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\ - j) for j in range(d + 1) if j != i))\n\nlagrange_basis(21, 0) \ \ # the next degree after this table"-Numbers: []+Numbers:+- params:+ d: '0'+ i: '0'+ number: '1'+- params:+ d: '1'+ i: '0'+ number: -x + 1+- params:+ d: '1'+ i: '1'+ number: x+- params:+ d: '2'+ i: '0'+ number: 1/2*x^2 - 3/2*x + 1+- params:+ d: '2'+ i: '1'+ number: -x^2 + 2*x+- params:+ d: '2'+ i: '2'+ number: 1/2*x^2 - 1/2*x+- params:+ d: '3'+ i: '0'+ number: -1/6*x^3 + x^2 - 11/6*x + 1+- params:+ d: '3'+ i: '1'+ number: 1/2*x^3 - 5/2*x^2 + 3*x+- params:+ d: '3'+ i: '2'+ number: -1/2*x^3 + 2*x^2 - 3/2*x+- params:+ d: '3'+ i: '3'+ number: 1/6*x^3 - 1/2*x^2 + 1/3*x+- params:+ d: '4'+ i: '0'+ number: 1/24*x^4 - 5/12*x^3 + 35/24*x^2 - 25/12*x + 1+- params:+ d: '4'+ i: '1'+ number: -1/6*x^4 + 3/2*x^3 - 13/3*x^2 + 4*x+- params:+ d: '4'+ i: '2'+ number: 1/4*x^4 - 2*x^3 + 19/4*x^2 - 3*x+- params:+ d: '4'+ i: '3'+ number: -1/6*x^4 + 7/6*x^3 - 7/3*x^2 + 4/3*x+- params:+ d: '4'+ i: '4'+ number: 1/24*x^4 - 1/4*x^3 + 11/24*x^2 - 1/4*x+- params:+ d: '5'+ i: '0'+ number: -1/120*x^5 + 1/8*x^4 - 17/24*x^3 + 15/8*x^2 - 137/60*x + 1+- params:+ d: '5'+ i: '1'+ number: 1/24*x^5 - 7/12*x^4 + 71/24*x^3 - 77/12*x^2 + 5*x+- params:+ d: '5'+ i: '2'+ number: -1/12*x^5 + 13/12*x^4 - 59/12*x^3 + 107/12*x^2 - 5*x+- params:+ d: '5'+ i: '3'+ number: 1/12*x^5 - x^4 + 49/12*x^3 - 13/2*x^2 + 10/3*x+- params:+ d: '5'+ i: '4'+ number: -1/24*x^5 + 11/24*x^4 - 41/24*x^3 + 61/24*x^2 - 5/4*x+- params:+ d: '5'+ i: '5'+ number: 1/120*x^5 - 1/12*x^4 + 7/24*x^3 - 5/12*x^2 + 1/5*x+- params:+ d: '6'+ i: '0'+ number: 1/720*x^6 - 7/240*x^5 + 35/144*x^4 - 49/48*x^3 + 203/90*x^2 - 49/20*x ++ 1+- params:+ d: '6'+ i: '1'+ number: -1/120*x^6 + 1/6*x^5 - 31/24*x^4 + 29/6*x^3 - 87/10*x^2 + 6*x+- params:+ d: '6'+ i: '2'+ number: 1/48*x^6 - 19/48*x^5 + 137/48*x^4 - 461/48*x^3 + 117/8*x^2 - 15/2*x+- params:+ d: '6'+ i: '3'+ number: -1/36*x^6 + 1/2*x^5 - 121/36*x^4 + 31/3*x^3 - 127/9*x^2 + 20/3*x+- params:+ d: '6'+ i: '4'+ number: 1/48*x^6 - 17/48*x^5 + 107/48*x^4 - 307/48*x^3 + 33/4*x^2 - 15/4*x+- params:+ d: '6'+ i: '5'+ number: -1/120*x^6 + 2/15*x^5 - 19/24*x^4 + 13/6*x^3 - 27/10*x^2 + 6/5*x+- params:+ d: '6'+ i: '6'+ number: 1/720*x^6 - 1/48*x^5 + 