Class: Polymath::Math

Inherits:
Object
  • Object
show all
Defined in:
lib/polymath/math/math.rb

Instance Method Summary collapse

Instance Method Details

#factor_rational_zeroes(polynomial:) ⇒ Object

Returns an array of Rational numbers.

Parameters:

  • polynomial —

    The polynomial

Returns:

  • an array of Rational numbers



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# File 'lib/polymath/math/math.rb', line 45

def factor_rational_zeroes(polynomial:)
  rational_zeroes(polynomial: polynomial).select { |test_value|
    is_a_zero?(test_value: test_value, polynomial: polynomial)
  }
end

#factor_zeroes(polynomial:) ⇒ Object 



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# File 'lib/polymath/math/math.rb', line 51

def factor_zeroes(polynomial:)
  case polynomial.classification[:len]
  when :monomial
    case polynomial.classification[:special]
    when :zero
      [Float::INFINITY]
    else
      [::ZeroRoot]
    end
  else
    factor_rational_zeroes(polynomial: polynomial)
  end
end

#factors_of(x) ⇒ Object

Returns an array of integers.

Parameters:

  • x —

    the integer to factor

Returns:

  • an array of integers



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# File 'lib/polymath/math/math.rb', line 87

def factors_of(x)
  (x.prime_division.map { |f| f[0] } + [1, x]).uniq.sort
end

#is_a_zero?(test_value:, polynomial:) ⇒ Boolean

Returns True if a zero, False otherwise.

Parameters:

  • polynomial —

    The polynomial

  • test_value —

    The test value

Returns:

  • (Boolean) —

    True if a zero, False otherwise.



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# File 'lib/polymath/math/math.rb', line 34

def is_a_zero?(test_value:, polynomial:)
  synthetic_remainder(polynomial: polynomial, divisor: test_value) == 0
end

#rational_zeroes(polynomial:) ⇒ Object

Returns an array of Rational numbers.

Parameters:

  • polynomial —

    The polynomial

Returns:

  • an array of Rational numbers



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# File 'lib/polymath/math/math.rb', line 16

def rational_zeroes(polynomial:)
  cnf = factors_of(polynomial.constant)
  lcf = factors_of(polynomial.leading_coefficient)

  cnf.map { |x|
    lcf.map { |y| [ Rational(x, y), -Rational(x, y) ] }
  }.flatten.uniq
end

#synthetic_remainder(polynomial:, divisor:) ⇒ Object

Returns a Rational number.

Parameters:

  • polynomial —

    The polynomial

  • value —

    The value

Returns:

  • a Rational number



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# File 'lib/polymath/math/math.rb', line 74

def synthetic_remainder(polynomial:, divisor:)
  polynomial.coefficients.reduce { |carry, next_cof|
    (carry * divisor) + next_cof
  }
end