#=================================================== # # Zolotarev Polynomials, sn n=2-4, # Version 1.0 - 25/02/23 #=================================================== # s2 # s2 = (-4 \[Alpha] + 2 \[Alpha]^2 + \[Alpha]^3 - 4 \[Beta] + 4 \[Alpha] \[Beta] - \[Alpha]^2 \[Beta] + 2 \[Beta]^2 - \[Alpha] \[Beta]^2 + \[Beta]^3)/(2 (-4 + 4 \[Alpha] + \[Alpha]^2 + 4 \[Beta] - 2 \[Alpha] \[Beta] + \[Beta]^2)); # s3 # s3 = (128 - 64 \[Alpha] - 224 \[Alpha]^2 + 144 \[Alpha]^3 + 56 \[Alpha]^4 - 76 \[Alpha]^5 + 30 \[Alpha]^6 + 3 \[Alpha]^7 - 64 \[Beta] - 64 \[Alpha] \[Beta] + 112 \[Alpha]^2 \[Beta] - 96 \[Alpha]^3 \[Beta] + 36 \[Alpha]^4 \[Beta] + 76 \[Alpha]^5 \[Beta] - 15 \[Alpha]^6 \[Beta] - 224 \[Beta]^2 + 112 \[Alpha] \[Beta]^2 + 80 \[Alpha]^2 \[Beta]^2 + 40 \[Alpha]^3 \[Beta]^2 - 62 \[Alpha]^4 \[Beta]^2 + 27 \[Alpha]^5 \[Beta]^2 + 144 \[Beta]^3 - 96 \[Alpha] \[Beta]^3 + 40 \[Alpha]^2 \[Beta]^3 - 88 \[Alpha]^3 \[Beta]^3 - 15 \[Alpha]^4 \[Beta]^3 + 56 \[Beta]^4 + 36 \[Alpha] \[Beta]^4 - 62 \[Alpha]^2 \[Beta]^4 - 15 \[Alpha]^3 \[Beta]^4 - 76 \[Beta]^5 + 76 \[Alpha] \[Beta]^5 + 27 \[Alpha]^2 \[Beta]^5 + 30 \[Beta]^6 - 15 \[Alpha] \[Beta]^6 + 3 \[Beta]^7)/(6 (-64 - 64 \[Alpha] + 112 \[Alpha]^2 + 32 \[Alpha]^3 - 28 \[Alpha]^4 + 12 \[Alpha]^5 + \[Alpha]^6 - 64 \[Beta] + 32 \[Alpha] \[Beta] - 32 \[Alpha]^2 \[Beta] + 48 \[Alpha]^3 \[Beta] + 28 \[Alpha]^4 \[Beta] - 6 \[Alpha]^5 \[Beta] + 112 \[Beta]^2 - 32 \[Alpha] \[Beta]^2 - 40 \[Alpha]^2 \[Beta]^2 - 40 \[Alpha]^3 \[Beta]^2 + 15 \[Alpha]^4 \[Beta]^2 + 32 \[Beta]^3 + 48 \[Alpha] \[Beta]^3 - 40 \[Alpha]^2 \[Beta]^3 - 20 \[Alpha]^3 \[Beta]^3 - 28 \[Beta]^4 + 28 \[Alpha] \[Beta]^4 + 15 \[Alpha]^2 \[Beta]^4 + 12 \[Beta]^5 - 6 \[Alpha] \[Beta]^5 + \[Beta]^6)) # s4 # s4 = (4096 \[Alpha] - 2048 \[Alpha]^2 - 8192 \[Alpha]^3 + 3584 \[Alpha]^4 + 5888 \[Alpha]^5 - 256 \[Alpha]^6 - 3072 \[Alpha]^7 - 1600 \[Alpha]^8 + 1392 \[Alpha]^9 + 280 \[Alpha]^10 - 96 \[Alpha]^11 + 22 \[Alpha]^12 + \[Alpha]^13 + 4096 \[Beta] - 4096 \[Alpha] \[Beta] + 4096 \[Alpha]^3 \[Beta] - 9472 \[Alpha]^4 \[Beta] + 4608 \[Alpha]^5 \[Beta] + 4096 \[Alpha]^6 \[Beta] - 4352 \[Alpha]^7 \[Beta] + 1008 \[Alpha]^8 \[Beta] - 