190818

Ruby


10-adic integer (p/9)^(1/3)

例えば、(1/9)^(1/3) = ...711529 を
9, 2, 5, 1, 1, 7, ...
のように出力してみた。

# q * x ** k - p == 0 mod base なるxを求める
def f(k, p, q, base)
  (0..base - 1).each{|i|
    return i if (q * i ** k - p) % base == 0
  }
end

# xから開始しk乗してp/q
def A(x, k, p, q, base, n)
  ary = [x]
  a, m = x, base
  n.times{
    (0..base - 1).each{|i|
      j = i * m + a
      if (q * j ** k - p) % (m * base) == 0
        ary << i
        a = j
        break
      end
    }
    m *= base
  }
  ary
end

def show(k, p, q, base)
  print "#{base}-adic integer "
  r = p / q.to_r
  r = p / q if r.denominator == 1
  if r.denominator == 1 && r >= 0
    print "#{r}"
  else
    print "(#{r})"
  end
  puts "^(#{1r / k})"
end

def B(k, p, q, base, n)
  show(k, p, q, base)
  x = f(k, p, q, base)
  p A(x, k, p, q, base, n)
end

n = 100
ary = []
[1, 3, 7, 9].each{|i|
  (0..9 - i).each{|j|
    ary << 10 * j + i
  }
}
ary.sort!
ary.each{|i| B(3,  i, 9, 10, n)}
ary.each{|i| B(3, -i, 9, 10, n)}

出力結果
10-adic integer (1/9)^(1/3)
[9, 2, 5, 1, 1, 7, 1, 3, 6, 2, 6, 3, 3, 8, 2, 1, 4, 1, 0, 2, 7, 1, 2, 2, 4, 6, 1, 6, 0, 1, 0, 1, 2, 7, 2, 8, 2, 8, 8, 3, 6, 7, 0, 7, 7, 7, 2, 2, 6, 2, 6, 9, 9, 6, 8, 1, 3, 2, 1, 5, 4, 3, 7, 4, 7, 7, 6, 9, 6, 1, 4, 0, 2, 0, 9, 6, 3, 6, 6, 1, 9, 1, 9, 9, 7, 4, 9, 8, 8, 7, 7, 3, 0, 8, 7, 7, 8, 8, 0, 8, 1]
10-adic integer (1/3)^(1/3)
[3, 2, 5, 3, 5, 5, 4, 1, 6, 5, 5, 3, 1, 6, 8, 4, 8, 9, 4, 8, 3, 0, 3, 8, 6, 8, 6, 2, 7, 7, 5, 3, 5, 5, 6, 1, 6, 4, 6, 6, 4, 3, 7, 4, 7, 6, 7, 1, 3, 6, 5, 8, 1, 0, 3, 2, 9, 5, 1, 6, 3, 2, 8, 8, 3, 3, 4, 7, 9, 2, 5, 9, 0, 7, 1, 9, 6, 9, 6, 9, 2, 6, 0, 2, 0, 2, 6, 5, 3, 4, 6, 8, 6, 9, 9, 1, 2, 5, 4, 2, 8]
10-adic integer (7/9)^(1/3)
