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Faulhaber's formula: Difference between revisions
Add Go example.
(Added Julia language) |
(Add Go example.) |
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Line 243:
1/9*n^9+1/2*n^8+2/3*n^7-7/15*n^5+2/9*n^3-1/30*n
1/10*n^10+1/2*n^9+3/4*n^8-7/10*n^6+1/2*n^4-3/20*n^2</lang>
=={{header|Go}}==
<lang Go>package main
import (
"fmt"
"math/big"
)
func bernoulli(z *big.Rat, n int64) *big.Rat {
if z == nil {
z = new(big.Rat)
}
a := make([]big.Rat, n+1)
for m := range a {
a[m].SetFrac64(1, int64(m+1))
for j := m; j >= 1; j-- {
d := &a[j-1]
d.Mul(z.SetInt64(int64(j)), d.Sub(d, &a[j]))
}
}
return z.Set(&a[0])
}
func main() {
// allocate needed big.Rat's once
q := new(big.Rat)
c := new(big.Rat) // coefficients
be := new(big.Rat) // for Bernoulli numbers
bi := big.NewRat(1, 1) // for binomials
for p := int64(0); p < 10; p++ {
fmt.Print(p, " : ")
q.SetFrac64(1, p+1)
neg := true
for j := int64(0); j <= p; j++ {
neg = !neg
if neg {
c.Neg(q)
} else {
c.Set(q)
}
bi.Num().Binomial(p+1, j)
bernoulli(be, j)
c.Mul(c, bi)
c.Mul(c, be)
if c.Num().BitLen() == 0 {
continue
}
if j == 0 {
fmt.Printf(" %4s", c.RatString())
} else {
fmt.Printf(" %+2d/%-2d", c.Num(), c.Denom())
}
fmt.Print("×n")
if exp := p + 1 - j; exp > 1 {
fmt.Printf("^%-2d", exp)
}
}
fmt.Println()
}
}</lang>
{{out}}
<pre>
0 : 1×n
1 : 1/2×n^2 -1/2 ×n
2 : 1/3×n^3 -1/2 ×n^2 +1/6 ×n
3 : 1/4×n^4 -1/2 ×n^3 +1/4 ×n^2
4 : 1/5×n^5 -1/2 ×n^4 +1/3 ×n^3 -1/30×n
5 : 1/6×n^6 -1/2 ×n^5 +5/12×n^4 -1/12×n^2
6 : 1/7×n^7 -1/2 ×n^6 +1/2 ×n^5 -1/6 ×n^3 +1/42×n
7 : 1/8×n^8 -1/2 ×n^7 +7/12×n^6 -7/24×n^4 +1/12×n^2
8 : 1/9×n^9 -1/2 ×n^8 +2/3 ×n^7 -7/15×n^5 +2/9 ×n^3 -1/30×n
9 : 1/10×n^10 -1/2 ×n^9 +3/4 ×n^8 -7/10×n^6 +1/2 ×n^4 -3/20×n^2
</pre>
=={{header|Haskell}}==
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