二次体 Q(√m) に付随する指標を計算する Ruby のスクリプトです

character.rb

# coding: utf-8
require 'prime'


# Legendre symbol
def legendre(a, p)

   p.times do |x|
      if (x*x - a) % p == 0 then
         return 1
      end
   end

   return -1
end



# Jacobi symbol
def jacobi(a, n)
   divisions = Prime.prime_division(n)

   jacobi_val = 1
   divisions.each do |tuple|
      p = tuple[0]
      e = tuple[1]
      
      jacobi_val *= (legendre(a, p)**e)
   end

   return jacobi_val
end




# Dirichlet's chi character
#    p が素数のとき
def chi_p(d, p)
   if 2*d % p != 0
      return legendre(d, p)

   elsif p == 2 && d%2 != 0
      return jacobi(2, d.abs.to_i)

   else
      return 0

   end
end


# a が合成数のとき
def chi(d, a)
   if a == 0 
      return 0
   end

   divisions = Prime.prime_division(a)

   chi_val = 1
   divisions.each do |tuple|
      p = tuple[0]
      e = tuple[1]
      
      chi_val *= (chi_p(d, p)**e)
   end

   return chi_val
end


# 判別式
def discriminant m
   if m % 4 == 1
      return m
   elsif m % 4 == 2 || m % 4 == 3
      return 4*m
   end
end