[7, 4, 2, 9, 3, 3, 0, 0, 1, 6, 6, 7, 2, 0, 5, 8, 6, 3, 0, 4, 4, 6, 0, 9, 7, 1, 9, 4, 2, 6, 8, 7, 9, 6, 8, 0, 5, 7, 1, 0, 6, 6, 9, 8, 6, 4, 9, 0, 9, 8, 5, 9, 0, 5, 9, 6, 5, 2, 1, 5, 3, 4, 6, 7, 2, 4, 4, 1, 6, 3, 2, 6, 1, 4, 1, 0, 2, 7, 0, 0, 5, 4, 1, 7, 9, 6, 4, 1, 3, 2, 1, 0, 4, 6, 1, 5, 6, 1, 5, 2, 9]
10-adic integer 1^(1/3)
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
10-adic integer (11/9)^(1/3)
[9, 5, 8, 6, 6, 5, 0, 7, 6, 0, 5, 1, 0, 8, 9, 4, 8, 5, 8, 5, 6, 2, 2, 5, 2, 1, 8, 7, 6, 9, 9, 8, 2, 3, 8, 1, 0, 5, 8, 5, 7, 0, 0, 9, 6, 7, 4, 2, 0, 6, 6, 7, 7, 1, 2, 4, 1, 7, 9, 1, 2, 5, 4, 8, 7, 7, 3, 4, 4, 9, 1, 7, 6, 9, 6, 7, 0, 7, 4, 1, 3, 3, 6, 9, 7, 4, 6, 9, 8, 8, 5, 9, 0, 0, 1, 5, 4, 0, 5, 4, 4]
10-adic integer (13/9)^(1/3)
[3, 9, 6, 9, 6, 6, 2, 5, 6, 6, 5, 7, 4, 8, 2, 6, 1, 5, 2, 3, 5, 4, 9, 5, 1, 2, 1, 5, 3, 6, 9, 7, 1, 6, 7, 5, 5, 3, 7, 6, 4, 9, 5, 3, 1, 7, 9, 8, 0, 4, 4, 5, 7, 1, 2, 1, 3, 3, 4, 9, 1, 0, 1, 7, 6, 1, 9, 8, 0, 4, 1, 3, 7, 6, 7, 1, 2, 2, 0, 1, 1, 5, 4, 9, 2, 5, 2, 8, 9, 7, 5, 0, 9, 1, 4, 5, 4, 9, 7, 3, 1]
10-adic integer (17/9)^(1/3)
[7, 1, 6, 8, 7, 0, 3, 3, 3, 6, 5, 2, 7, 8, 7, 2, 6, 7, 1, 1, 0, 3, 3, 2, 4, 5, 6, 5, 3, 6, 5, 3, 3, 3, 7, 5, 2, 4, 7, 5, 0, 2, 9, 0, 6, 7, 0, 8, 8, 6, 6, 7, 0, 1, 2, 4, 5, 3, 2, 8, 6, 9, 7, 3, 1, 6, 6, 9, 5, 0, 1, 6, 4, 6, 8, 0, 3, 8, 5, 9, 6, 1, 3, 5, 3, 7, 9, 7, 2, 3, 6, 6, 9, 0, 0, 0, 5, 3, 7, 7, 2]
10-adic integer (7/3)^(1/3)
[9, 8, 9, 5, 3, 2, 3, 2, 4, 1, 6, 2, 9, 4, 0, 2, 1, 9, 1, 1, 8, 3, 0, 8, 2, 5, 0, 7, 5, 0, 5, 2, 5, 3, 6, 7, 4, 5, 2, 9, 9, 0, 0, 7, 2, 2, 4, 5, 9, 7, 0, 1, 7, 6, 9, 4, 0, 1, 7, 0, 7, 0, 6, 9, 8, 1, 5, 9, 7, 0, 8, 2, 8, 6, 8, 0, 4, 1, 8, 7, 5, 9, 6, 4, 7, 2, 7, 6, 4, 4, 4, 3, 4, 0, 0, 5, 8, 8, 9, 0, 0]
10-adic integer (23/9)^(1/3)