400 \[Alpha]^9 \[Beta] + 320 \[Alpha]^10 \[Beta] + 96 \[Alpha]^11 \[Beta] - 11 \[Alpha]^12 \[Beta] - 2048 \[Beta]^2 + 1024 \[Alpha]^2 \[Beta]^2 + 3584 \[Alpha]^3 \[Beta]^2 + 256 \[Alpha]^4 \[Beta]^2 - 10240 \[Alpha]^5 \[Beta]^2 + 2816 \[Alpha]^6 \[Beta]^2 + 6848 \[Alpha]^7 \[Beta]^2 - 1480 \[Alpha]^8 \[Beta]^2 - 576 \[Alpha]^9 \[Beta]^2 - 292 \[Alpha]^10 \[Beta]^2 + 54 \[Alpha]^11 \[Beta]^2 - 8192 \[Beta]^3 + 4096 \[Alpha] \[Beta]^3 + 3584 \[Alpha]^2 \[Beta]^3 - 9216 \[Alpha]^3 \[Beta]^3 + 9216 \[Alpha]^4 \[Beta]^3 + 4352 \[Alpha]^5 \[Beta]^3 - 7744 \[Alpha]^6 \[Beta]^3 + 2880 \[Alpha]^7 \[Beta]^3 + 1440 \[Alpha]^8 \[Beta]^3 - 416 \[Alpha]^9 \[Beta]^3 - 154 \[Alpha]^10 \[Beta]^3 + 3584 \[Beta]^4 - 9472 \[Alpha] \[Beta]^4 + 256 \[Alpha]^2 \[Beta]^4 + 9216 \[Alpha]^3 \[Beta]^4 - 2432 \[Alpha]^4 \[Beta]^4 - 1504 \[Alpha]^5 \[Beta]^4 + 1200 \[Alpha]^6 \[Beta]^4 - 2624 \[Alpha]^7 \[Beta]^4 + 1226 \[Alpha]^8 \[Beta]^4 + 275 \[Alpha]^9 \[Beta]^4 + 5888 \[Beta]^5 + 4608 \[Alpha] \[Beta]^5 - 10240 \[Alpha]^2 \[Beta]^5 + 4352 \[Alpha]^3 \[Beta]^5 - 1504 \[Alpha]^4 \[Beta]^5 - 4960 \[Alpha]^5 \[Beta]^5 + 1536 \[Alpha]^6 \[Beta]^5 + 320 \[Alpha]^7 \[Beta]^5 - 297 \[Alpha]^8 \[Beta]^5 - 256 \[Beta]^6 + 4096 \[Alpha] \[Beta]^6 + 2816 \[Alpha]^2 \[Beta]^6 - 7744 \[Alpha]^3 \[Beta]^6 + 1200 \[Alpha]^4 \[Beta]^6 + 1536 \[Alpha]^5 \[Beta]^6 - 1912 \[Alpha]^6 \[Beta]^6 + 132 \[Alpha]^7 \[Beta]^6 - 3072 \[Beta]^7 - 4352 \[Alpha] \[Beta]^7 + 6848 \[Alpha]^2 \[Beta]^7 + 2880 \[Alpha]^3 \[Beta]^7 - 2624 \[Alpha]^4 \[Beta]^7 + 320 \[Alpha]^5 \[Beta]^7 + 132 \[Alpha]^6 \[Beta]^7 - 1600 \[Beta]^8 + 1008 \[Alpha] \[Beta]^8 - 1480 \[Alpha]^2 \[Beta]^8 + 1440 \[Alpha]^3 \[Beta]^8 + 1226 \[Alpha]^4 \[Beta]^8 - 297 \[Alpha]^5 \[Beta]^8 + 1392 \[Beta]^9 - 400 \[Alpha] \[Beta]^9 - 576 \[Alpha]^2 \[Beta]^9 - 416 \[Alpha]^3 \[Beta]^9 + 275 \[Alpha]^4 \[Beta]^9 + 280 \[Beta]^10 + 320 \[Alpha] \[Beta]^10 - 292 \[Alpha]^2 \[Beta]^10 - 154 \[Alpha]^3 \[Beta]^10 - 96 \[Beta]^11 + 96 \[Alpha] \[Beta]^11 + 54 \[Alpha]^2 \[Beta]^11 + 22 \[Beta]^12 - 11 \[Alpha] \[Beta]^12 + \[Beta]^13)/(2 (4096 - 8192 \[Alpha] - 10240 \[Alpha]^2 + 14336 \[Alpha]^3 + 7936 \[Alpha]^4 - 5120 \[Alpha]^5 - 3840 \[Alpha]^6 - 1280 \[Alpha]^7 + 2032 \[Alpha]^8 + 352 \[Alpha]^9 - 104 \[Alpha]^10 + 24 \[Alpha]^11 + \[Alpha]^12 - 8192 \[Beta] + 4096 \[Alpha] \[Beta] + 2048 \[Alpha]^2 \[Beta] - 15360 \[Alpha]^3 \[Beta] + 15360 \[Alpha]^4 \[Beta] + 8704 \[Alpha]^5 \[Beta] - 7936 \[Alpha]^6 \[Beta] + 1152 \[Alpha]^7 \[Beta] - 416 \[Alpha]^8 \[Beta] + 464 \[Alpha]^9 \[Beta] + 104 \[Alpha]^10 \[Beta] - 12 \[Alpha]^11 \[Beta] - 10240 \[Beta]^2 + 2048 \[Alpha] \[Beta]^2 + 14848 \[Alpha]^2 \[Beta]^2 - 10240 \[Alpha]^3 \[Beta]^2 - 16640 \[Alpha]^4 \[Beta]^2 + 15104 \[Alpha]^5 \[Beta]^2 + 9792 \[Alpha]^6 \[Beta]^2 - 3200 \[Alpha]^7 \[Beta]^2 - 1096 \[Alpha]^8 \[Beta]^2 - 376 \[Alpha]^9 \[Beta]^2 + 66 \[Alpha]^10 \[Beta]^2 + 14336 \[Beta]^3 - 15360 \[Alpha] \[Beta]^3 - 10240 \[Alpha]^2 \[Beta]^3 + 23552 \[Alpha]^3 \[Beta]^3 - 5888 \[Alpha]^4 \[Beta]^3 - 16512 \[Alpha]^5 \[Beta]^3 + 8576 \[Alpha]^6 \[Beta]^3 + 2496 \[Alpha]^7 \[Beta]^3 - 520 \[Alpha]^8 \[Beta]^3 - 220 \[Alpha]^9 \[Beta]^3 + 7936 \[Beta]^4 + 15360 \[Alpha] \[Beta]^4 - 16640 \[Alpha]^2 \[Beta]^4 - 5888 \[Alpha]^3 \[Beta]^4 + 7072 \[Alpha]^4 \[Beta]^4 - 5312 \[Alpha]^5 \[Beta]^4 - 4944 \[Alpha]^6 \[Beta]^4 + 2416 \[Alpha]^7 \[Beta]^4 + 495 \[Alpha]^8 \[Beta]^4 - 5120 \[Beta]^5 + 8704 \[Alpha] \[Beta]^5 + 15104 \[Alpha]^2 \[Beta]^5 - 16512 \[Alpha]^3 \[Beta]^5 - 5312 \[Alpha]^4 \[Beta]^5 + 6368 \[Alpha]^5 \[Beta]^5 - 1648 \[Alpha]^6 \[Beta]^5 - 792 \[Alpha]^7 \[Beta]^5 - 3840 \[Beta]^6 - 7936 \[Alpha] \[Beta]^6 + 9792 \[Alpha]^2 \[Beta]^6 + 8576 \[Alpha]^3 \[Beta]^6 - 4944 \[Alpha]^4 \[Beta]^6 - 1648 \[Alpha]^5 \[Beta]^6 + 924 \[Alpha]^6 \[Beta]^6 - 1280 \[Beta]^7 + 1152 \[Alpha] \[Beta]^7 - 3200 \[Alpha]^2 \[Beta]^7 + 2496 \[Alpha]^3 \[Beta]^7 + 2416 \[Alpha]^4 \[Beta]^7 - 792 \[Alpha]^5 \[Beta]^7 + 2032 \[Beta]^8 - 416 \[Alpha] \[Beta]^8 - 1096 \[Alpha]^2 \[Beta]^8 - 520 \[Alpha]^3 \[Beta]^8 + 495 \[Alpha]^4 \[Beta]^8 + 352 \[Beta]^9 + 464 \[Alpha] \[Beta]^9 - 376 \[Alpha]^2 \[Beta]^9 - 220 \[Alpha]^3 \[Beta]^9 - 104 \[Beta]^10 + 104 \[Alpha] \[Beta]^10 + 66 \[Alpha]^2 \[Beta]^10 + 24 \[Beta]^11 - 12 \[Alpha] \[Beta]^11 + \[Beta]^12));