17/144*x^4 - 5/16*x^3 + 137/360*x^2 - 1/6*x+- params:+ d: '7'+ i: '0'+ number: -1/5040*x^7 + 1/180*x^6 - 23/360*x^5 + 7/18*x^4 - 967/720*x^3 + 469/180*x^2+ - 363/140*x + 1+- params:+ d: '7'+ i: '1'+ number: 1/720*x^7 - 3/80*x^6 + 59/144*x^5 - 37/16*x^4 + 319/45*x^3 - 223/20*x^2+ + 7*x+- params:+ d: '7'+ i: '2'+ number: -1/240*x^7 + 13/120*x^6 - 9/8*x^5 + 71/12*x^4 - 3929/240*x^3 + 879/40*x^2+ - 21/2*x+- params:+ d: '7'+ i: '3'+ number: 1/144*x^7 - 25/144*x^6 + 247/144*x^5 - 1219/144*x^4 + 389/18*x^3 - 949/36*x^2+ + 35/3*x+- params:+ d: '7'+ i: '4'+ number: -1/144*x^7 + 1/6*x^6 - 113/72*x^5 + 22/3*x^4 - 2545/144*x^3 + 41/2*x^2 -+ 35/4*x+- params:+ d: '7'+ i: '5'+ number: 1/240*x^7 - 23/240*x^6 + 69/80*x^5 - 185/48*x^4 + 134/15*x^3 - 201/20*x^2+ + 21/5*x+- params:+ d: '7'+ i: '6'+ number: -1/720*x^7 + 11/360*x^6 - 19/72*x^5 + 41/36*x^4 - 1849/720*x^3 + 1019/360*x^2+ - 7/6*x+- params:+ d: '7'+ i: '7'+ number: 1/5040*x^7 - 1/240*x^6 + 5/144*x^5 - 7/48*x^4 + 29/90*x^3 - 7/20*x^2 + 1/7*x+- params:+ d: '8'+ i: '0'+ number: 1/40320*x^8 - 1/1120*x^7 + 13/960*x^6 - 9/80*x^5 + 1069/1920*x^4 - 267/160*x^3+ + 29531/10080*x^2 - 761/280*x + 1+- params:+ d: '8'+ i: '1'+ number: -1/5040*x^8 + 1/144*x^7 - 73/720*x^6 + 115/144*x^5 - 329/90*x^4 + 349/36*x^3+ - 481/35*x^2 + 8*x+- params:+ d: '8'+ i: '2'+ number: 1/1440*x^8 - 17/720*x^7 + 239/720*x^6 - 179/72*x^5 + 15289/1440*x^4 - 18353/720*x^3+ + 621/20*x^2 - 14*x+- params:+ d: '8'+ i: '3'+ number: -1/720*x^8 + 11/240*x^7 - 149/240*x^6 + 71/16*x^5 - 268/15*x^4 + 797/20*x^3+ - 2003/45*x^2 + 56/3*x+- params:+ d: '8'+ i: '4'+ number: 1/576*x^8 - 1/18*x^7 + 209/288*x^6 - 179/36*x^5 + 10993/576*x^4 - 1457/36*x^3+ + 691/16*x^2 - 35/2*x+- params:+ d: '8'+ i: '5'+ number: -1/720*x^8 + 31/720*x^7 - 391/720*x^6 + 2581/720*x^5 - 1193/90*x^4 + 4891/180*x^3+ - 141/5*x^2 + 56/5*x+- params:+ d: '8'+ i: '6'+ number: 1/1440*x^8 - 1/48*x^7 + 61/240*x^6 - 13/8*x^5 + 2803/480*x^4 - 187/16*x^3+ + 2143/180*x^2 - 14/3*x+- params:+ d: '8'+ i: '7'+ number: -1/5040*x^8 + 29/5040*x^7 - 49/720*x^6 + 61/144*x^5 - 67/45*x^4 + 527/180*x^3+ - 103/35*x^2 + 8/7*x+- params:+ d: '8'+ i: '8'+ number: 1/40320*x^8 - 1/1440*x^7 + 23/2880*x^6 - 7/144*x^5 + 967/5760*x^4 - 469/1440*x^3+ + 363/1120*x^2 - 1/8*x+- params:+ d: '9'+ i: '0'+ number: -1/362880*x^9 + 1/8064*x^8 - 29/12096*x^7 + 5/192*x^6 - 3013/17280*x^5 ++ 95/128*x^4 - 4523/2268*x^3 + 6515/2016*x^2 - 7129/2520*x + 1+- params:+ d: '9'+ i: '1'+ number: 1/40320*x^9 - 11/10080*x^8 + 59/2880*x^7 - 77/360*x^6 + 7807/5760*x^5 -+ 7667/1440*x^4 + 14139/1120*x^3 - 4609/280*x^2 + 9*x+- params:+ d: '9'+ i: '2'+ number: -1/10080*x^9 + 43/10080*x^8 - 7/90*x^7 + 563/720*x^6 - 6787/1440*x^5 + 24901/1440*x^4+ - 20837/560*x^3 + 5869/140*x^2 - 18*x+- params:+ d: '9'+ i: '3'+ number: 1/4320*x^9 - 7/720*x^8 + 31/180*x^7 - 401/240*x^6 + 13873/1440*x^5 - 4013/120*x^4+ + 72569/1080*x^3 - 6289/90*x^2 + 28*x+- params:+ d: '9'+ i: '4'+ number: -1/2880*x^9 + 41/2880*x^8 - 353/1440*x^7 + 3313/1440*x^6 - 36769/2880*x^5+ + 122249/2880*x^4 - 6519/80*x^3 + 6499/80*x^2 - 63/2*x+- params:+ d: '9'+ i: '5'+ number: 1/2880*x^9 - 1/72*x^8 + 67/288*x^7 - 305/144*x^6 + 32773/2880*x^5 - 5273/144*x^4+ + 1091/16*x^3 - 265/4*x^2 + 126/5*x+- params:+ d: '9'+ i: '6'+ number: -1/4320*x^9 + 13/1440*x^8 - 53/360*x^7 + 313/240*x^6 - 9823/1440*x^5 + 10279/480*x^4+ - 84307/2160*x^3 + 6709/180*x^2 - 14*x+- params:+ d: '9'+ i: '7'+ number: 1/10080*x^9 - 19/5040*x^8 + 151/2520*x^7 - 373/720*x^6 + 3817/1440*x^5 -+ 2939/360*x^4 + 4101/280*x^3 - 967/70*x^2 + 36/7*x+- params:+ d: '9'+ i: '8'+ number: -1/40320*x^9 + 37/40320*x^8 - 41/2880*x^7 + 347/2880*x^6 - 3487/5760*x^5+ + 10579/5760*x^4 - 1823/560*x^3 + 3407/1120*x^2 - 9/8*x+- params:+ d: '9'+ i: '9'+ number: 1/362880*x^9 - 1/10080*x^8 + 13/8640*x^7 - 1/80*x^6 + 1069/17280*x^5 - 89/480*x^4+ + 29531/90720*x^3 - 761/2520*x^2 + 1/9*x+- params:+ d: '10'+ i: '0'+ number: 1/3628800*x^10 - 11/725760*x^9 + 11/30240*x^8 - 121/24192*x^7 + 7513/172800*x^6+ - 8591/34560*x^5 + 341693/362880*x^4 - 84095/36288*x^3 + 177133/50400*x^2 - 7381/2520*x+ + 1+- params:+ d: '10'+ i: '1'+ number: -1/362880*x^10 + 1/6720*x^9 - 211/60480*x^8 + 67/1440*x^7 - 6709/17280*x^6+ + 6041/2880*x^5 - 663941/90720*x^4 + 79913/5040*x^3 - 4861/252*x^2 + 10*x+- params:+ d: '10'+ i: '2'+ number: 1/80640*x^10 - 53/80640*x^9 + 607/40320*x^8 - 1123/5760*x^7 + 18047/11520*x^6+ - 92771/11520*x^5 + 264767/10080*x^4 - 115923/2240*x^3 + 6121/112*x^2 - 45/2*x+- params:+ d: '10'+ i: '3'+ number: -1/30240*x^10 + 13/7560*x^9 - 97/2520*x^8 + 349/720*x^7 - 5419/1440*x^6+ + 13349/720*x^5 - 433739/7560*x^4 + 400579/3780*x^3 - 6541/63*x^2 + 40*x+- params:+ d: '10'+ i: '4'+ number: 1/17280*x^10 - 17/5760*x^9 + 31/480*x^8 - 2281/2880*x^7 + 34343/5760*x^6+ - 163313/5760*x^5 + 728587/8640*x^4 - 71689/480*x^3 + 6751/48*x^2 - 105/2*x+- params:+ d: '10'+ i: '5'+ number: -1/14400*x^10 + 1/288*x^9 - 107/1440*x^8 + 8/9*x^7 - 93773/14400*x^6 + 43319/1440*x^5+ - 62549/720*x^4 + 1197/8*x^3 - 6877/50*x^2 + 252/5*x+- params:+ d: '10'+ i: '6'+ number: 1/17280*x^10 - 49/17280*x^9 + 19/320*x^8 - 1999/2880*x^7 + 28603/5760*x^6+ - 129067/5760*x^5 + 273431/4320*x^4 - 461789/4320*x^3 + 6961/72*x^2 - 35*x+- params:+ d: '10'+ i: '7'+ number: -1/30240*x^10 + 1/630*x^9 - 41/1260*x^8 + 1877/5040*x^7 - 1253/480*x^6 ++ 8321/720*x^5 - 242639/7560*x^4 + 22439/420*x^3 - 1003/21*x^2 + 120/7*x+- params:+ d: '10'+ i: '8'+ number: 1/80640*x^10 - 47/80640*x^9 + 59/5040*x^8 - 757/5760*x^7 + 10427/11520*x^6+ - 45449/11520*x^5 + 435893/40320*x^4 - 39867/2240*x^3 + 3533/224*x^2 - 45/8*x+- params:+ d: '10'+ i: '9'+ number: -1/362880*x^10 + 23/181440*x^9 - 151/60480*x^8 + 119/4320*x^7 - 3229/17280*x^6+ + 6947/8640*x^5 - 197741/90720*x^4 + 161353/45360*x^3 - 263/84*x^2 + 10/9*x+- params:+ d: '10'+ i: '10'+ number: 1/3628800*x^10 - 1/80640*x^9 + 29/120960*x^8 - 1/384*x^7 + 3013/172800*x^6+ - 19/256*x^5 + 4523/22680*x^4 - 1303/4032*x^3 + 7129/25200*x^2 - 1/10*x+- params:+ d: '11'+ i: '0'+ number: -1/39916800*x^11 + 1/604800*x^10 - 1/20736*x^9 + 11/13440*x^8 - 10831/1209600*x^7+ + 1903/28800*x^6 - 242537/725760*x^5 + 139381/120960*x^4 - 341747/129600*x^3 ++ 190553/50400*x^2 - 83711/27720*x + 1+- params:+ d: '11'+ i: '1'+ number: 1/3628800*x^11 - 13/725760*x^10 + 31/60480*x^9 - 1027/120960*x^8 + 15553/172800*x^7+ - 22009/34560*x^6 + 1102859/362880*x^5 - 1748357/181440*x^4 + 325421/16800*x^3+ - 55991/2520*x^2 + 11*x+- params:+ d: '11'+ i: '2'+ number: -1/725760*x^11 + 1/11340*x^10 - 599/241920*x^9 + 2423/60480*x^8 - 14251/34560*x^7+ + 12137/4320*x^6 - 9261503/725760*x^5 + 6868181/181440*x^4 - 1397573/20160*x^3+ + 69851/1008*x^2 - 55/2*x+- params:+ d: '11'+ i: '3'+ number: 1/241920*x^11 - 1/3840*x^10 + 31/4320*x^9 - 4577/40320*x^8 + 13097/11520*x^7+ - 28769/3840*x^6 + 3951097/120960*x^5 - 29483/320*x^4 + 685547/4320*x^3 - 74471/504*x^2+ + 55*x+- params:+ d: '11'+ i: '4'+ number: -1/120960*x^11 + 31/60480*x^10 - 559/40320*x^9 + 4327/20160*x^8 - 805/384*x^7+ + 12883/960*x^6 - 6846503/120960*x^5 + 9304859/60480*x^4 - 285363/1120*x^3 + 76781/336*x^2+ - 165/2*x+- params:+ d: '11'+ i: '5'+ number: 1/86400*x^11 - 61/86400*x^10 + 3/160*x^9 - 91/320*x^8 + 78191/28800*x^7+ - 488231/28800*x^6 + 601607/8640*x^5 - 795769/4320*x^4 + 356683/1200*x^3 - 78167/300*x^2+ + 462/5*x+- params:+ d: '11'+ i: '6'+ number: -1/86400*x^11 + 1/1440*x^10 - 313/17280*x^9 + 97/360*x^8 - 72581/28800*x^7+ + 493/32*x^6 - 1070587/17280*x^5 + 115651/720*x^4 - 5497339/21600*x^3 + 79091/360*x^2+ - 77*x+- params:+ d: '11'+ i: '7'+ number: 1/120960*x^11 - 59/120960*x^10 + 1/80*x^9 - 409/2240*x^8 + 67607/40320*x^7+ - 57991/5760*x^6 + 2407429/60480*x^5 - 3072931/30240*x^4 + 12709/80*x^3 - 11393/84*x^2+ + 330/7*x+- params:+ d: '11'+ i: '8'+ number: -1/241920*x^11 + 29/120960*x^10 - 487/80640*x^9 + 3497/40320*x^8 - 1003/1280*x^7+ + 8897/1920*x^6 - 4371359/241920*x^5 + 5512429/120960*x^4 - 473867/6720*x^3 ++ 40123/672*x^2 - 165/8*x+- params:+ d: '11'+ i: '9'+ number: 1/725760*x^11 - 19/241920*x^10 + 353/181440*x^9 - 1109/40320*x^8 + 1693/6912*x^7+ - 16471/11520*x^6 + 2000239/362880*x^5 - 832619/60480*x^4 + 1916903/90720*x^3+ - 8959/504*x^2 + 55/9*x+- params:+ d: '11'+ i: '10'+ number: -1/3628800*x^11 + 1/64800*x^10 - 13/34560*x^9 + 317/60480*x^8 - 7963/172800*x^7+ + 2873/10800*x^6 - 737251/725760*x^5 + 65237/25920*x^4 - 18421/4800*x^3 + 80939/25200*x^2+ - 11/10*x+- params:+ d: '11'+ i: '11'+ number: 1/39916800*x^11 - 1/725760*x^10 + 1/30240*x^9 - 11/24192*x^8 + 683/172800*x^7+ - 781/34560*x^6 + 31063/362880*x^5 - 7645/36288*x^4 + 16103/50400*x^3 - 671/2520*x^2+ + 1/11*x+- params:+ d: '12'+ i: '0'+ number: 1/479001600*x^12 - 13/79833600*x^11 + 247/43545600*x^10 - 169/1451520*x^9+ + 22711/14515200*x^8 - 3887/268800*x^7 + 4090021/43545600*x^6 - 124891/290304*x^5+ + 14936519/10886400*x^4 - 5356117/1814400*x^3 + 1676701/415800*x^2 - 86021/27720*x+ + 1+- params:+ d: '12'+ i: '1'+ number: -1/39916800*x^12 + 1/518400*x^11 - 1/15120*x^10 + 23/17280*x^9 - 21101/1209600*x^8+ + 26971/172800*x^7 - 352363/362880*x^6 + 108643/25920*x^5 - 1855669/151200*x^4+ + 5209/225*x^3 - 58301/2310*x^2 + 12*x+- params:+ d: '12'+ i: '2'+ number: 1/7257600*x^12 - 19/1814400*x^11 + 19/53760*x^10 - 211/30240*x^9 + 216061/2419200*x^8+ - 67027/86400*x^7 + 6745939/1451520*x^6 - 3465269/181440*x^5 + 31665443/604800*x^4+ - 2270987/25200*x^3 + 72161/840*x^2 - 33*x+- params:+ d: '12'+ i: '3'+ number: -1/2177280*x^12 + 5/145152*x^11 - 89/77760*x^10 + 2683/120960*x^9 - 201527/725760*x^8+ + 81157/34560*x^7 - 14825779/1088640*x^6 + 9759623/181440*x^5 - 5461793/38880*x^4+ + 71822/315*x^3 - 76781/378*x^2 + 220/3*x+- params:+ d: '12'+ i: '4'+ number: 1/967680*x^12 - 37/483840*x^11 + 269/107520*x^10 - 7681/161280*x^9 + 62791/107520*x^8+ - 37033/7680*x^7 + 26325599/967680*x^6 - 50383877/483840*x^5 + 4235597/16128*x^4+ - 5520439/13440*x^3 + 79091/224*x^2 - 495/4*x+- params:+ d: '12'+ i: '5'+ number: -1/604800*x^12 + 73/604800*x^11 - 7/1800*x^10 + 163/2240*x^9 - 176471/201600*x^8+ + 203789/28800*x^7 - 11796193/302400*x^6 + 4405411/30240*x^5 - 1289677/3600*x^4+ + 287054/525*x^3 - 80477/175*x^2 + 792/5*x+- params:+ d: '12'+ i: '6'+ number: 1/518400*x^12 - 1/7200*x^11 + 457/103680*x^10 - 701/8640*x^9 + 165701/172800*x^8+ - 27389/3600*x^7 + 4265227/103680*x^6 - 433963/2880*x^5 + 47131699/129600*x^4+ - 2946397/5400*x^3 + 81401/180*x^2 - 154*x+- params:+ d: '12'+ i: '7'+ number: -1/604800*x^12 + 71/604800*x^11 - 37/10080*x^10 + 149/2240*x^9 - 155951/201600*x^8+ + 1217221/201600*x^7 - 1942859/60480*x^6 + 3503501/30240*x^5 - 6946529/25200*x^4+ + 214408/525*x^3 - 11723/35*x^2 + 792/7*x+- params:+ d: '12'+ i: '8'+ number: 1/967680*x^12 - 1/13824*x^11 + 719/322560*x^10 - 917/23040*x^9 + 49039/107520*x^8+ - 26951/7680*x^7 + 17823623/967680*x^6 - 4534369/69120*x^5 + 12446459/80640*x^4+ - 434831/1920*x^3 + 20639/112*x^2 - 495/8*x+- params:+ d: '12'+ i: '9'+ number: -1/2177280*x^12 + 23/725760*x^11 - 131/136080*x^10 + 6151/362880*x^9 - 139103/725760*x^8+ + 16777/11520*x^7 - 8226277/1088640*x^6 + 4833097/181440*x^5 - 3380809/54432*x^4+ + 256411/2835*x^3 - 27647/378*x^2 + 220/9*x+- params:+ d: '12'+ i: '10'+ number: 1/7257600*x^12 - 17/1814400*x^11 + 97/345600*x^10 - 59/12096*x^9 + 131821/2419200*x^8+ - 35381/86400*x^7 + 15270191/7257600*x^6 - 667103/90720*x^5 + 1470529/86400*x^4+ - 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