82 lines
1.7 KiB
Go
82 lines
1.7 KiB
Go
package primes
|
|
|
|
import "opslag.de/schobers/geom/ints"
|
|
|
|
// GreatestCommonDivisor returns the greatest common divisor of a and b.
|
|
func GreatestCommonDivisor(a, b int64) int64 { return GCD(a, b) }
|
|
|
|
// GCD returns the greatest common divisor of a and b.
|
|
func GCD(a, b int64) int64 {
|
|
factors := Factorize(a)
|
|
var i int
|
|
var gcd int64 = 1
|
|
for _, f := range Factorize(b) {
|
|
for ; i < len(factors) && factors[i].Prime < f.Prime; i++ {
|
|
}
|
|
if i < len(factors) && factors[i].Prime == f.Prime {
|
|
var exponent = ints.Min(f.Exponent, factors[i].Exponent)
|
|
gcd *= ints.Pow64(f.Prime, int64(exponent))
|
|
i++
|
|
}
|
|
}
|
|
return gcd
|
|
}
|
|
|
|
// LeastCommonMultiple returns the least common multiple of a and b.
|
|
func LeastCommonMultiple(a, b int64) int64 { return LCM(a, b) }
|
|
|
|
// LCM returns the least common multiple of a and b.
|
|
func LCM(a, b int64) int64 {
|
|
factors := Factorize(a)
|
|
var i int
|
|
var lcm int64 = 1
|
|
for _, f := range Factorize(b) {
|
|
for i < len(factors) {
|
|
var p = factors[i].Prime
|
|
if p < f.Prime {
|
|
lcm *= p
|
|
i++
|
|
} else {
|
|
break
|
|
}
|
|
}
|
|
var exponent = f.Exponent
|
|
if i < len(factors) && factors[i].Prime == f.Prime {
|
|
exponent = ints.Max(exponent, factors[i].Exponent)
|
|
i++
|
|
}
|
|
lcm *= ints.Pow64(f.Prime, int64(exponent))
|
|
}
|
|
for ; i < len(factors); i++ {
|
|
f := factors[i]
|
|
lcm *= ints.Pow64(f.Prime, int64(f.Exponent))
|
|
}
|
|
return lcm
|
|
}
|
|
|
|
// RadInt returns the radical of integer n.
|
|
func RadInt(n int) int {
|
|
if 1 == n {
|
|
return 1
|
|
}
|
|
factors := Factorize(int64(n))
|
|
var r int = 1
|
|
for _, f := range factors {
|
|
r *= int(f.Prime)
|
|
}
|
|
return r
|
|
}
|
|
|
|
// RadInt64 returns the radical of integer n.
|
|
func RadInt64(n int64) int64 {
|
|
if 1 == n {
|
|
return 1
|
|
}
|
|
factors := Factorize(n)
|
|
var r int64 = 1
|
|
for _, f := range factors {
|
|
r *= f.Prime
|
|
}
|
|
return r
|
|
}
|