-20250t95-20250t94-11262t93-11262t92-48t91-48t90-114t89-90t88+390t87+582t86+2334t85+2166t84+2814t83-2370t82+1530t81-18150t80+5850t79-36750t78+10125t77-31868t76+5673t75-9325t74+288t73+143t72+1044t71+656t70+1788t69+887t68+336t67-322t66-2424t65+3037t64+1020t63+18240t62+3909t61+41152t60+6723t59+43421t58+3731t57+16672t56-267t55-679t54-975t53-2163t52-3161t51-4041t50-4860t49-4560t48-2150t47-2150t46-18t43+62t42+106t41+194t40+74t39+182t38+30t37+634t36+78t35+1946t34+1322t33+3182t32+3120t31+3620t30+2300t29+1800t28+8t26-24t25-8t24-164t23-180t22-244t21+20t20+40t19+184t18-8t8+24t7-24t6+80t5+72t4+120t3+8t2-32t-80); // c21; // -3t140-66t138-573t136-2460t134-5325t132-5250t130-1875t128+3t125a+3t125+3t124a+3t124+33t123a+33t123+21t122a+45t122+108t121a+108t121-156t120a+372t120+138t119a+138t119-2154t118a+2430t118+510t117a+510t117-9330t116a+10350t116+1950t115a+1950t115-19350t114a+23250t114+3375t113a+3375t113-17625t112a+24375t112+1875t111a+1875t111-5625t110a+9375t110-30t107-6t106a-30t106-12t105a-330t105-30t104a-330t104-120t103a-1068t103+582t102a-1068t102-300t101a-1128t101+6726t100a-1128t100-3060t99+29520t98a-3060t98-11700t97+63900t96a-11700t96-20250t95+63000t94a-20250t94-11262t93+22500t92a-11262t92-36t91a-48t91-36t90a-48t90-234t89a-114t89-210t88a-90t88-930t87a+390t87-738t86a+582t86-1890t85a+2334t85-2058t84a+2166t84-690t83a+2814t83-5874t82a-2370t82-2550t81a+1530t81-22230t80a-18150t80-9750t79a+5850t79-52342t78a-36750t78-16859t77a+10125t77-58847t76a-31868t76-9403t75a+5673t75-24341t74a-9325t74-16t73a+288t73+342t72a+143t72+312t71a+1044t71+1246t70a+656t70+2068t69a+1788t69+2998t68a+887t68+5280t67a+336t67+5530t66a-322t66+3700t65a-2424t65+3450t64a+3037t64+1020t63+18240t62-3t61a+3909t61-35t60a+41152t60-83t59a+6723t59-111t58a+43421t58+9t57a+3731t57-47t56a+16672t56+285t55a-267t55-679t54a-679t54+417t53a-975t53-2131t52a-2163t52-713t51a-3161t51-3553t50a-4041t50-3780t49a-4860t49-5080t48a-4560t48-3950t47a-2150t47-2950t46a-2150t46-4t44a+36t43a-18t43+12t42a+62t42+152t41a+106t41+132t40a+194t40+196t39a+74t39-172t38a+182t38-208t37a+30t37-288t36a+634t36+78t35+1946t34+1322t33+3182t32+3120t31+3620t30+2300t29+1800t28+8t26a+8t26-48t25a-24t25+32t24a-8t24-108t23a-164t23-60t22a-180t22-180t21a-244t21+68t20a+20t20+120t19a+40t19+152t18a+184t18-8t8+24t7-24t6+80t5+72t4+120t3+8t2-32t-80 setring(ra); poly cc21 = -80; setring(rra); poly c12 = (-3t125-3t124-33t123-21t122-108t121+156t120-138t119+2154t118-510t117+9330t116-1950t115+19350t114-3375t113+17625t112-1875t111+5625t110+6t106+12t105+30t104+120t103-582t102+300t101-6726t100-29520t98-63900t96-63000t94-3t93-22503t92-3t91-3t90+60t89+36t88+612t87+420t86+1635t85+1803t84+615t83+5799t82+2550t81+22230t80+9750t79+52350t78+16875t77+58875t76+9435t75+24429t74+48t73+54t72-120t71-126t70-1332t69-1386t68-4320t67-4410t66-3300t65-3150t64-36t58-171t57-267t56-219t55-231t54+69t53+105t52+831t51+1155t50+3135t49+3675t48+3525t47+2625t46+108t40+120t39+480t38+408t37+372t36-72t22-12t21-276t20-252t19-204t18)*a+(3t140+66t138+573t136+2460t134+5325t132+5250t130+1875t128-3t125-3t124-33t123-45t122-108t121-372t120-138t119-2430t118-510t117-10350t116-1950t115-23250t114-3375t113-24375t112-1875t111-9375t110+30t107+30t106+330t105+330t104+1068t103+1068t102+1128t101+1128t100+3060t99+3060t98+11700t97+11700t96+20250t95+20250t94+11259t93+11259t92+9t91+9t90-60t89-84t88-708t87-900t86-2589t85-2421t84-2889t83+2295t82-1530t81+18150t80-5850t79+36750t78-10125t77+31866t76-5655t75+9315t74-54t73-51t72+60t70+120t69+639t68+1194t67+1632t66+2874t65-2637t64-1020t63-18240t62-3900t61-41175t60-6750t59-43464t58-3801t57-16782t56+93t55+57t54+69t53+57t52+735t51+627t50+2175t49+1995t48+1125t47+1425t46+186t39+126t38+66t37+126t36-42t35-54t34-486t33-594t32-1710t31-1890t30-1650t29-1350t28-72t22-132t21-348t20-276t19-276t18+24t4+48t3+144t2+144t+120); // c12; // 