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\ for m in range(s + 1)]\n return dict(zip(nodes, matrix(QQ, rows).solve_right(vector(QQ,\ \ rhs))))\n\nadams_moulton_coefficients(3)"-Numbers: []+Numbers:+- params:+ s: '0'+ j: '0'+ number: '1'+ comment: 'Backward Euler method: $1$.'+- params:+ s: '1'+ j: '0'+ number: 1/2+ comment: 'Trapezoidal rule, from newest to oldest: $\tfrac{1}{2}(1,1)$.'+- params:+ s: '1'+ j: '1'+ number: 1/2+- params:+ s: '2'+ j: '0'+ number: -1/12+ comment: '2-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{12}(5,8,-1)$.'+- params:+ s: '2'+ j: '1'+ number: 2/3+- params:+ s: '2'+ j: '2'+ number: 5/12+- params:+ s: '3'+ j: '0'+ number: 1/24+ comment: '3-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{24}(9,19,-5,1)$.'+- params:+ s: '3'+ j: '1'+ number: -5/24+- params:+ s: '3'+ j: '2'+ number: 19/24+- params:+ s: '3'+ j: '3'+ number: 3/8+- params:+ s: '4'+ j: '0'+ number: -19/720+ comment: '4-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{720}(251,646,-264,106,-19)$.'+- params:+ s: '4'+ j: '1'+ number: 53/360+- params:+ s: '4'+ j: '2'+ number: -11/30+- params:+ s: '4'+ j: '3'+ number: 323/360+- params:+ s: '4'+ j: '4'+ number: 251/720+- params:+ s: '5'+ j: '0'+ number: 3/160+ comment: '5-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{1440}(475,1427,-798,482,-173,27)$.'+- params:+ s: '5'+ j: '1'+ number: -173/1440+- params:+ s: '5'+ j: '2'+ number: 241/720+- params:+ s: '5'+ j: '3'+ number: -133/240+- params:+ s: '5'+ j: '4'+ number: 1427/1440+- params:+ s: '5'+ j: '5'+ number: 95/288+- params:+ s: '6'+ j: '0'+ number: -863/60480+ comment: '6-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{60480}(19087,65112,-46461,37504,-20211,6312,-863)$.'+- params:+ s: '6'+ j: '1'+ number: 263/2520+- params:+ s: '6'+ j: '2'+ number: -6737/20160+- params:+ s: '6'+ j: '3'+ number: 586/945+- params:+ s: '6'+ j: '4'+ number: -15487/20160+- params:+ s: '6'+ j: '5'+ number: 2713/2520+- params:+ s: '6'+ j: '6'+ number: 19087/60480+- params:+ s: '7'+ j: '0'+ number: 275/24192+ comment: '7-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{120960}(36799,139849,-121797,123133,-88547,41499,-11351,1375)$.'+- params:+ s: '7'+ j: '1'+ number: -11351/120960+- params:+ s: '7'+ j: '2'+ number: 1537/4480+- params:+ s: '7'+ j: '3'+ number: -88547/120960+- params:+ s: '7'+ j: '4'+ number: 123133/120960+- params:+ s: '7'+ j: '5'+ number: -4511/4480+- params:+ s: '7'+ j: '6'+ number: 139849/120960+- params:+ s: '7'+ j: '7'+ number: 5257/17280+- params:+ s: '8'+ j: '0'+ number: -33953/3628800+ comment: '8-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{3628800}(1070017,4467094,-4604594,5595358,-5033120,3146338,-1291214,312874,-33953)$.'+- params:+ s: '8'+ j: '1'+ number: 156437/1814400+- params:+ s: '8'+ j: '2'+ number: -645607/1814400+- params:+ s: '8'+ j: '3'+ number: 1573169/1814400+- params:+ s: '8'+ j: '4'+ number: -31457/22680+- params:+ s: '8'+ j: '5'+ number: 2797679/1814400+- params:+ s: '8'+ j: '6'+ number: -2302297/1814400+- params:+ s: '8'+ j: '7'+ number: 2233547/1814400+- params:+ s: '8'+ j: '8'+ number: 1070017/3628800+- params:+ s: '9'+ j: '0'+ number: 8183/1036800+ comment: '9-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{7257600}(2082753,9449717,-11271304,16002320,-17283646,13510082,-7394032,2687864,-583435,57281)$.'