#

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# mathn.rb -

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# $Release Version: 0.5 $

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# $Revision: 1.1.1.1.4.1 $

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# $Date: 1998/01/16 12:36:05 $

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# by Keiju ISHITSUKA(SHL Japan Inc.)

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#

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# --

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#

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#

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#

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require "complex.rb"

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require "rational.rb"

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require "matrix.rb"

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class Integer

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def gcd2(int)

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a = self.abs

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b = int.abs

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a, b = b, a if a < b

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pd_a = a.prime_division

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pd_b = b.prime_division

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gcd = 1

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for pair in pd_a

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as = pd_b.assoc(pair[0])

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if as

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gcd *= as[0] ** [as[1], pair[1]].min

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end

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end

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return gcd

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end

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def Integer.from_prime_division(pd)

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value = 1

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for prime, index in pd

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value *= prime**index

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end

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value

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end

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def prime_division

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raise ZeroDivisionError if self == 0

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ps = Prime.new

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value = self

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pv = []

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for prime in ps

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count = 0

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while (value1, mod = value.divmod(prime)

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mod) == 0

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value = value1

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count += 1

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end

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if count != 0

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pv.push [prime, count]

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end

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break if prime * prime >= value

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end

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if value > 1

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pv.push [value, 1]

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end

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return pv

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end

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end

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class Prime

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include Enumerable

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def initialize

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@seed = 1

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@primes = []

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@counts = []

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end

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def succ

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i = -1

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size = @primes.size

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while i < size

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if i == -1

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@seed += 1

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i += 1

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else

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while @seed > @counts[i]

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@counts[i] += @primes[i]

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end

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if @seed != @counts[i]

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i += 1

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else

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i = -1

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end

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end

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end

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@primes.push @seed

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@counts.push @seed + @seed

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return @seed

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end

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alias next succ

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def each

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loop do

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yield succ

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end

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end

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end

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class Fixnum

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alias / quo

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end

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class Bignum

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alias / quo

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end

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class Rational

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Unify = true

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def inspect

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format "%s/%s", numerator.inspect, denominator.inspect

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end

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alias power! **

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def ** (other)

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if other.kind_of?(Rational)

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other2 = other

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if self < 0

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return Complex.new!(self, 0) ** other

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elsif other == 0

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return Rational(1,1)

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elsif self == 0

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return Rational(0,1)

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elsif self == 1

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return Rational(1,1)

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end

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npd = numerator.prime_division

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dpd = denominator.prime_division

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if other < 0

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other = -other

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npd, dpd = dpd, npd

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end

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for elm in npd

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elm[1] = elm[1] * other

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if !elm[1].kind_of?(Integer) and elm[1].denominator != 1

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return Float(self) ** other2

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end

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elm[1] = elm[1].to_i

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end

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for elm in dpd

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elm[1] = elm[1] * other

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if !elm[1].kind_of?(Integer) and elm[1].denominator != 1

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return Float(self) ** other2

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end

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elm[1] = elm[1].to_i

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end

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num = Integer.from_prime_division(npd)

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den = Integer.from_prime_division(dpd)

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Rational(num,den)

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elsif other.kind_of?(Integer)

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if other > 0

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num = numerator ** other

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den = denominator ** other

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elsif other < 0

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num = denominator ** -other

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den = numerator ** -other

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elsif other == 0

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num = 1

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den = 1

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end

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Rational.new!(num, den)

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elsif other.kind_of?(Float)

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Float(self) ** other

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else

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x , y = other.coerce(self)

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x ** y

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end

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end

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def power2(other)

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if other.kind_of?(Rational)

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if self < 0

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return Complex(self, 0) ** other

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elsif other == 0

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return Rational(1,1)

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elsif self == 0

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return Rational(0,1)

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elsif self == 1

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return Rational(1,1)

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end

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dem = nil

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x = self.denominator.to_f.to_i

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neard = self.denominator.to_f ** (1.0/other.denominator.to_f)

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loop do

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if (neard**other.denominator == self.denominator)

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dem = neaed

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break

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end

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end

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nearn = self.numerator.to_f ** (1.0/other.denominator.to_f)

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Rational(num,den)

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elsif other.kind_of?(Integer)

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if other > 0

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num = numerator ** other

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den = denominator ** other

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elsif other < 0

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num = denominator ** -other

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den = numerator ** -other

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elsif other == 0

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num = 1

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den = 1

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end

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Rational.new!(num, den)

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elsif other.kind_of?(Float)

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Float(self) ** other

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else

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x , y = other.coerce(self)

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x ** y

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end

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end

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end

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module Math

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def sqrt(a)

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if a.kind_of?(Complex)

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abs = sqrt(a.real*a.real + a.image*a.image)

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# if not abs.kind_of?(Rational)

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# return a**Rational(1,2)

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# end

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x = sqrt((a.real + abs)/Rational(2))

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y = sqrt((-a.real + abs)/Rational(2))

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# if !(x.kind_of?(Rational) and y.kind_of?(Rational))

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# return a**Rational(1,2)

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# end

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if a.image >= 0

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Complex(x, y)

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else

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Complex(x, -y)

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end

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elsif a >= 0

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rsqrt(a)

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else

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Complex(0,rsqrt(-a))

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end

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end

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def rsqrt(a)

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if a.kind_of?(Float)

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sqrt!(a)

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elsif a.kind_of?(Rational)

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rsqrt(a.numerator)/rsqrt(a.denominator)

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else

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src = a

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max = 2 ** 32

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byte_a = [src & 0xffffffff]

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# ruby's bug

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while (src >= max) and (src >>= 32)

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byte_a.unshift src & 0xffffffff

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end

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answer = 0

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main = 0

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side = 0

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for elm in byte_a

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main = (main << 32) + elm

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side <<= 16

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if answer != 0

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if main * 4 < side * side

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applo = main.div(side)

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else

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applo = ((sqrt!(side * side + 4 * main) - side)/2.0).to_i + 1

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end

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else

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applo = sqrt!(main).to_i + 1

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end

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while (x = (side + applo) * applo) > main

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applo -= 1

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end

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main -= x

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answer = (answer << 16) + applo

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side += applo * 2

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end

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if main == 0

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answer

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else

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sqrt!(a)

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end

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end

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end

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module_function :sqrt

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module_function :rsqrt

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end

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class Complex

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Unify = true

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end

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