3t140+66t138+573t136+2460t134+5325t132+5250t130+1875t128-3t125a-3t125-3t124a-3t124-33t123a-33t123-21t122a-45t122-108t121a-108t121+156t120a-372t120-138t119a-138t119+2154t118a-2430t118-510t117a-510t117+9330t116a-10350t116-1950t115a-1950t115+19350t114a-23250t114-3375t113a-3375t113+17625t112a-24375t112-1875t111a-1875t111+5625t110a-9375t110+30t107+6t106a+30t106+12t105a+330t105+30t104a+330t104+120t103a+1068t103-582t102a+1068t102+300t101a+1128t101-6726t100a+1128t100+3060t99-29520t98a+3060t98+11700t97-63900t96a+11700t96+20250t95-63000t94a+20250t94-3t93a+11259t93-22503t92a+11259t92-3t91a+9t91-3t90a+9t90+60t89a-60t89+36t88a-84t88+612t87a-708t87+420t86a-900t86+1635t85a-2589t85+1803t84a-2421t84+615t83a-2889t83+5799t82a+2295t82+2550t81a-1530t81+22230t80a+18150t80+9750t79a-5850t79+52350t78a+36750t78+16875t77a-10125t77+58875t76a+31866t76+9435t75a-5655t75+24429t74a+9315t74+48t73a-54t73+54t72a-51t72-120t71a-126t70a+60t70-1332t69a+120t69-1386t68a+639t68-4320t67a+1194t67-4410t66a+1632t66-3300t65a+2874t65-3150t64a-2637t64-1020t63-18240t62-3900t61-41175t60-6750t59-36t58a-43464t58-171t57a-3801t57-267t56a-16782t56-219t55a+93t55-231t54a+57t54+69t53a+69t53+105t52a+57t52+831t51a+735t51+1155t50a+627t50+3135t49a+2175t49+3675t48a+1995t48+3525t47a+1125t47+2625t46a+1425t46+108t40a+120t39a+186t39+480t38a+126t38+408t37a+66t37+372t36a+126t36-42t35-54t34-486t33-594t32-1710t31-1890t30-1650t29-1350t28-72t22a-72t22-12t21a-132t21-276t20a-348t20-252t19a-276t19-204t18a-276t18+24t4+48t3+144t2+144t+120 setring(ra); poly cc12 = 120; setring(rra); poly c03 = (t125+t124+11t123+7t122+36t121-52t120+46t119-718t118+170t117-3110t116+650t115-6450t114+1125t113-5875t112+625t111-1875t110-2t106-4t105-10t104-40t103+194t102-100t101+2242t100+9840t98+21300t96+21000t94+t93+7501t92+t91+t90-20t89-12t88-204t87-140t86-545t85-601t84-205t83-1933t82-850t81-7410t80-3250t79-17450t78-5625t77-19625t76-3145t75-8143t74-16t73-18t72+40t71+42t70+444t69+462t68+1440t67+1470t66+1100t65+1050t64+12t58+57t57+89t56+73t55+77t54-23t53-35t52-277t51-385t50-1045t49-1225t48-1175t47-875t46-36t40-40t39-160t38-136t37-124t36+24t22+4t21+92t20+84t19+68t18)*a+(-t140-22t138-191t136-820t134-1775t132-1750t130-625t128+t125+t124+11t123+15t122+36t121+124t120+46t119+810t118+170t117+3450t116+650t115+7750t114+1125t113+8125t112+625t111+3125t110-10t107-10t106-110t105-110t104-356t103-356t102-376t101-376t100-1020t99-1020t98-3900t97-3900t96-6750t95-6750t94-3753t93-3753t92-3t91-3t90+20t89+28t88+236t87+300t86+863t85+807t84+963t83-765t82+510t81-6050t80+1950t79-12250t78+3375t77-10622t76+1885t75-3105t74+18t73+17t72-20t70-40t69-213t68-398t67-544t66-958t65+879t64+340t63+6080t62+1300t61+13725t60+2250t59+14488t58+1267t57+5594t56-31t55-19t54-23t53-19t52-245t51-209t50-725t49-665t48-375t47-475t46-62t39-42t38-22t37-42t36+14t35+18t34+162t33+198t32+570t31+630t30+550t29+450t28+24t22+44t21+116t20+92t19+92t18-8t4-16t3-48t2-48t-40); // c03; // -t140-22t138-191t136-820t134-1775t132-1750t130-625t128+t125a+t125+t124a+t124+11t123a+11t123+7t122a+15t122+36t121a+36t121-52t120a+124t120+46t119a+46t119-718t118a+810t118+170t117a+170t117-3110t116a+3450t116+650t115a+650t115-6450t114a+7750t114+1125t113a+1125t113-5875t112a+8125t112+625t111a+625t111-1875t110a+3125t110-10t107-2t106a-10t106-4t105a-110t105-10t104a-110t104-40t103a-356t103+194t102a-356t102-100t101a-376t101+2242t100a-376t100-1020t99+9840t98a-1020t98-3900t97+21300t96a-3900t96-6750t95+21000t94a-6750t94+t93a-3753t93+7501t92a-3753t92+t91a-3t91+t90a-3t90-20t89a+20t89-12t88a+28t88-204t87a+236t87-140t86a+300t86-545t85a+863t85-601t84a+807t84-205t83a+963t83-1933t82a-765t82-850t81a+510t81-7410t80a-6050t80-3250t79a+1950t79-17450t78a-12250t78-5625t77a+3375t77-19625t76a-10622t76-3145t75a+1885t75-8143t74a-3105t74-16t73a+18t73-18t72a+17t72+40t71a+42t70a-20t70+444t69a-40t69+462t68a-213t68+1440t67a-398t67+1470t66a-544t66+1100t65a-958t65+1050t64a+879t64+340t63+6080t62+1300t61+13725t60+2250t59+12t58a+14488t58+57t57a+1267t57+89t56a+5594t56+73t55a-31t55+77t54a-19t54-23t53a-23t53-35t52a-19t52-277t51a-245t51-385t50a-209t50-1045t49a-725t49-1225t48a-665t48-1175t47a-375t47-875t46a-475t46-36t40a-40t39a-62t39-160t38a-42t38-136t37a-22t37-124t36a-42t36+14t35+18t34+162t33+198t32+570t31+630t30+550t29+450t28+24t22a+24t22+4t21a+44t21+92t20a+116t20+84t19a+92t19+68t18a+92t18-8t4-16t3-48t2-48t-40 setring(ra); poly cc03 = -40; setring(rra); poly c20 = (-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146-2t144-4t143-24t142-24t141-74t140+296t139+276t138+3636t137+3388t136+15720t135+14760t134+32900t133+31950t132+30500t131+31500t130+9998t129+11244t128-27t127-83t126-146t125-402t124-501t123-1021t122-2010t121-4286t120-11448t119-24672t118-49460t117-84440t116-111575t115-157675t114-117750t113-142252t112-45609t111-48093t110+248t109+712t108+1616t107+4016t106+5824t105+9678t104+11616t103+17224t102+15256t101+56004t100+49120t99+165580t98+133406t97+283094t96+177934t95+239406t94+84900t93+77224t92-728t91-2232t90-5352t89-11184t88-19078t87-27422t86-33258t85-34590t84-22544t83-42068t82-16880t81-98360t80-59120t79-162648t78-96644t77-133412t76-52012t75-41484t74+712t73+3176t72+6776t71+12456t70+24756t69+32340t68+40860t67+39700t66+27400t65+12000t64+16t62-12t61-196t60-596t59-1316t58-1400t57-1576t56-392t55-1576t54-2728t53-4904t52-10884t51-13548t50-17740t49-18180t48-12600t47-5200t46-48t44+64t43+288t42+320t41+1328t40+1664t39+1312t38+448t37+32t26-32t25-128t24-16t23-496t22-624t21-496t20-160t19)*a+(3t159+3t158+66t157+66t156+573t155+573t154+2460t153+2460t152+5325t151+5325t150+5250t149+5250t148+1875t147+1875t146-4t144-8t143-51t142-98t141-267t140-508t139-1187t138-2278t137-5807t136-9560t135-19265t134-22950t133-35425t132-26500t131-31625t130-11248t129-10619t128+33t127+113t126+274t125+786t124+1335t123+2591t122+2894t121+5490t120-64t119+14544t118-5780t117+36880t116+1025t115+54721t114+24234t113+40722t112+19343t111+11795t110-158t109-442t108-1176t107-2264t106-4742t105-7086t104-8516t103-9056t102+3652t101+4572t100+44040t99+34440t98+84052t97+74580t96+63606t95+73698t94+13922t93+26614t92+96t91+432t90+832t89-88t88+3118t87+2710t86+4954t85+3742t84-2112t83-34252t82-44240t81-118036t80-109332t79-205404t78-131160t77-176424t76-57996t75-57988t74+176t73+816t72+2544t71+6928t70+9744t69+14860t68+16864t67+12848t66+10928t65+17800t64+18560t63+46984t62+49284t61+85156t60+63884t59+75172t58+30456t57+24960t56+56t55-1704t54-3624t53-7944t52-15172t51-20412t50-25420t49-22820t48-15800t47-6800t46-56t43-24t42+344t41+536t40+496t39+656t38-16t37+592t36+944t35+2416t34+5080t33+6856t32+9000t31+8360t30+6000t29+2400t28+32t26-96t24-144t23-688t22-848t21-720t20-224t19-16t8+32t6+208t4+256t3+224t2+64t); // c20; // -t159a+3t159-t158a+3t158-22t157a+66t157-22t156a+66t156-191t155a+573t155-191t154a+573t154-820t153a+2460t153-820t152a+2460t152-1775t151a+5325t151-1775t150a+5325t150-1750t149a+5250t149-1750t148a+5250t148-625t147a+1875t147-625t146a+1875t146-2t144a-4t144-4t143a-8t143-24t142a-51t142-24t141a-98t141-74t140a-267t140+296t139a-508t139+276t138a-1187t138+3636t137a-2278t137+3388t136a-5807t136+15720t135a-9560t135+14760t134a-19265t134+32900t133a-22950t133+31950t132a-35425t132+30500t131a-26500t131+31500t130a-31625t130+9998t129a-11248t129+11244t128a-10619t128-27t127a+33t127-83t126a+113t126-146t125a+274t125-402t124a+786t124-501t123a+1335t123-1021t122a+2591t122-2010t121a+2894t121-4286t120a+5490t120-11448t119a-64t119-24672t118a+14544t118-49460t117a-5780t117-84440t116a+36880t116-111575t115a+1025t115-157675t114a+54721t114-117750t113a+24234t113-142252t112a+40722t112-45609t111a+19343t111-48093t110a+11795t110+248t109a-158t109+712t108a-442t108+1616t107a-1176t107+4016t106a-2264t106+5824t105a-4742t105+9678t104a-7086t104+11616t103a-8516t103+17224t102a-9056t102+15256t101a+3652t101+56004t100a+4572t100+49120t99a+44040t99+165580t98a+34440t98+133406t97a+84052t97+283094t96a+74580t96+177934t95a+63606t95+239406t94a+73698t94+84900t93a+13922t93+77224t92a+26614t92-728t91a+96t91-2232t90a+432t90-5352t89a+832t89-11184t88a-88t88-19078t87a+3118t87-27422t86a+2710t86-33258t85a+4954t85-34590t84a+3742t84-22544t83a-2112t83-42068t82a-34252t82-16880t81a-44240t81-98360t80a-118036t80-59120t79a-109332t79-162648t78a-205404t78-96644t77a-131160t77-133412t76a-176424t76-52012t75a-57996t75-41484t74a-57988t74+712t73a+176t73+3176t72a+816t72+6776t71a+2544t71+12456t70a+6928t70+24756t69a+9744t69+32340t68a+14860t68+40860t67a+16864t67+39700t66a+12848t66+27400t65a+10928t65+12000t64a+17800t64+18560t63+16t62a+46984t62-12t61a+49284t61-196t60a+85156t60-596t59a+63884t59-1316t58a+75172t58-1400t57a+30456t57-1576t56a+24960t56-392t55a+56t55-1576t54a-1704t54-2728t53a-3624t53-4904t52a-7944t52-10884t51a-15172t51-13548t50a-20412t50-17740t49a-25420t49-18180t48a-22820t48-12600t47a-15800t47-5200t46a-6800t46-48t44a+64t43a-56t43+288t42a-24t42+320t41a+344t41+1328t40a+536t40+1664t39a+496t39+1312t38a+656t38+448t37a-16t37+592t36+944t35+2416t34+5080t33+6856t32+9000t31+8360t30+6000t29+2400t28+32t26a+32t26-32t25a-128t24a-96t24-16t23a-144t23-496t22a-688t22-624t21a-848t21-496t20a-720t20-160t19a-224t19-16t8+32t6+208t4+256t3+224t2+64t