+- params:+ s: '9'+ j: '1'+ number: -116687/1451520+- params:+ s: '9'+ j: '2'+ number: 335983/907200+- params:+ s: '9'+ j: '3'+ number: -462127/453600+- params:+ s: '9'+ j: '4'+ number: 6755041/3628800+- params:+ s: '9'+ j: '5'+ number: -8641823/3628800+- params:+ s: '9'+ j: '6'+ number: 200029/90720+- params:+ s: '9'+ j: '7'+ number: -1408913/907200+- params:+ s: '9'+ j: '8'+ number: 9449717/7257600+- params:+ s: '9'+ j: '9'+ number: 25713/89600+- params:+ s: '10'+ j: '0'+ number: -3250433/479001600+ comment: '10-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{479001600}(134211265,656185652,-890175549,1446205080,-1823311566,1710774528,-1170597042,567450984,-184776195,36284876,-3250433)$.'+- params:+ s: '10'+ j: '1'+ number: 9071219/119750400+- params:+ s: '10'+ j: '2'+ number: -12318413/31933440+- params:+ s: '10'+ j: '3'+ number: 23643791/19958400+- params:+ s: '10'+ j: '4'+ number: -21677723/8870400+- params:+ s: '10'+ j: '5'+ number: 2227571/623700+- params:+ s: '10'+ j: '6'+ number: -33765029/8870400+- params:+ s: '10'+ j: '7'+ number: 12051709/3991680+- params:+ s: '10'+ j: '8'+ number: -296725183/159667200+- params:+ s: '10'+ j: '9'+ number: 164046413/119750400+- params:+ s: '10'+ j: '10'+ number: 26842253/95800320+- params:+ s: '11'+ j: '0'+ number: 4671/788480+ comment: '11-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{958003200}(262747265,1374799219,-2092490673,3828828885,-5519460582,6043521486,-4963166514,3007739418,-1305971115,384709327,-68928781,5675265)$.'+- params:+ s: '11'+ j: '1'+ number: -68928781/958003200+- params:+ s: '11'+ j: '2'+ number: 384709327/958003200+- params:+ s: '11'+ j: '3'+ number: -87064741/63866880+- params:+ s: '11'+ j: '4'+ number: 501289903/159667200+- params:+ s: '11'+ j: '5'+ number: -91910491/17740800+- params:+ s: '11'+ j: '6'+ number: 1007253581/159667200+- params:+ s: '11'+ j: '7'+ number: -102212233/17740800+- params:+ s: '11'+ j: '8'+ number: 36465037/9123840+- params:+ s: '11'+ j: '9'+ number: -99642413/45619200+- params:+ s: '11'+ j: '10'+ number: 1374799219/958003200+- params:+ s: '11'+ j: '11'+ number: 4777223/17418240+- params:+ s: '12'+ j: '0'+ number: -13695779093/2615348736000+ comment: '12-step Adams-Moulton formula, from newest to oldest: $\tfrac{1}{2615348736000}(703604254357,3917551216986,-6616420957428,13465774256510,-21847538039895,27345870698436,-26204344465152,19058185652796,-10344711794985,4063327863170,-1092096992268,179842822566,-13695779093)$.'+- params:+ s: '12'+ j: '1'+ number: 2724891251/39626496000+- params:+ s: '12'+ j: '2'+ number: -30336027563/72648576000+- params:+ s: '12'+ j: '3'+ number: 406332786317/261534873600+- params:+ s: '12'+ j: '4'+ number: -229882484333/58118860800+- params:+ s: '12'+ j: '5'+ number: 529394045911/72648576000+- params:+ s: '12'+ j: '6'+ number: -4874320027/486486000+- params:+ s: '12'+ j: '7'+ number: 84400835489/8072064000+- params:+ s: '12'+ j: '8'+ number: -485500845331/58118860800+- params:+ s: '12'+ j: '9'+ number: 1346577425651/261534873600+- params:+ s: '12'+ j: '10'+ number: -551368413119/217945728000+- params:+ s: '12'+ j: '11'+ number: 6595204069/4402944000+- params:+ s: '12'+ j: '12'+ number: 703604254357/2615348736000
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