[3, 6, 2, 9, 7, 6, 0, 4, 7, 4, 2, 3, 4, 9, 0, 2, 1, 6, 5, 5, 4, 5, 9, 7, 3, 3, 2, 6, 4, 9, 6, 0, 0, 6, 4, 9, 5, 3, 2, 3, 1, 9, 6, 3, 3, 0, 5, 6, 1, 1, 4, 7, 2, 3, 1, 6, 2, 5, 7, 9, 9, 7, 3, 5, 1, 0, 8, 4, 2, 0, 2, 6, 3, 1, 6, 8, 2, 6, 4, 8, 4, 3, 4, 5, 9, 5, 3, 8, 9, 8, 6, 5, 7, 9, 1, 7, 2, 7, 6, 1, 7]
10-adic integer 3^(1/3)
[7, 8, 5, 4, 3, 1, 5, 9, 8, 7, 8, 0, 0, 5, 8, 3, 2, 4, 0, 6, 1, 5, 6, 6, 2, 9, 4, 8, 1, 3, 0, 3, 6, 1, 8, 4, 8, 4, 6, 1, 9, 2, 2, 1, 3, 3, 8, 6, 8, 7, 8, 8, 9, 0, 6, 5, 9, 6, 3, 5, 3, 0, 2, 4, 2, 3, 0, 9, 0, 5, 2, 1, 6, 0, 7, 0, 1, 9, 9, 4, 7, 5, 7, 9, 3, 4, 8, 6, 6, 3, 3, 1, 1, 4, 3, 3, 6, 6, 2, 4, 5]
10-adic integer (31/9)^(1/3)
[9, 1, 9, 8, 8, 1, 3, 3, 5, 8, 3, 9, 6, 0, 0, 9, 0, 6, 1, 9, 2, 8, 3, 4, 4, 7, 9, 1, 1, 5, 3, 2, 0, 1, 6, 9, 3, 2, 9, 2, 5, 9, 4, 0, 0, 4, 7, 9, 3, 2, 1, 0, 2, 1, 2, 7, 8, 7, 9, 2, 5, 1, 1, 5, 6, 3, 9, 3, 1, 7, 8, 5, 7, 1, 3, 2, 9, 4, 2, 5, 0, 2, 2, 4, 1, 5, 4, 0, 4, 2, 1, 5, 2, 0, 5, 5, 6, 2, 0, 8, 5]
10-adic integer (11/3)^(1/3)
[3, 3, 2, 2, 5, 8, 6, 8, 3, 1, 7, 3, 2, 6, 1, 0, 0, 1, 3, 2, 5, 3, 3, 5, 5, 5, 0, 8, 8, 9, 0, 9, 1, 7, 3, 2, 9, 4, 3, 9, 9, 8, 3, 3, 0, 1, 4, 2, 7, 6, 9, 5, 1, 5, 9, 3, 2, 5, 3, 7, 3, 1, 4, 8, 9, 7, 0, 1, 9, 1, 1, 4, 1, 4, 7, 4, 9, 0, 7, 7, 1, 2, 4, 9, 3, 4, 3, 8, 0, 8, 1, 8, 9, 8, 3, 5, 5, 1, 9, 2, 6]
10-adic integer (41/9)^(1/3)
[9, 4, 6, 5, 9, 6, 4, 6, 9, 6, 3, 6, 9, 7, 3, 3, 0, 2, 6, 9, 3, 9, 8, 4, 7, 8, 8, 6, 1, 5, 5, 7, 1, 8, 4, 4, 0, 3, 6, 1, 8, 2, 1, 5, 9, 2, 0, 3, 8, 9, 5, 6, 4, 1, 5, 7, 2, 0, 1, 8, 9, 8, 3, 1, 1, 7, 3, 6, 8, 6, 1, 3, 7, 2, 5, 7, 1, 7, 7, 3, 7, 1, 7, 6, 9, 7, 1, 7, 0, 3, 1, 8, 7, 3, 1, 0, 6, 2, 3, 3, 4]
10-adic integer (43/9)^(1/3)