setring(ra); poly cc20 = 64*t; setring(rra); poly c11 = (2t159+2t158+44t157+44t156+382t155+382t154+1640t153+1640t152+3550t151+3550t150+3500t149+3500t148+1250t147+1250t146+4t144+8t143+48t142+48t141+148t140-592t139-552t138-7272t137-6776t136-31440t135-29520t134-65800t133-63900t132-61000t131-63000t130-20000t129-22500t128-6t127+18t126-36t125+204t124+210t123+1138t122+3200t121+8032t120+22596t119+49244t118+98920t117+168880t116+223150t115+315350t114+235500t113+284500t112+91250t111+96250t110-228t108-416t107-2688t106-4576t105-11080t104-15712t103-29488t102-27712t101-111108t100-98240t99-331160t98-266800t97-566200t96-355988t95-479036t94-170064t93-155048t92+60t91+524t90+2392t89+6936t88+16176t87+29312t86+42616t85+52760t84+36088t83+81336t82+33760t81+196720t80+118200t79+325400t78+193960t77+268184t76+105368t75+85368t74+168t73-312t72-3712t71-6912t70-20832t69-32736t68-49920t67-56960t66-42800t65-20400t64+32t60-88t59-216t58-784t57-1008t56-904t55-280t54+1632t53+2496t52+8704t51+13312t50+20640t49+25920t48+19600t47+8800t46-96t42+320t41-64t40+768t39+1120t38+1088t37+448t36+64t24-192t23+128t22-288t21-416t20-416t19-160t18)*a+(-6t159-6t158-132t157-132t156-1146t155-1146t154-4920t153-4920t152-10650t151-10650t150-10500t149-10500t148-3750t147-3750t146+8t144+16t143+102t142+196t141+534t140+1016t139+2374t138+4556t137+11614t136+19120t135+38530t134+45900t133+70850t132+53000t131+63250t130+22500t129+21250t128-6t127-78t126-220t125-972t124-1878t123-4278t122-4968t121-10440t120+428t119-28988t118+11560t117-73760t116-2050t115-109450t114-48500t113-81508t112-38766t111-23766t110+44t109+172t108+1040t107+2400t106+6316t105+10676t104+13752t103+15752t102-8504t101-9544t100-88080t99-68880t98-168100t97-149100t96-126996t95-146948t94-27388t93-52372t92+4t91+52t90-1448t89-744t88-5984t87-6320t86-10088t85-6984t84+4024t83+68504t82+88480t81+236080t80+218600t79+410608t78+261920t77+351952t76+114776t75+114640t74-304t73-472t72-544t71-3616t70-5792t69-12048t68-17568t67-14976t66-15456t65-33800t64-37120t63-94000t62-98400t61-170032t60-127768t59-150152t58-59952t57-49728t56+248t55+392t54+1888t53+4224t52+11392t51+18688t50+28320t49+30080t48+22800t47+11200t46-112t41+176t40+352t39+352t38+432t37+80t36-576t35-1344t34-3712t33-6400t32-9920t31-11200t30-8800t29-4000t28+64t24-128t23+64t22-416t21-544t20-608t19-224t18-32t6+64t5-64t4+128t3+160t2+192t+64); // c11; // 2t159a-6t159+2t158a-6t158+44t157a-132t157+44t156a-132t156+382t155a-1146t155+382t154a-1146t154+1640t153a-4920t153+1640t152a-4920t152+3550t151a-10650t151+3550t150a-10650t150+3500t149a-10500t149+3500t148a-10500t148+1250t147a-3750t147+1250t146a-3750t146+4t144a+8t144+8t143a+16t143+48t142a+102t142+48t141a+196t141+148t140a+534t140-592t139a+1016t139-552t138a+2374t138-7272t137a+4556t137-6776t136a+11614t136-31440t135a+19120t135-29520t134a+38530t134-65800t133a+45900t133-63900t132a+70850t132-61000t131a+53000t131-63000t130a+63250t130-20000t129a+22500t129-22500t128a+21250t128-6t127a-6t127+18t126a-78t126-36t125a-220t125+204t124a-972t124+210t123a-1878t123+1138t122a-4278t122+3200t121a-4968t121+8032t120a-10440t120+22596t119a+428t119+49244t118a-28988t118+98920t117a+11560t117+168880t116a-73760t116+223150t115a-2050t115+315350t114a-109450t114+235500t113a-48500t113+284500t112a-81508t112+91250t111a-38766t111+96250t110a-23766t110+44t109-228t108a+172t108-416t107a+1040t107-2688t106a+2400t106-4576t105a+6316t105-11080t104a+10676t104-15712t103a+13752t103-29488t102a+15752t102-27712t101a-8504t101-111108t100a-9544t100-98240t99a-88080t99-331160t98a-68880t98-266800t97a-168100t97-566200t96a-149100t96-355988t95a-126996t95-479036t94a-146948t94-170064t93a-27388t93-155048t92a-52372t92+60t91a+4t91+524t90a+52t90+2392t89a-1448t89+6936t88a-744t88+16176t87a-5984t87+29312t86a-6320t86+42616t85a-10088t85+52760t84a-6984t84+36088t83a+4024t83+81336t82a+68504t82+33760t81a+88480t81+196720t80a+236080t80+118200t79a+218600t79+325400t78a+410