Bernoulli numbers: Difference between revisions

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Line 2,818: 58 84483613348880041862046775994036021/354 60 -(1215233140483755572040304994079820246041491/56786730)</pre> =={{header\|Maxima}}== Using built-in function bern <syntaxhighlight lang="maxima"> block(makelist([sconcat("B","(",i,")","="),bern(i)],i,0,60), sublist(%%,lambda([x],x[2]#0)), table_form(%%)) </syntaxhighlight> {{out}}▼ <pre> matrix( ["B(0)=", 1], ["B(1)=", -1/2], ["B(2)=", 1/6], ["B(4)=", -1/30], ["B(6)=", 1/42], ["B(8)=", -1/30], ["B(10)=", 5/66], ["B(12)=", -691/2730], ["B(14)=", 7/6], ["B(16)=", -3617/510], ["B(18)=", 43867/798], ["B(20)=", -174611/330], ["B(22)=", 854513/138], ["B(24)=", -236364091/2730], ["B(26)=", 8553103/6], ["B(28)=", -23749461029/870], ["B(30)=", 8615841276005/14322], ["B(32)=", -7709321041217/510], ["B(34)=", 2577687858367/6], ["B(36)=", -26315271553053477373/1919190], ["B(38)=", 2929993913841559/6], ["B(40)=", -261082718496449122051/13530], ["B(42)=", 1520097643918070802691/1806], ["B(44)=", -27833269579301024235023/690], ["B(46)=", 596451111593912163277961/282], ["B(48)=", -5609403368997817686249127547/46410], ["B(50)=", 495057205241079648212477525/66], ["B(52)=", -801165718135489957347924991853/1590], ["B(54)=", 29149963634884862421418123812691/798], ["B(56)=", -2479392929313226753685415739663229/870], ["B(58)=", 84483613348880041862046775994036021/354], ["B(60)=", -1215233140483755572040304994079820246041491/56786730] ) </pre> =={{header\|Nim}}== <syntaxhighlight lang="nim">import bignum Line 3,978 ⟶ 4,024: ===HP-49+ version=== ~~From HP-49 models,~~Latest RPL implementations can natively handle ~~(not too)~~ long fractions and generate Bernoulli numbers. {{works with\|HP\|49}} ~~≪ { }~~ ~~1 ROT 1 + '''FOR''' m~~ ~~m INV +~~ ~~m 1 + → j~~ ~~≪ '''WHILE''' 'j' DECR 2 ≥ '''REPEAT'''~~ ~~j 1 - DUP2 GETI UNROT GET -~~ ~~OVER * EVAL PUT~~ ~~'''END'''~~ ≫ ~~'''NEXT'''~~ ~~HEAD~~ ~~≫ '<span style="color:blue">BRNOU</span>' STO~~ ≪ { } 0 ROT '''FOR''' n '''IF''' n 2 > LASTARG MOD AND NOT '''THEN''' n ~~<span style="color:blue">BRNOU</span>~~IBERNOULLI + '''END''' '''NEXT''' ≫ '<span style="color:blue">TASK</span>' STO ▲{{out}} 3060 <span style="color:blue">TASK</span> {{out}} <pre> 1: {1 -1/2 1/6 -1/30 1/42 -1/30 5/66 -691/2730 7/6 -3617/510 43867/798 -174611/330 854513/138 -236364091/2730 8553103/6 -23749461029/870 8615841276005/14322 -7709321041217/510 2577687858367/6 -26315271553053477373/1919190 2929993913841559/6 -261082718496449122051/13530 1520097643918070802691/1806 -27833269579301024235023/690 596451111593912163277961/282 -5609403368997817686249127547/46410 495057205241079648212477525/66 -801165718135489957347924991853/1590 9149963634884862421418123812691/798 -2479392929313226753685415739663229/870 84483613348880041862046775994036021/354 -1215233140483755572040304994079820246041491/56786730} </pre> Runs in ~~1 hour 30~~3 minutes 40 on a HP-50g, against 1 hour and 30 minutes if calculating Bernoulli numbers with the above function. =={{header\|Ruby}}== Line 4,929 ⟶ 4,961: {{libheader\|Wren-fmt}} {{libheader\|Wren-big}} <syntaxhighlight lang="~~ecmascript~~wren">import "./fmt" for Fmt import "./big" for BigRat var bernoulli = Fn.new { \|n\| Line 4,986 ⟶ 5,018: B(60) = -1215233140483755572040304994079820246041491 / 56786730 </pre> =={{header\|zkl}}== {{trans\|EchoLisp}}