Faulhaber's triangle: Difference between revisions
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(Added solution for Pascal.) |
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Line 3,366:
-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|Vlang}}==
{{trans|Go}}
<lang vlang>import math.fractions
import math.big
fn bernoulli(n int) fractions.Fraction {
mut a := []fractions.Fraction{len: n+1}
for m,_ in a {
a[m] = fractions.fraction(1, i64(m+1))
for j := m; j >= 1; j-- {
mut d := a[j-1]
d = fractions.fraction(i64(j),i64(1)) * (d-a[j])
a[j-1]=d
}
}
// return the 'first' Bernoulli number
if n != 1 {
return a[0]
}
a[0] = a[0].negate()
return a[0]
}
fn binomial(n int, k int) i64 {
if n <= 0 || k <= 0 || n < k {
return 1
}
mut num, mut den := i64(1), i64(1)
for i := k + 1; i <= n; i++ {
num *= i64(i)
}
for i := 2; i <= n-k; i++ {
den *= i64(i)
}
return num / den
}
fn faulhaber_triangle(p int) []fractions.Fraction {
mut coeffs := []fractions.Fraction{len: p+1}
q := fractions.fraction(1, i64(p)+1)
mut t := fractions.fraction(1,1)
mut u := fractions.fraction(1,1)
mut sign := -1
for j,_ in coeffs {
sign *= -1
mut d := coeffs[p-j]
t=fractions.fraction(i64(sign),1)
u = fractions.fraction(binomial(p+1, j),1)
d=q*t
d*=u
d*=bernoulli(j)
coeffs[p-j]=d
}
return coeffs
}
fn main() {
for i in 0..10 {
coeffs := faulhaber_triangle(i)
for coeff in coeffs {
print("${coeff:5} ")
}
println('')
}
println('')
}</lang>
{{out}}
<pre>
1/1
1/2 1/2
1/6 1/2 1/3
0/1 1/4 1/2 1/4
-1/30 0/1 1/3 1/2 1/5
0/1 -1/12 0/1 5/12 1/2 1/6
1/42 0/1 -1/6 0/1 1/2 1/2 1/7
0/1 1/12 0/1 -7/24 0/1 7/12 1/2 1/8
-1/30 0/1 2/9 0/1 -7/15 0/1 2/3 1/2 1/9
0/1 -3/20 0/1 1/2 0/1 -7/10 0/1 3/4 1/2 1/10
</pre>
=={{header|Wren}}==
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