[3, 0, 6, 8, 5, 0, 7, 1, 6, 9, 9, 9, 1, 7, 3, 8, 5, 6, 2, 9, 8, 1, 0, 9, 6, 8, 3, 0, 5, 1, 5, 1, 5, 7, 7, 1, 1, 5, 9, 9, 9, 9, 1, 2, 9, 9, 2, 1, 0, 3, 6, 9, 9, 5, 9, 4, 0, 5, 3, 0, 3, 0, 7, 9, 8, 1, 4, 6, 7, 9, 8, 7, 9, 4, 2, 0, 6, 6, 0, 5, 4, 3, 7, 9, 6, 8, 6, 4, 8, 5, 9, 4, 1, 7, 4, 2, 7, 3, 5, 0, 9]
10-adic integer (17/3)^(1/3)
[9, 7, 1, 6, 2, 8, 6, 6, 2, 1, 4, 1, 3, 6, 8, 9, 5, 4, 5, 0, 1, 9, 9, 1, 2, 8, 8, 9, 3, 1, 1, 7, 6, 9, 9, 2, 5, 2, 5, 2, 9, 5, 6, 9, 2, 0, 0, 1, 7, 3, 4, 5, 3, 1, 2, 3, 2, 7, 3, 1, 5, 5, 4, 5, 2, 4, 6, 6, 8, 2, 5, 6, 6, 6, 8, 0, 0, 9, 0, 9, 8, 8, 7, 0, 6, 1, 6, 1, 5, 8, 1, 2, 4, 2, 5, 0, 3, 2, 7, 2, 1]
10-adic integer (53/9)^(1/3)
[3, 7, 3, 8, 6, 7, 0, 5, 3, 0, 8, 5, 3, 4, 8, 1, 3, 0, 9, 0, 3, 2, 9, 2, 3, 6, 3, 2, 4, 3, 5, 1, 5, 2, 9, 8, 0, 7, 6, 0, 3, 9, 9, 4, 2, 5, 3, 0, 3, 2, 0, 3, 2, 8, 2, 8, 7, 8, 3, 1, 0, 0, 4, 6, 4, 1, 8, 9, 4, 8, 5, 3, 5, 3, 7, 3, 1, 6, 7, 9, 1, 1, 8, 5, 0, 2, 5, 7, 6, 3, 8, 9, 4, 2, 7, 3, 0, 3, 6, 6, 1]
10-adic integer (61/9)^(1/3)
[9, 0, 5, 0, 5, 4, 7, 1, 9, 1, 6, 0, 9, 8, 5, 7, 1, 0, 7, 3, 1, 0, 9, 5, 1, 4, 9, 9, 5, 7, 9, 3, 0, 1, 1, 9, 0, 1, 4, 1, 4, 0, 6, 4, 4, 1, 8, 0, 0, 1, 7, 6, 9, 1, 5, 3, 8, 1, 4, 2, 6, 7, 1, 3, 3, 9, 8, 0, 4, 5, 3, 7, 2, 5, 2, 7, 5, 5, 4, 6, 1, 0, 0, 2, 2, 3, 2, 0, 7, 3, 4, 2, 7, 7, 1, 0, 3, 1, 0, 9, 1]
10-adic integer 7^(1/3)
[3, 4, 5, 1, 5, 0, 7, 1, 2, 2, 2, 4, 4, 2, 9, 6, 0, 7, 3, 5, 4, 5, 8, 8, 8, 0, 4, 1, 8, 5, 1, 4, 0, 0, 6, 1, 3, 5, 4, 4, 8, 1, 3, 7, 4, 0, 7, 4, 8, 5, 5, 1, 6, 7, 4, 5, 5, 0, 0, 4, 9, 0, 4, 7, 0, 8, 6, 8, 4, 7, 4, 4, 2, 2, 0, 3, 2, 2, 0, 1, 6, 5, 5, 4, 3, 0, 3, 4, 9, 7, 1, 5, 1, 2, 3, 0, 2, 5, 6, 8, 7]
10-adic integer (71/9)^(1/3)
