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\ return dict(zip(nodes, matrix(QQ, rows).solve_right(vector(QQ, rhs))))\n\ \nprint(adams_bashforth_coefficients(3))"-Numbers: []+Numbers:+- params:+ s: '1'+ j: '0'+ number: '1'+ comment: 'Euler method: $1(1)$.'+- params:+ s: '2'+ j: '0'+ number: -1/2+ comment: '2-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{2}(3,-1)$.'+- params:+ s: '2'+ j: '1'+ number: 3/2+- params:+ s: '3'+ j: '0'+ number: 5/12+ comment: '3-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{12}(23,-16,5)$.'+- params:+ s: '3'+ j: '1'+ number: -4/3+- params:+ s: '3'+ j: '2'+ number: 23/12+- params:+ s: '4'+ j: '0'+ number: -3/8+ comment: '4-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{24}(55,-59,37,-9)$.'+- params:+ s: '4'+ j: '1'+ number: 37/24+- params:+ s: '4'+ j: '2'+ number: -59/24+- params:+ s: '4'+ j: '3'+ number: 55/24+- params:+ s: '5'+ j: '0'+ number: 251/720+ comment: '5-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{720}(1901,-2774,2616,-1274,251)$.'+- params:+ s: '5'+ j: '1'+ number: -637/360+- params:+ s: '5'+ j: '2'+ number: 109/30+- params:+ s: '5'+ j: '3'+ number: -1387/360+- params:+ s: '5'+ j: '4'+ number: 1901/720+- params:+ s: '6'+ j: '0'+ number: -95/288+ comment: '6-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{1440}(4277,-7923,9982,-7298,2877,-475)$.'+- params:+ s: '6'+ j: '1'+ number: 959/480+- params:+ s: '6'+ j: '2'+ number: -3649/720+- params:+ s: '6'+ j: '3'+ number: 4991/720+- params:+ s: '6'+ j: '4'+ number: -2641/480+- params:+ s: '6'+ j: '5'+ number: 4277/1440+- params:+ s: '7'+ j: '0'+ number: 19087/60480+ comment: '7-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{60480}(198721,-447288,705549,-688256,407139,-134472,19087)$.'+- params:+ s: '7'+ j: '1'+ number: -5603/2520+- params:+ s: '7'+ j: '2'+ number: 135713/20160+- params:+ s: '7'+ j: '3'+ number: -10754/945+- params:+ s: '7'+ j: '4'+ number: 235183/20160+- params:+ s: '7'+ j: '5'+ number: -18637/2520+- params:+ s: '7'+ j: '6'+ number: 198721/60480+- params:+ s: '8'+ j: '0'+ number: -5257/17280+ comment: '8-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{120960}(434241,-1152169,2183877,-2664477,2102243,-1041723,295767,-36799)$.'+- params:+ s: '8'+ j: '1'+ number: 32863/13440+- params:+ s: '8'+ j: '2'+ number: -115747/13440+- params:+ s: '8'+ j: '3'+ number: 2102243/120960+- params:+ s: '8'+ j: '4'+ number: -296053/13440+- params:+ s: '8'+ j: '5'+ number: 242653/13440+- params:+ s: '8'+ j: '6'+ number: -1152169/120960+- params:+ s: '8'+ j: '7'+ number: 16083/4480+- params:+ s: '9'+ j: '0'+ number: 1070017/3628800+ comment: '9-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{3628800}(14097247,-43125206,95476786,-139855262,137968480,-91172642,38833486,-9664106,1070017)$.'+- params:+ s: '9'+ j: '1'+ number: -4832053/1814400+- params:+ s: '9'+ j: '2'+ number: 19416743/1814400+- params:+ s: '9'+ j: '3'+ number: -45586321/1814400+- params:+ s: '9'+ j: '4'+ number: 862303/22680+- params:+ s: '9'+ j: '5'+ number: -69927631/1814400+- params:+ s: '9'+ j: '6'+ number: 47738393/1814400+- params:+ s: '9'+ j: '7'+ number: -21562603/1814400+- params:+ s: '9'+ j: '8'+ number: 14097247/3628800+- params:+ s: '10'+ j: '0'+ number: -25713/89600+ comment: '10-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{7257600}(30277247,-104995189,265932680,-454661776,538363838,-444772162,252618224,-94307320,20884811,-2082753)$.'+- params:+ s: '10'+ j: '1'+ number: 20884811/7257600+- params:+ s: '10'+ j: '2'+ number: -2357683/181440+- params:+ s: '10'+ j: '3'+ number: 15788639/453600+- params:+ s: '10'+ j: '4'+ number: -222386081/3628800+- params:+ s: '10'+ j: '5'+ number: 269181919/3628800+- params:+ s: '10'+ j: '6'+ number: -28416361/453600+- params:+ s: '10'+ j: '7'+ number: 6648317/181440+- params:+ s: '10'+ j: '8'+ number: -104995189/7257600+- params:+ s: '10'+ j: '9'+ number: 4325321/1036800+- params:+ s: '11'+ j: '0'+ number: 26842253/95800320+ comment: '11-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{479001600}(2132509567,-8271795124,23591063805,-46113029016,63716378958,-63176201472,44857168434,-22329634920,7417904451,-1479574348,134211265)$.'+- params:+ s: '11'+ j: '1'+ number: -52841941/17107200+- params:+ s: '11'+ j: '2'+ number: 2472634817/159667200+- params:+ s: '11'+ j: '3'+ number: -186080291/3991680+- params:+ s: '11'+ j: '4'+ number: 2492064913/26611200+- params:+ s: '11'+ j: '5'+ number: -82260679/623700+- params:+ s: '11'+ j: '6'+ number: 3539798831/26611200+- params:+ s: '11'+ j: '7'+ number: -1921376209/19958400+- params:+ s: '11'+ j: '8'+ number: 1572737587/31933440+- params:+ s: '11'+ j: '9'+ number: -2067948781/119750400+- params:+ s: '11'+ j: '10'+ number: 2132509567/479001600+- params:+ s: '12'+ j: '0'+ number: -4777223/17418240+ comment: '12-step Adams-Bashforth formula, from newest to oldest: $\tfrac{1}{958003200}(4527766399,-19433810163,61633227185,-135579356757,214139355366,-247741639374,211103573298,-131365867290,58189107627,-17410248271,3158642445,-262747265)$.'+- params:+ s: '12'+ j: '1'+ number: 30082309/9123840+- params:+ s: '12'+ j: '2'+ number: -17410248271/958003200+- params:+ s: '12'+ j: '3'+ number: 923636629/15206400+- params:+ s: '12'+ j: '4'+ number: -625551749/4561920+- params:+ s: '12'+ j: '5'+ number: 35183928883/159667200+- params:+ s: '12'+ j: '6'+ number: -41290273229/159667200+- params:+ s: '12'+ j: '7'+ number: 35689892561/159667200+- params:+ s: '12'+ j: '8'+ number: -15064372973/106444800+- params:+ s: '12'+ j: '9'+ number: 12326645437/191600640+- params:+ s: '12'+ j: '10'+ number: -6477936721/319334400+- params:+ s: '12'+ j: '11'+ number: 4527766399/958003200
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