Module: Algebra::PolynomialFactorization

Includes:
Q, Z, Zp
Included in:
Polynomial
Defined in:
lib/algebra/polynomial-factor.rb,
lib/algebra/polynomial-factor-zp.rb,
lib/algebra/polynomial-factor-int.rb

Defined Under Namespace

Modules: Q, Z, Zp

Instance Method Summary collapse

Methods included from Q

#contQ, #factorize_rational, #ppQ

Methods included from Z

#_factorize, #centorize, #divmod_ED, #factorize_int, #hensel_lift, #lifting, #reduce_over_prime_field, #resolve_c, #resultant_by_elimination, #sqfree_over_integral, #try_e

Methods included from Zp

#factorize_modp, #factors_of_sqfree, #verschiebung, #weak_factors_and_r

Instance Method Details

#factorize ⇒ Object 



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# File 'lib/algebra/polynomial-factor.rb', line 55

def factorize
  return Algebra::Factors.new([[zero, 1]]) if zero?
  fact0 = if ground <= Integer
            factorize_int
          elsif defined?(Rational) && ground <= Rational ||
                defined?(Algebra::LocalizedRing) && ground <= Algebra::LocalizedRing
            factorize_rational
          elsif defined?(Algebra::ResidueClassRing) && ground <= Algebra::ResidueClassRing
            if ground.ground <= Integer
              factorize_modp
            else
              factorize_alg
            end
          elsif ground <= Algebra::Polynomial
            require 'algebra/m-polynomial-factor'
            require 'algebra/polynomial-converter'
            mp = self.class.convert_to(Algebra::MPolynomial)
            f = value_on(mp)
            fact = f.factorize
            fact.map { |g| g.value_on(self.class) }
          else
            raise "(factor) unknown data type : #{self.class}"
          end
  fact0.normalize!
end

#irreducible? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/polynomial-factor.rb', line 81

def irreducible?
  factorize.size == 1
end

#monic_int(a = lc) ⇒ Object 



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# File 'lib/algebra/polynomial-factor.rb', line 28

def monic_int(a = lc)
  d = deg
  project(self.class) do |c, n|
    if n == d
      ground.unity
    elsif n < d
      c * a**(d - 1 - n)
    else
      # p [self, d, n]; exit
      raise
    end
  end
end

#monic_int_rev(a) ⇒ Object 



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# File 'lib/algebra/polynomial-factor.rb', line 42

def monic_int_rev(a)
  d = deg
  project(self.class) do |c, n|
    if n == d
      a
    elsif n < d
      c / a**(d - 1 - n)
    else
      raise
    end
  end
end

#psqfree? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/polynomial-factor.rb', line 24

def psqfree?
  pgcd(derivate).deg <= 0
end

#sqfree ⇒ Object 



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# File 'lib/algebra/polynomial-factor.rb', line 14

def sqfree
  f = self
  g = gcd(derivate)
  f / g * g.lc
end

#sqfree? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/algebra/polynomial-factor.rb', line 20

def sqfree?
  gcd(derivate).deg <= 0
end