[9, 3, 6, 8, 3, 2, 7, 4, 5, 4, 1, 1, 9, 2, 2, 9, 0, 0, 3, 4, 5, 8, 1, 0, 7, 1, 6, 4, 6, 5, 3, 0, 3, 1, 5, 6, 9, 7, 3, 2, 4, 2, 4, 2, 0, 6, 2, 2, 0, 2, 3, 6, 7, 8, 4, 6, 5, 1, 5, 7, 5, 0, 9, 4, 4, 0, 9, 5, 5, 1, 9, 0, 2, 4, 7, 7, 6, 6, 4, 0, 1, 0, 6, 2, 9, 6, 8, 3, 9, 7, 9, 6, 0, 2, 3, 4, 6, 8, 6, 8, 6]
10-adic integer 9^(1/3)
[9, 6, 5, 0, 6, 6, 3, 4, 8, 6, 6, 0, 4, 8, 5, 4, 5, 9, 4, 5, 1, 1, 9, 4, 0, 6, 0, 8, 1, 3, 7, 0, 6, 6, 9, 4, 8, 3, 9, 9, 3, 0, 2, 4, 2, 0, 3, 5, 9, 8, 6, 5, 5, 0, 9, 6, 7, 7, 4, 8, 0, 7, 4, 6, 1, 0, 3, 2, 9, 8, 5, 8, 2, 1, 5, 7, 0, 9, 0, 9, 8, 8, 1, 6, 0, 6, 8, 6, 0, 3, 9, 5, 0, 9, 9, 5, 6, 5, 3, 7, 4]
10-adic integer (-1/9)^(1/3)
[1, 7, 4, 8, 8, 2, 8, 6, 3, 7, 3, 6, 6, 1, 7, 8, 5, 8, 9, 7, 2, 8, 7, 7, 5, 3, 8, 3, 9, 8, 9, 8, 7, 2, 7, 1, 7, 1, 1, 6, 3, 2, 9, 2, 2, 2, 7, 7, 3, 7, 3, 0, 0, 3, 1, 8, 6, 7, 8, 4, 5, 6, 2, 5, 2, 2, 3, 0, 3, 8, 5, 9, 7, 9, 0, 3, 6, 3, 3, 8, 0, 8, 0, 0, 2, 5, 0, 1, 1, 2, 2, 6, 9, 1, 2, 2, 1, 1, 9, 1, 8]
10-adic integer (-1/3)^(1/3)
[7, 7, 4, 6, 4, 4, 5, 8, 3, 4, 4, 6, 8, 3, 1, 5, 1, 0, 5, 1, 6, 9, 6, 1, 3, 1, 3, 7, 2, 2, 4, 6, 4, 4, 3, 8, 3, 5, 3, 3, 5, 6, 2, 5, 2, 3, 2, 8, 6, 3, 4, 1, 8, 9, 6, 7, 0, 4, 8, 3, 6, 7, 1, 1, 6, 6, 5, 2, 0, 7, 4, 0, 9, 2, 8, 0, 3, 0, 3, 0, 7, 3, 9, 7, 9, 7, 3, 4, 6, 5, 3, 1, 3, 0, 0, 8, 7, 4, 5, 7, 1]
10-adic integer (-7/9)^(1/3)
[3, 5, 7, 0, 6, 6, 9, 9, 8, 3, 3, 2, 7, 9, 4, 1, 3, 6, 9, 5, 5, 3, 9, 0, 2, 8, 0, 5, 7, 3, 1, 2, 0, 3, 1, 9, 4, 2, 8, 9, 3, 3, 0, 1, 3, 5, 0, 9, 0, 1, 4, 0, 9, 4, 0, 3, 4, 7, 8, 4, 6, 5, 3, 2, 7, 5, 5, 8, 3, 6, 7, 3, 8, 5, 8, 9, 7, 2, 9, 9, 4, 5, 8, 2, 0, 3, 5, 8, 6, 7, 8, 9, 5, 3, 8, 4, 3, 8, 4, 7, 0]
10-adic integer (-1)^(1/3)
[9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9]
10-adic integer (-11/9)^(1/3)