608t78+193960t77a+261920t77+268184t76a+351952t76+105368t75a+114776t75+85368t74a+114640t74+168t73a-304t73-312t72a-472t72-3712t71a-544t71-6912t70a-3616t70-20832t69a-5792t69-32736t68a-12048t68-49920t67a-17568t67-56960t66a-14976t66-42800t65a-15456t65-20400t64a-33800t64-37120t63-94000t62-98400t61+32t60a-170032t60-88t59a-127768t59-216t58a-150152t58-784t57a-59952t57-1008t56a-49728t56-904t55a+248t55-280t54a+392t54+1632t53a+1888t53+2496t52a+4224t52+8704t51a+11392t51+13312t50a+18688t50+20640t49a+28320t49+25920t48a+30080t48+19600t47a+22800t47+8800t46a+11200t46-96t42a+320t41a-112t41-64t40a+176t40+768t39a+352t39+1120t38a+352t38+1088t37a+432t37+448t36a+80t36-576t35-1344t34-3712t33-6400t32-9920t31-11200t30-8800t29-4000t28+64t24a+64t24-192t23a-128t23+128t22a+64t22-288t21a-416t21-416t20a-544t20-416t19a-608t19-160t18a-224t18-32t6+64t5-64t4+128t3+160t2+192t+64 setring(ra); poly cc11 = 64; setring(rra); poly c02 = (-t159-t158-22t157-22t156-191t155-191t154-820t153-820t152-1775t151-1775t150-1750t149-1750t148-625t147-625t146-2t144-4t143-24t142-24t141-74t140+296t139+276t138+3636t137+3388t136+15720t135+14760t134+32900t133+31950t132+30500t131+31500t130+10000t129+11250t128+3t127-9t126+18t125-102t124-105t123-569t122-1600t121-4016t120-11298t119-24622t118-49460t117-84440t116-111575t115-157675t114-117750t113-142250t112-45625t111-48125t110+114t108+208t107+1344t106+2288t105+5540t104+7856t103+14744t102+13856t101+55554t100+49120t99+165580t98+133400t97+283100t96+177994t95+239518t94+85032t93+77524t92-30t91-262t90-1196t89-3468t88-8088t87-14656t86-21308t85-26380t84-18044t83-40668t82-16880t81-98360t80-59100t79-162700t78-96980t77-134092t76-52684t75-42684t74-84t73+156t72+1856t71+3456t70+10416t69+16368t68+24960t67+28480t66+21400t65+10200t64-16t60+44t59+108t58+392t57+504t56+452t55+140t54-816t53-1248t52-4352t51-6656t50-10320t49-12960t48-9800t47-4400t46+48t42-160t41+32t40-384t39-560t38-544t37-224t36-32t24+96t23-64t22+144t21+208t20+208t19+80t18)*a+(3t159+3t158+66t157+66t156+573t155+573t154+2460t153+2460t152+5325t151+5325t150+5250t149+5250t148+1875t147+1875t146-4t144-8t143-51t142-98t141-267t140-508t139-1187t138-2278t137-5807t136-9560t135-19265t134-22950t133-35425t132-26500t131-31625t130-11250t129-10625t128+3t127+39t126+110t125+486t124+939t123+2139t122+2484t121+5220t120-214t119+14494t118-5780t117+36880t116+1025t115+54725t114+24250t113+40754t112+19383t111+11883t110-22t109-86t108-520t107-1200t106-3158t105-5338t104-6876t103-7876t102+4252t101+4772t100+44040t99+34440t98+84050t97+74550t96+63498t95+73474t94+13694t93+26186t92-2t91-26t90+724t89+372t88+2992t87+3160t86+5044t85+3492t84-2012t83-34252t82-44240t81-118040t80-109300t79-205304t78-130960t77-175976t76-57388t75-57320t74+152t73+236t72+272t71+1808t70+2896t69+6024t68+8784t67+7488t66+7728t65+16900t64+18560t63+47000t62+49200t61+85016t60+63884t59+75076t58+29976t57+24864t56-124t55-196t54-944t53-2112t52-5696t51-9344t50-14160t49-15040t48-11400t47-5600t46+56t41-88t40-176t39-176t38-216t37-40t36+288t35+672t34+1856t33+3200t32+4960t31+5600t30+4400t29+2000t28-32t24+64t23-32t22+208t21+272t20+304t19+112t18+16t6-32t5+32t4-64t3-80t2-96t-32); // c02; // -t159a+3t159-t158a+3t158-22t157a+66t157-22t156a+66t156-191t155a+573t155-191t154a+573t154-820t153a+2460t153-820t152a+2460t152-1775t151a+5325t151-1775t150a+5325t150-1750t149a+5250t149-1750t148a+5250t148-625t147a+1875t147-625t146a+1875t146-2t144a-4t144-4t143a-8t143-24t142a-51t142-24t141a-98t141-74t140a-267t140+296t139a-508t139+276t138a-1187t138+3636t137a-2278t137+3388t136a-5807t136+15720t135a-9560t135+14760t134a-19265t134+32900t133a-22950t133+31950t132a-35425t132+30500t131a-26500t131+31500t130a-31625t130+10000t129a-11250t129+11250t128a-10625t128+3t127a+3t127-9t126a+39t126+18t125a+110t125-102t124a+486t124-105t123a+939t123-569t122a+2139t122-1600t121a+2484t121-4016t120a+5220t120-11298t119a-214t119-24622t118a+14494t118-49460t117a-5780t117-84440t116a+36880t116-111575t115a+1025t115-157675t114a+54725t114-117750t113a+24250t113-142250t112a+40754t112-45625t111a+19383t111-48125t110a+11883t110-22t109+114t108a-86t108+208t107a-520t107+1344t106a-1200t106+2288t105a-3158t105+5540t104a-5338t104+7856t103a-6876t103+14744t102a-7876t102+13856