Finding unique top sums from multiple lists
I am not sure if your post and my answer fits to code review because it is about algorithm design. But here is my proposal for a better algorithm. Use dynamic programming as my slow CAS does by multiplying from left to right.
(%i15)  (x^9+x^8+x^7+x^6+x^5)*(x^15+x^13+x^11+x^9+x^2)*(x^16+x^13+x^12+x^11+x)*(x^17+x^12+x^4+x^2+x)*(x^19+x^9+x^8+x^7+1)*(x^21+x^17+x^13+x^9+x^4)*(x^23+x^5+x^3+x^2+x)*(x^27+x^22+x^14+x^7+x^3)*(x^27+x^23+x^21+x^18+x^4)*(x^31+x^25+x^24+x^12+x), expand;
Evaluation took 0.3906 seconds (0.3999 elapsed) using 1.737 MB.
(%o15)  x^205+x^204+2*x^203+3*x^202+7*x^201+10*x^200+16*x^199+22*x^198+32*x^197+46*x^196+63*x^195+86*x^194+111*x^193+147*x^192+185*x^191+240*x^190+299*x^189+377*x^188+458*x^187+566*x^186+684*x^185+832*x^184+998*x^183+1198*x^182+1424*x^181+1681*x^180+1984*x^179+2323*x^178+2729*x^177+3159*x^176+3665*x^175+4200*x^174+4838*x^173+5516*x^172+6296*x^171+7124*x^170+8067*x^169+9079*x^168+10206*x^167+11441*x^166+12794*x^165+14277*x^164+15859*x^163+17612*x^162+19469*x^161+21536*x^160+23690*x^159+26067*x^158+28532*x^157+31226*x^156+34016*x^155+37030*x^154+40181*x^153+43503*x^152+46960*x^151+50574*x^150+54399*x^149+58318*x^148+62441*x^147+66633*x^146+71075*x^145+75517*x^144+80157*x^143+84816*x^142+89656*x^141+94450*x^140+99306*x^139+104175*x^138+109042*x^137+113903*x^136+118633*x^135+123410*x^134+127975*x^133+132545*x^132+136833*x^131+141134*x^130+145121*x^129+149024*x^128+152623*x^127+156096*x^126+159287*x^125+162190*x^124+164887*x^123+167197*x^122+169335*x^121+170943*x^120+172463*x^119+173393*x^118+174221*x^117+174442*x^116+174604*x^115+174190*x^114+173616*x^113+172588*x^112+171336*x^111+169705*x^110+167725*x^109+165584*x^108+162978*x^107+160261*x^106+157026*x^105+153909*x^104+150226*x^103+146659*x^102+142597*x^101+138750*x^100+134440*x^99+130219*x^98+125758*x^97+121379*x^96+116816*x^95+112165*x^94+107623*x^93+102964*x^92+98456*x^91+93757*x^90+89435*x^89+84873*x^88+80597*x^87+76125*x^86+72062*x^85+67811*x^84+63813*x^83+59784*x^82+56067*x^81+52360*x^80+48788*x^79+45413*x^78+42168*x^77+39094*x^76+36034*x^75+33312*x^74+30608*x^73+28148*x^72+25669*x^71+23529*x^70+21382*x^69+19446*x^68+17551*x^67+15916*x^66+14326*x^65+12869*x^64+11538*x^63+10365*x^62+9281*x^61+8241*x^60+7346*x^59+6504*x^58+5751*x^57+5004*x^56+4397*x^55+3813*x^54+3309*x^53+2833*x^52+2472*x^51+2135*x^50+1845*x^49+1581*x^48+1362*x^47+1153*x^46+956*x^45+792*x^44+649*x^43+533*x^42+426*x^41+354*x^40+291*x^39+247*x^38+199*x^37+163*x^36+128*x^35+98*x^34+71*x^33+51*x^32+39*x^31+28*x^30+21*x^29+16*x^28+14*x^27+10*x^26+7*x^25+5*x^24+3*x^23+x^22

If my post  is not clear please tell me.