[1, 4, 1, 3, 3, 4, 9, 2, 3, 9, 4, 8, 9, 1, 0, 5, 1, 4, 1, 4, 3, 7, 7, 4, 7, 8, 1, 2, 3, 0, 0, 1, 7, 6, 1, 8, 9, 4, 1, 4, 2, 9, 9, 0, 3, 2, 5, 7, 9, 3, 3, 2, 2, 8, 7, 5, 8, 2, 0, 8, 7, 4, 5, 1, 2, 2, 6, 5, 5, 0, 8, 2, 3, 0, 3, 2, 9, 2, 5, 8, 6, 6, 3, 0, 2, 5, 3, 0, 1, 1, 4, 0, 9, 9, 8, 4, 5, 9, 4, 5, 5]
10-adic integer (-13/9)^(1/3)
[7, 0, 3, 0, 3, 3, 7, 4, 3, 3, 4, 2, 5, 1, 7, 3, 8, 4, 7, 6, 4, 5, 0, 4, 8, 7, 8, 4, 6, 3, 0, 2, 8, 3, 2, 4, 4, 6, 2, 3, 5, 0, 4, 6, 8, 2, 0, 1, 9, 5, 5, 4, 2, 8, 7, 8, 6, 6, 5, 0, 8, 9, 8, 2, 3, 8, 0, 1, 9, 5, 8, 6, 2, 3, 2, 8, 7, 7, 9, 8, 8, 4, 5, 0, 7, 4, 7, 1, 0, 2, 4, 9, 0, 8, 5, 4, 5, 0, 2, 6, 8]
10-adic integer (-17/9)^(1/3)
[3, 8, 3, 1, 2, 9, 6, 6, 6, 3, 4, 7, 2, 1, 2, 7, 3, 2, 8, 8, 9, 6, 6, 7, 5, 4, 3, 4, 6, 3, 4, 6, 6, 6, 2, 4, 7, 5, 2, 4, 9, 7, 0, 9, 3, 2, 9, 1, 1, 3, 3, 2, 9, 8, 7, 5, 4, 6, 7, 1, 3, 0, 2, 6, 8, 3, 3, 0, 4, 9, 8, 3, 5, 3, 1, 9, 6, 1, 4, 0, 3, 8, 6, 4, 6, 2, 0, 2, 7, 6, 3, 3, 0, 9, 9, 9, 4, 6, 2, 2, 7]
10-adic integer (-7/3)^(1/3)
[1, 1, 0, 4, 6, 7, 6, 7, 5, 8, 3, 7, 0, 5, 9, 7, 8, 0, 8, 8, 1, 6, 9, 1, 7, 4, 9, 2, 4, 9, 4, 7, 4, 6, 3, 2, 5, 4, 7, 0, 0, 9, 9, 2, 7, 7, 5, 4, 0, 2, 9, 8, 2, 3, 0, 5, 9, 8, 2, 9, 2, 9, 3, 0, 1, 8, 4, 0, 2, 9, 1, 7, 1, 3, 1, 9, 5, 8, 1, 2, 4, 0, 3, 5, 2, 7, 2, 3, 5, 5, 5, 6, 5, 9, 9, 4, 1, 1, 0, 9, 9]
10-adic integer (-23/9)^(1/3)
[7, 3, 7, 0, 2, 3, 9, 5, 2, 5, 7, 6, 5, 0, 9, 7, 8, 3, 4, 4, 5, 4, 0, 2, 6, 6, 7, 3, 5, 0, 3, 9, 9, 3, 5, 0, 4, 6, 7, 6, 8, 0, 3, 6, 6, 9, 4, 3, 8, 8, 5, 2, 7, 6, 8, 3, 7, 4, 2, 0, 0, 2, 6, 4, 8, 9, 1, 5, 7, 9, 7, 3, 6, 8, 3, 1, 7, 3, 5, 1, 5, 6, 5, 4, 0, 4, 6, 1, 0, 1, 3, 4, 2, 0, 8, 2, 7, 2, 3, 8, 2]
10-adic integer (-3)^(1/3)
[3, 1, 4, 5, 6, 8, 4, 0, 1, 2, 1, 9, 9, 4, 1, 6, 7, 5, 9, 3, 8, 4, 3, 3, 7, 0, 5, 1, 8, 6, 9, 6, 3, 8, 1, 5, 1, 5, 3, 8, 0, 7, 7, 8, 6, 6, 1, 3, 1, 2, 1, 1, 0, 9, 3, 4, 0, 3, 6, 4, 6, 9, 7, 5, 7, 6, 9, 0, 9, 4, 7, 8, 3, 9, 2, 9, 8, 0, 0, 5, 2, 4, 2, 0, 6, 5, 1, 3, 3, 6, 6, 8, 8, 5, 6, 6, 3, 3, 7, 5, 4]
