Cyclotomic polynomial: Difference between revisions

Solution based on polynomial interpolation (slow).

<syntaxhighlight lang="ruby">var Poly = require('Math::Polynomial')

Poly.string_config(Hash(fold_sign => true, prefix => "", suffix => ""))

func poly_interpolation(v) {

v.len.of {|n| v.len.of {|k| n**k } }.msolve(v)

}

say "First 30 cyclotomic polynomials:"

var a = (k+1).of { cyclotomic(k, _) }

var Φ = poly_interpolation(a)

say ("Φ(#{k}) = ", Poly.new(Φ...))

for n in (1..10) { # very slow

poly_interpolation((k+1).of { cyclotomic(k, _) }).first { .abs == n }

}</syntaxhighlight>

Slightly faster solution, using the '''Math::Polynomial::Cyclotomic''' Perl module.

<syntaxhighlight lang="ruby">var Poly = require('Math::Polynomial')

require('Math::Polynomial::Cyclotomic')

Poly.string_config(Hash(fold_sign => true, prefix => "", suffix => ""))

say "First 30 cyclotomic polynomials:"

for k in (1..30) {

say ("Φ(#{k}) = ", Poly.new.cyclotomic(k))

}

say "\nSmallest cyclotomic polynomial with n or -n as a coefficient:"

for n in (1..10) {

var p = Poly.new

var k = (1..Inf -> first {|k|

[p.cyclotomic(k).coeff].first { .abs == n }

})

say "Φ(#{k}) has coefficient with magnitude = #{n}"