t101a+4252t101+55554t100a+4772t100+49120t99a+44040t99+165580t98a+34440t98+133400t97a+84050t97+283100t96a+74550t96+177994t95a+63498t95+239518t94a+73474t94+85032t93a+13694t93+77524t92a+26186t92-30t91a-2t91-262t90a-26t90-1196t89a+724t89-3468t88a+372t88-8088t87a+2992t87-14656t86a+3160t86-21308t85a+5044t85-26380t84a+3492t84-18044t83a-2012t83-40668t82a-34252t82-16880t81a-44240t81-98360t80a-118040t80-59100t79a-109300t79-162700t78a-205304t78-96980t77a-130960t77-134092t76a-175976t76-52684t75a-57388t75-42684t74a-57320t74-84t73a+152t73+156t72a+236t72+1856t71a+272t71+3456t70a+1808t70+10416t69a+2896t69+16368t68a+6024t68+24960t67a+8784t67+28480t66a+7488t66+21400t65a+7728t65+10200t64a+16900t64+18560t63+47000t62+49200t61-16t60a+85016t60+44t59a+63884t59+108t58a+75076t58+392t57a+29976t57+504t56a+24864t56+452t55a-124t55+140t54a-196t54-816t53a-944t53-1248t52a-2112t52-4352t51a-5696t51-6656t50a-9344t50-10320t49a-14160t49-12960t48a-15040t48-9800t47a-11400t47-4400t46a-5600t46+48t42a-160t41a+56t41+32t40a-88t40-384t39a-176t39-560t38a-176t38-544t37a-216t37-224t36a-40t36+288t35+672t34+1856t33+3200t32+4960t31+5600t30+4400t29+2000t28-32t24a-32t24+96t23a+64t23-64t22a-32t22+144t21a+208t21+208t20a+272t20+208t19a+304t19+80t18a+112t18+16t6-32t5+32t4-64t3-80t2-96t-32 setring(ra); poly cc02 = -32; setring(rra); poly c10 = (-4t163-12t162-62t161-118t160-366t159-62t158-838t157+3138t156+1870t155+15974t154+19150t153+38230t152+51750t151+47350t150+53750t149+30750t148+18750t147+8758t146+16t145+112t144+244t143+500t142+1324t141-580t140+1412t139-17636t138-21364t137-92612t136-131780t135-238740t134-327100t133-324300t132-344500t131-218500t130-127496t129-57568t128+72t127-456t126+652t125+636t124+4156t123+7740t122+22520t121+23344t120+109908t119+143700t118+390660t117+476500t116+798700t115+777500t114+816500t113+562500t112+317500t111+137612t110-256t109+64t108-4192t107-8784t106-26080t105-35536t104-84768t103-18624t102-211104t101-34304t100-522080t99-336080t98-885600t97-755600t96-852000t95-602000t94-340080t93-139888t92-336t91+2704t90+5824t89+21760t88+47184t87+69936t86+122192t85+68688t84+154848t83-21760t82+236960t81+56800t80+357200t79+246000t78+324000t77+220000t76+130160t75+49680t74+1280t73-4160t72-1920t71-20800t70-37440t69-56640t68-90400t67-86400t66-56000t65-16000t64-80t57+144t56-736t55+1632t54-512t53+6528t52+10784t51+15072t50+28240t49+27120t48+17600t47+4800t46)*a+(4t178+8t177+92t176+176t175+852t174+1528t173+4044t172+6560t171+10380t170+14200t169+14100t168+14000t167+9500t166+5000t165+2500t164-4t163-12t162-58t161-162t160-370t159-1074t158-2098t157-6234t156-12422t155-28510t154-49190t153-75950t152-104550t151-107750t150-104750t149-73750t148-38750t147-18754t146+48t145+112t144+728t143+1612t142+4392t141+6076t140+16104t139+11152t138+52232t137+44512t136+143640t135+153740t134+249800t133+264300t132+241000t131+193500t130+95004t129+44980t128-152t127-760t126-2836t125-6820t124-16964t123-20164t122-49832t121-6112t120-98508t119+37924t118-157660t117+980t116-143700t115-128900t114-91500t113-125500t112-42540t111-22300t110-80t109+2720t108+3896t107+13992t106+26680t105+35176t104+59392t103+32256t102+33608t101-78968t100-90840t99-228360t98-313800t97-310200t96-371000t95-209000t94-144920t93-55368t92+624t91-3696t90-608t89-10848t88-12624t87-16688t86-13808t85-50096t84+66944t83-13408t82+258880t81+139840t80+471600t79+358800t78+472000t77+296000t76+190000t75+70144t74-64t73+832t72-1504t71-3248t70-11424t69-22256t68-35360t67-12352t66-52896t65+19328t64-93920t63-11440t62-154400t61-90800t60-148000t59-86000t58-60080t57-19920t56-736t55+1184t54-256t53+7168t52+13600t51+23136t50+37200t49+35760t48+24000t47+6400t46+32t39-32t38+320t37-384t36+512t35-1792t34-3136t33-5184t32-9760t31-9440t30-6400t29-1600t28); // c10; // 