10-adic integer (-31/9)^(1/3)
[1, 8, 0, 1, 1, 8, 6, 6, 4, 1, 6, 0, 3, 9, 9, 0, 9, 3, 8, 0, 7, 1, 6, 5, 5, 2, 0, 8, 8, 4, 6, 7, 9, 8, 3, 0, 6, 7, 0, 7, 4, 0, 5, 9, 9, 5, 2, 0, 6, 7, 8, 9, 7, 8, 7, 2, 1, 2, 0, 7, 4, 8, 8, 4, 3, 6, 0, 6, 8, 2, 1, 4, 2, 8, 6, 7, 0, 5, 7, 4, 9, 7, 7, 5, 8, 4, 5, 9, 5, 7, 8, 4, 7, 9, 4, 4, 3, 7, 9, 1, 4]
10-adic integer (-11/3)^(1/3)
[7, 6, 7, 7, 4, 1, 3, 1, 6, 8, 2, 6, 7, 3, 8, 9, 9, 8, 6, 7, 4, 6, 6, 4, 4, 4, 9, 1, 1, 0, 9, 0, 8, 2, 6, 7, 0, 5, 6, 0, 0, 1, 6, 6, 9, 8, 5, 7, 2, 3, 0, 4, 8, 4, 0, 6, 7, 4, 6, 2, 6, 8, 5, 1, 0, 2, 9, 8, 0, 8, 8, 5, 8, 5, 2, 5, 0, 9, 2, 2, 8, 7, 5, 0, 6, 5, 6, 1, 9, 1, 8, 1, 0, 1, 6, 4, 4, 8, 0, 7, 3]
10-adic integer (-41/9)^(1/3)
[1, 5, 3, 4, 0, 3, 5, 3, 0, 3, 6, 3, 0, 2, 6, 6, 9, 7, 3, 0, 6, 0, 1, 5, 2, 1, 1, 3, 8, 4, 4, 2, 8, 1, 5, 5, 9, 6, 3, 8, 1, 7, 8, 4, 0, 7, 9, 6, 1, 0, 4, 3, 5, 8, 4, 2, 7, 9, 8, 1, 0, 1, 6, 8, 8, 2, 6, 3, 1, 3, 8, 6, 2, 7, 4, 2, 8, 2, 2, 6, 2, 8, 2, 3, 0, 2, 8, 2, 9, 6, 8, 1, 2, 6, 8, 9, 3, 7, 6, 6, 5]
10-adic integer (-43/9)^(1/3)
[7, 9, 3, 1, 4, 9, 2, 8, 3, 0, 0, 0, 8, 2, 6, 1, 4, 3, 7, 0, 1, 8, 9, 0, 3, 1, 6, 9, 4, 8, 4, 8, 4, 2, 2, 8, 8, 4, 0, 0, 0, 0, 8, 7, 0, 0, 7, 8, 9, 6, 3, 0, 0, 4, 0, 5, 9, 4, 6, 9, 6, 9, 2, 0, 1, 8, 5, 3, 2, 0, 1, 2, 0, 5, 7, 9, 3, 3, 9, 4, 5, 6, 2, 0, 3, 1, 3, 5, 1, 4, 0, 5, 8, 2, 5, 7, 2, 6, 4, 9, 0]
10-adic integer (-17/3)^(1/3)
[1, 2, 8, 3, 7, 1, 3, 3, 7, 8, 5, 8, 6, 3, 1, 0, 4, 5, 4, 9, 8, 0, 0, 8, 7, 1, 1, 0, 6, 8, 8, 2, 3, 0, 0, 7, 4, 7, 4, 7, 0, 4, 3, 0, 7, 9, 9, 8, 2, 6, 5, 4, 6, 8, 7, 6, 7, 2, 6, 8, 4, 4, 5, 4, 7, 5, 3, 3, 1, 7, 4, 3, 3, 3, 1, 9, 9, 0, 9, 0, 1, 1, 2, 9, 3, 8, 3, 8, 4, 1, 8, 7, 5, 7, 4, 9, 6, 7, 2, 7, 8]
