Faulhaber's formula: Difference between revisions
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Thundergnat (talk | contribs) (Rename Perl 6 -> Raku, alphabetize, minor clean-up) |
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f(9) = 1/10 * (n^10 + (5/1)*n^9 + (15/2)*n^8 + (-7/1)*n^6 + (5/1)*n^4 + (-3/2)*n^2) |
f(9) = 1/10 * (n^10 + (5/1)*n^9 + (15/2)*n^8 + (-7/1)*n^6 + (5/1)*n^4 + (-3/2)*n^2) |
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</pre> |
</pre> |
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=={{header|Ruby}}== |
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{{trans|C}} |
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<lang ruby>def binomial(n,k) |
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if n < 0 or k < 0 or n < k then |
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return -1 |
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end |
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if n == 0 or k == 0 then |
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return 1 |
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end |
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num = 1 |
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for i in k+1 .. n do |
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num = num * i |
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end |
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denom = 1 |
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for i in 2 .. n-k do |
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denom = denom * i |
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end |
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return num / denom |
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end |
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def bernoulli(n) |
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if n < 0 then |
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raise "n cannot be less than zero" |
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end |
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a = Array.new(16) |
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for m in 0 .. n do |
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a[m] = Rational(1, m + 1) |
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for j in m.downto(1) do |
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a[j-1] = (a[j-1] - a[j]) * Rational(j) |
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end |
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end |
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if n != 1 then |
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return a[0] |
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end |
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return -a[0] |
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end |
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def faulhaber(p) |
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print("%d : " % [p]) |
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q = Rational(1, p + 1) |
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sign = -1 |
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for j in 0 .. p do |
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sign = -1 * sign |
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coeff = q * Rational(sign) * Rational(binomial(p+1, j)) * bernoulli(j) |
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if coeff == 0 then |
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next |
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end |
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if j == 0 then |
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if coeff != 1 then |
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if coeff == -1 then |
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print "-" |
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else |
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print coeff |
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end |
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end |
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else |
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if coeff == 1 then |
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print " + " |
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elsif coeff == -1 then |
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print " - " |
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elsif 0 < coeff then |
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print " + " |
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print coeff |
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else |
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print " - " |
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print -coeff |
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end |
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end |
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pwr = p + 1 - j |
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if pwr > 1 then |
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print "n^%d" % [pwr] |
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else |
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print "n" |
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end |
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end |
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print "\n" |
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end |
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def main |
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for i in 0 .. 9 do |
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faulhaber(i) |
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end |
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end |
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main()</lang> |
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{{out}} |
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<pre>0 : n |
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1 : 1/2n^2 + 1/2n |
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2 : 1/3n^3 + 1/2n^2 + 1/6n |
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3 : 1/4n^4 + 1/2n^3 + 1/4n^2 |
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4 : 1/5n^5 + 1/2n^4 + 1/3n^3 - 1/30n |
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5 : 1/6n^6 + 1/2n^5 + 5/12n^4 - 1/12n^2 |
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6 : 1/7n^7 + 1/2n^6 + 1/2n^5 - 1/6n^3 + 1/42n |
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7 : 1/8n^8 + 1/2n^7 + 7/12n^6 - 7/24n^4 + 1/12n^2 |
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8 : 1/9n^9 + 1/2n^8 + 2/3n^7 - 7/15n^5 + 2/9n^3 - 1/30n |
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9 : 1/10n^10 + 1/2n^9 + 3/4n^8 - 7/10n^6 + 1/2n^4 - 3/20n^2</pre> |
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=={{header|Sidef}}== |
=={{header|Sidef}}== |
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