4t178+8t177+92t176+176t175+852t174+1528t173+4044t172+6560t171+10380t170+14200t169+14100t168+14000t167+9500t166+5000t165+2500t164-4t163a-4t163-12t162a-12t162-62t161a-58t161-118t160a-162t160-366t159a-370t159-62t158a-1074t158-838t157a-2098t157+3138t156a-6234t156+1870t155a-12422t155+15974t154a-28510t154+19150t153a-49190t153+38230t152a-75950t152+51750t151a-104550t151+47350t150a-107750t150+53750t149a-104750t149+30750t148a-73750t148+18750t147a-38750t147+8758t146a-18754t146+16t145a+48t145+112t144a+112t144+244t143a+728t143+500t142a+1612t142+1324t141a+4392t141-580t140a+6076t140+1412t139a+16104t139-17636t138a+11152t138-21364t137a+52232t137-92612t136a+44512t136-131780t135a+143640t135-238740t134a+153740t134-327100t133a+249800t133-324300t132a+264300t132-344500t131a+241000t131-218500t130a+193500t130-127496t129a+95004t129-57568t128a+44980t128+72t127a-152t127-456t126a-760t126+652t125a-2836t125+636t124a-6820t124+4156t123a-16964t123+7740t122a-20164t122+22520t121a-49832t121+23344t120a-6112t120+109908t119a-98508t119+143700t118a+37924t118+390660t117a-157660t117+476500t116a+980t116+798700t115a-143700t115+777500t114a-128900t114+816500t113a-91500t113+562500t112a-125500t112+317500t111a-42540t111+137612t110a-22300t110-256t109a-80t109+64t108a+2720t108-4192t107a+3896t107-8784t106a+13992t106-26080t105a+26680t105-35536t104a+35176t104-84768t103a+59392t103-18624t102a+32256t102-211104t101a+33608t101-34304t100a-78968t100-522080t99a-90840t99-336080t98a-228360t98-885600t97a-313800t97-755600t96a-310200t96-852000t95a-371000t95-602000t94a-209000t94-340080t93a-144920t93-139888t92a-55368t92-336t91a+624t91+2704t90a-3696t90+5824t89a-608t89+21760t88a-10848t88+47184t87a-12624t87+69936t86a-16688t86+122192t85a-13808t85+68688t84a-50096t84+154848t83a+66944t83-21760t82a-13408t82+236960t81a+258880t81+56800t80a+139840t80+357200t79a+471600t79+246000t78a+358800t78+324000t77a+472000t77+220000t76a+296000t76+130160t75a+190000t75+49680t74a+70144t74+1280t73a-64t73-4160t72a+832t72-1920t71a-1504t71-20800t70a-3248t70-37440t69a-11424t69-56640t68a-22256t68-90400t67a-35360t67-86400t66a-12352t66-56000t65a-52896t65-16000t64a+19328t64-93920t63-11440t62-154400t61-90800t60-148000t59-86000t58-80t57a-60080t57+144t56a-19920t56-736t55a-736t55+1632t54a+1184t54-512t53a-256t53+6528t52a+7168t52+10784t51a+13600t51+15072t50a+23136t50+28240t49a+37200t49+27120t48a+35760t48+17600t47a+24000t47+4800t46a+6400t46+32t39-32t38+320t37-384t36+512t35-1792t34-3136t33-5184t32-9760t31-9440t30-6400t29-1600t28 setring(ra); poly cc10 = -1600*t^28; setring(rra); poly c01 = (4t163+12t162+62t161+118t160+366t159+62t158+838t157-3138t156-1870t155-15974t154-19150t153-38230t152-51750t151-47350t150-53750t149-30750t148-18750t147-8758t146-16t145-112t144-244t143-500t142-1324t141+580t140-1412t139+17636t138+21364t137+92612t136+131780t135+238740t134+327100t133+324300t132+344500t131+218500t130+127496t129+57568t128-72t127+456t126-652t125-636t124-4156t123-7740t122-22520t121-23344t120-109908t119-143700t118-390660t117-476500t116-798700t115-777500t114-816500t113-562500t112-317500t111-137612t110+256t109-64t108+4192t107+8784t106+26080t105+35536t104+84768t103+18624t102+211104t101+34304t100+522080t99+336080t98+885600t97+755600t96+852000t95+602000t94+340080t93+139888t92+336t91-2704t90-5824t89-21760t88-47184t87-69936t86-122192t85-68688t84-154848t83+21760t82-236960t81-56800t80-357200t79-246000t78-324000t77-220000t76-130160t75-49680t74-1280t73+4160t72+1920t71+20800t70+37440t69+56640t68+90400t67+86400t66+56000t65+16000t64+80t57-144t56+736t55-1632t54+512t53-6528t52-10784t51-15072t50-28240t49-27120t48-17600t47-4800t46)*a+(-4t178-8t177-92t176-176t175-852t174-1528t173-4044t172-6560t171-10380t170-14200t169-14100t168-14000t167-9500t166-5000t165-2500t164+4t163+12t162+58t161+162t160+370t159+1074t158+2098t157+6234t156+12422t155+28510t154+49190t153+75950t152+104550t151+107750t150+104750t149+73750t148+38750t147+18754t146-48t145-112t144-728t143-1612t142-4392t141-6076t140-16104t139-11152t138-52232t137-44512t136-143640t135-153740t134-249800t133-264300t132-241000t131-193500t130-95004t129-44980t128+152t127+760t126+2836t125+6820t124+16964t123+20164t122+49832t121+6112t120+98508t119-37924t118+157660t117-980t116+143700t115+128900t114+91500t113+125500t112+42540t111+22300t110+80t109-2720t108-3896t107-13992t106-26680t105-35176t104-59392t103-32256t102-33608t101+78968t100+90840t99+228360t98+313800t97+310200t96+371000t95+209000t94+144920t93+55368t92-624t91+3696t90+608t89+10848t88+12624t87+16688t86+13808t85+50096t84-66944t83+13408t82-258880t81-139840t80-471600t79-358800t78-472000t77-296000t76-190000t75-70144t74+64t73-832t72+1504t71+3248t70