Faulhaber's triangle: Difference between revisions
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56056972216555580111030077961944183400198333273050000
56056972216555580111030077961944183400198333273050000</pre>
=={{header|Ruby}}==
{{trans|D}}
<lang ruby>class Frac
attr_accessor:num
attr_accessor:denom
def initialize(n,d)
if d == 0 then
raise ArgumentError.new('d cannot be zero')
end
nn = n
dd = d
if nn == 0 then
dd = 1
elsif dd < 0 then
nn = -nn
dd = -dd
end
g = nn.abs.gcd(dd.abs)
if g > 1 then
nn = nn / g
dd = dd / g
end
@num = nn
@denom = dd
end
def to_s
if self.denom == 1 then
return self.num.to_s
else
return "%d/%d" % [self.num, self.denom]
end
end
def -@
return Frac.new(-self.num, self.denom)
end
def +(rhs)
return Frac.new(self.num * rhs.denom + self.denom * rhs.num, rhs.denom * self.denom)
end
def -(rhs)
return Frac.new(self.num * rhs.denom - self.denom * rhs.num, rhs.denom * self.denom)
end
def *(rhs)
return Frac.new(self.num * rhs.num, rhs.denom * self.denom)
end
end
FRAC_ZERO = Frac.new(0, 1)
FRAC_ONE = Frac.new(1, 1)
def bernoulli(n)
if n < 0 then
raise ArgumentError.new('n cannot be negative')
end
a = Array.new(n + 1)
a[0] = FRAC_ZERO
for m in 0 .. n do
a[m] = Frac.new(1, m + 1)
m.downto(1) do |j|
a[j - 1] = (a[j - 1] - a[j]) * Frac.new(j, 1)
end
end
if n != 1 then
return a[0]
end
return -a[0]
end
def binomial(n, k)
if n < 0 then
raise ArgumentError.new('n cannot be negative')
end
if k < 0 then
raise ArgumentError.new('k cannot be negative')
end
if n < k then
raise ArgumentError.new('n cannot be less than k')
end
if n == 0 or k == 0 then
return 1
end
num = 1
for i in k + 1 .. n do
num = num * i
end
den = 1
for i in 2 .. n - k do
den = den * i
end
return num / den
end
def faulhaberTriangle(p)
coeffs = Array.new(p + 1)
coeffs[0] = FRAC_ZERO
q = Frac.new(1, p + 1)
sign = -1
for j in 0 .. p do
sign = -sign
coeffs[p - j] = q * Frac.new(sign, 1) * Frac.new(binomial(p + 1, j), 1) * bernoulli(j)
end
return coeffs
end
def main
for i in 0 .. 9 do
coeffs = faulhaberTriangle(i)
coeffs.each do |coeff|
print "%5s " % [coeff]
end
puts
end
end
main()</lang>
{{out}}
<pre> 1
1/2 1/2
1/6 1/2 1/3
0 1/4 1/2 1/4
-1/30 0 1/3 1/2 1/5
0 -1/12 0 5/12 1/2 1/6
1/42 0 -1/6 0 1/2 1/2 1/7
0 1/12 0 -7/24 0 7/12 1/2 1/8
-1/30 0 2/9 0 -7/15 0 2/3 1/2 1/9
0 -3/20 0 1/2 0 -7/10 0 3/4 1/2 1/10</pre>
=={{header|Sidef}}==
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