10-adic integer (-53/9)^(1/3)
[7, 2, 6, 1, 3, 2, 9, 4, 6, 9, 1, 4, 6, 5, 1, 8, 6, 9, 0, 9, 6, 7, 0, 7, 6, 3, 6, 7, 5, 6, 4, 8, 4, 7, 0, 1, 9, 2, 3, 9, 6, 0, 0, 5, 7, 4, 6, 9, 6, 7, 9, 6, 7, 1, 7, 1, 2, 1, 6, 8, 9, 9, 5, 3, 5, 8, 1, 0, 5, 1, 4, 6, 4, 6, 2, 6, 8, 3, 2, 0, 8, 8, 1, 4, 9, 7, 4, 2, 3, 6, 1, 0, 5, 7, 2, 6, 9, 6, 3, 3, 8]
10-adic integer (-61/9)^(1/3)
[1, 9, 4, 9, 4, 5, 2, 8, 0, 8, 3, 9, 0, 1, 4, 2, 8, 9, 2, 6, 8, 9, 0, 4, 8, 5, 0, 0, 4, 2, 0, 6, 9, 8, 8, 0, 9, 8, 5, 8, 5, 9, 3, 5, 5, 8, 1, 9, 9, 8, 2, 3, 0, 8, 4, 6, 1, 8, 5, 7, 3, 2, 8, 6, 6, 0, 1, 9, 5, 4, 6, 2, 7, 4, 7, 2, 4, 4, 5, 3, 8, 9, 9, 7, 7, 6, 7, 9, 2, 6, 5, 7, 2, 2, 8, 9, 6, 8, 9, 0, 8]
10-adic integer (-7)^(1/3)
[7, 5, 4, 8, 4, 9, 2, 8, 7, 7, 7, 5, 5, 7, 0, 3, 9, 2, 6, 4, 5, 4, 1, 1, 1, 9, 5, 8, 1, 4, 8, 5, 9, 9, 3, 8, 6, 4, 5, 5, 1, 8, 6, 2, 5, 9, 2, 5, 1, 4, 4, 8, 3, 2, 5, 4, 4, 9, 9, 5, 0, 9, 5, 2, 9, 1, 3, 1, 5, 2, 5, 5, 7, 7, 9, 6, 7, 7, 9, 8, 3, 4, 4, 5, 6, 9, 6, 5, 0, 2, 8, 4, 8, 7, 6, 9, 7, 4, 3, 1, 2]
10-adic integer (-71/9)^(1/3)
[1, 6, 3, 1, 6, 7, 2, 5, 4, 5, 8, 8, 0, 7, 7, 0, 9, 9, 6, 5, 4, 1, 8, 9, 2, 8, 3, 5, 3, 4, 6, 9, 6, 8, 4, 3, 0, 2, 6, 7, 5, 7, 5, 7, 9, 3, 7, 7, 9, 7, 6, 3, 2, 1, 5, 3, 4, 8, 4, 2, 4, 9, 0, 5, 5, 9, 0, 4, 4, 8, 0, 9, 7, 5, 2, 2, 3, 3, 5, 9, 8, 9, 3, 7, 0, 3, 1, 6, 0, 2, 0, 3, 9, 7, 6, 5, 3, 1, 3, 1, 3]
10-adic integer (-9)^(1/3)
[1, 3, 4, 9, 3, 3, 6, 5, 1, 3, 3, 9, 5, 1, 4, 5, 4, 0, 5, 4, 8, 8, 0, 5, 9, 3, 9, 1, 8, 6, 2, 9, 3, 3, 0, 5, 1, 6, 0, 0, 6, 9, 7, 5, 7, 9, 6, 4, 0, 1, 3, 4, 4, 9, 0, 3, 2, 2, 5, 1, 9, 2, 5, 3, 8, 9, 6, 7, 0, 1, 4, 1, 7, 8, 4, 2, 9, 0, 9, 0, 1, 1, 8, 3, 9, 3, 1, 3, 9, 6, 0, 4, 9, 0, 0, 4, 3, 4, 6, 2, 5]