+11424t69+22256t68+35360t67+12352t66+52896t65-19328t64+93920t63+11440t62+154400t61+90800t60+148000t59+86000t58+60080t57+19920t56+736t55-1184t54+256t53-7168t52-13600t51-23136t50-37200t49-35760t48-24000t47-6400t46-32t39+32t38-320t37+384t36-512t35+1792t34+3136t33+5184t32+9760t31+9440t30+6400t29+1600t28); // c01; // -4t178-8t177-92t176-176t175-852t174-1528t173-4044t172-6560t171-10380t170-14200t169-14100t168-14000t167-9500t166-5000t165-2500t164+4t163a+4t163+12t162a+12t162+62t161a+58t161+118t160a+162t160+366t159a+370t159+62t158a+1074t158+838t157a+2098t157-3138t156a+6234t156-1870t155a+12422t155-15974t154a+28510t154-19150t153a+49190t153-38230t152a+75950t152-51750t151a+104550t151-47350t150a+107750t150-53750t149a+104750t149-30750t148a+73750t148-18750t147a+38750t147-8758t146a+18754t146-16t145a-48t145-112t144a-112t144-244t143a-728t143-500t142a-1612t142-1324t141a-4392t141+580t140a-6076t140-1412t139a-16104t139+17636t138a-11152t138+21364t137a-52232t137+92612t136a-44512t136+131780t135a-143640t135+238740t134a-153740t134+327100t133a-249800t133+324300t132a-264300t132+344500t131a-241000t131+218500t130a-193500t130+127496t129a-95004t129+57568t128a-44980t128-72t127a+152t127+456t126a+760t126-652t125a+2836t125-636t124a+6820t124-4156t123a+16964t123-7740t122a+20164t122-22520t121a+49832t121-23344t120a+6112t120-109908t119a+98508t119-143700t118a-37924t118-390660t117a+157660t117-476500t116a-980t116-798700t115a+143700t115-777500t114a+128900t114-816500t113a+91500t113-562500t112a+125500t112-317500t111a+42540t111-137612t110a+22300t110+256t109a+80t109-64t108a-2720t108+4192t107a-3896t107+8784t106a-13992t106+26080t105a-26680t105+35536t104a-35176t104+84768t103a-59392t103+18624t102a-32256t102+211104t101a-33608t101+34304t100a+78968t100+522080t99a+90840t99+336080t98a+228360t98+885600t97a+313800t97+755600t96a+310200t96+852000t95a+371000t95+602000t94a+209000t94+340080t93a+144920t93+139888t92a+55368t92+336t91a-624t91-2704t90a+3696t90-5824t89a+608t89-21760t88a+10848t88-47184t87a+12624t87-69936t86a+16688t86-122192t85a+13808t85-68688t84a+50096t84-154848t83a-66944t83+21760t82a+13408t82-236960t81a-258880t81-56800t80a-139840t80-357200t79a-471600t79-246000t78a-358800t78-324000t77a-472000t77-220000t76a-296000t76-130160t75a-190000t75-49680t74a-70144t74-1280t73a+64t73+4160t72a-832t72+1920t71a+1504t71+20800t70a+3248t70+37440t69a+11424t69+56640t68a+22256t68+90400t67a+35360t67+86400t66a+12352t66+56000t65a+52896t65+16000t64a-19328t64+93920t63+11440t62+154400t61+90800t60+148000t59+86000t58+80t57a+60080t57-144t56a+19920t56+736t55a+736t55-1632t54a-1184t54+512t53a+256t53-6528t52a-7168t52-10784t51a-13600t51-15072t50a-23136t50-28240t49a-37200t49-27120t48a-35760t48-17600t47a-24000t47-4800t46a-6400t46-32t39+32t38-320t37+384t36-512t35+1792t34+3136t33+5184t32+9760t31+9440t30+6400t29+1600t28 setring(ra); poly cc01 = 1600*t^28; setring(rra); poly newfnoxrra = c50*x^5 + c41*x^4*y + c32*x^3*y^2 + c23*x^2*y^3+c14*x*y^4 + c05*y^5 + c40*x^4 + c31*x^3*y+ c22*x^2*y^2 + c13*x*y^3 + c04*y^4 + c30*x^3 + c21*x^2*y + c12*x*y^2 + c03*y^3 + c20*x^2 + c11*x*y + c02*y^2 + c10*x + c01*y; // poly newfnoxrra = 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// We draw the simplified polynomial, since the values of the initial terms of each coefficient is the same. setring(ra); poly newfnox = cc50*x^5 + cc41*x^4*y + cc32*x^3*y^2 + cc23*x^2*y^3+cc14*x*y^4 + cc05*y^5+ cc40*x^4 + cc31*x^3*y+ cc22*x^2*y^2 + cc13*x*y^3 + cc04*y^4 + cc30*x^3 + cc21*x^2*y + cc12*x*y^2 + cc03*y^3 + cc20*x^2 + cc11*x*y + cc02*y^2 + cc10*x + cc01*y; // newfnox; // x5-5*x4y+(8t)*x4+10*x3y2+20*x3y+(-64t)*x3-10*x2y3-46*x2y2-80*x2y+(64t)*x2+5*xy4+36*xy3+120*xy2+64*xy+(-1600t28)*x-y5-9*y4-40*y3-32*y2+(1600t28)*y setring(r); map newP2zy = ra, 91,x,y,0; poly newfnoxrat = newP2zy(newfnox); // newfnoxrat; // x5-5*x4y+(8t)*x4+10*x3y2+20*x3y+(-64t)*x3-10*x2y3-46*x2y2-80*x2y+(64t)*x2+5*xy4+36*xy3+120*xy2+64*xy+(-1600t28)*x-y5-9*y4-40*y3-32*y2+(1600t28)*y setring(r); poly newfnoxrat = x5-5*x4y+(8t)*x4+10*x3y2+20*x3y+(-64t)*x3-10*x2y3-46*x2y2-80*x2y+(64t)*x2+5*xy4+36*xy3+120*xy2+64*xy+(-1600t28)*x-y5-9*y4-40*y3-32*y2+(1600t28)*y; // drawTropicalCurve(newfnoxrat,"max");