Class: Polymath::Nomial::Polynomial

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

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(exp) ⇒ Object

Returns a new Polynomial object.

Parameters:

  • exp —

    the string polynomial expression



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# File 'lib/polymath/nomial/polynomial.rb', line 36

def initialize(exp)
  @exp             = Parser.sanitize(exp)
  @monomials       = Parser.parse(@exp)
  @monomials      << ::ZeroMonomial if @monomials.length == 0

  @variable        = Parser.guess_variable(self)
  @homogenized_exp = Parser.set_variable(exp, @variable)

  @gcd             = ::UnitMonomial
end

Instance Attribute Details

#exp ⇒ Object (readonly)

Returns the value of attribute exp.



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# File 'lib/polymath/nomial/polynomial.rb', line 22

def exp
  @exp
end

#homogenized_exp ⇒ Object (readonly)

Returns the value of attribute homogenized_exp.



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# File 'lib/polymath/nomial/polynomial.rb', line 22

def homogenized_exp
  @homogenized_exp
end

#monomials ⇒ Object (readonly)

Returns the value of attribute monomials.



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# File 'lib/polymath/nomial/polynomial.rb', line 22

def monomials
  @monomials
end

#variable ⇒ Object

Returns the value of attribute variable.



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# File 'lib/polymath/nomial/polynomial.rb', line 23

def variable
  @variable
end

Instance Method Details

#classification ⇒ Object

Returns a hash.

Returns:

  • a hash



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# File 'lib/polymath/nomial/polynomial.rb', line 173

def classification
  if (1..3).include?(monomials.length)
    basic = [
      :monomial,
      :binomial,
      :trinomial
    ][monomials.length - 1]

    if basic == :monomial
      if monomials.first.cof == 0
        special = :zero
      elsif monomials.first.deg == 0
        special = :constant
      end
    end
  end

  if (0..10).include?(deg)
    degree = [
      :undefinded,
      :linear,
      :quadratic,
      :qubic,
      :quartic,
      :quintic,
      :hexic,
      :heptic,
      :octic,
      :nonic,
      :decic
    ][deg]
  end

  basic   ||= :polynomial
  special ||= :normal
  degree  ||= :"#{deg}th_degree"

  { :special => special, :deg => degree, :len => basic }
end

#cleanup! ⇒ Object

Returns nil.

Returns:

  • nil



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# File 'lib/polymath/nomial/polynomial.rb', line 93

def cleanup!
  homogenize!

  @monomials = order

  @monomials = collect_terms

  @monomials = factor_gcd
end

#coefficients ⇒ Object

Returns an array of integers.

Returns:

  • an array of integers



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# File 'lib/polymath/nomial/polynomial.rb', line 148

def coefficients
  monomials.map { |monomial| monomial.cof }
end

#collect_terms ⇒ Object

Returns an array of monomials where all like degrees are merged.

Returns:

  • an array of monomials where all like degrees are merged



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# File 'lib/polymath/nomial/polynomial.rb', line 79

def collect_terms
  c = (0..deg).map { |n|
    collected = monomials_where_deg(n).reduce(:+)
    collected.cof == 0 ? nil : collected if collected
  }.compact.reverse

  c.empty? ? [::ZeroMonomial] : c
end

#constant ⇒ Object

Returns an integer.

Parameters:

  • cof —

    The cof

Returns:

  • an integer



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# File 'lib/polymath/nomial/polynomial.rb', line 130

def constant
  (monomials_where_deg(0).first || Monomial.new(cof: 0)).cof
end

#deg ⇒ Object

Returns an integer degree.

Returns:

  • an integer degree



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# File 'lib/polymath/nomial/polynomial.rb', line 119

def deg
  order.first.deg
end

#factor_gcd ⇒ Object

Returns nil.

Returns:

  • nil



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# File 'lib/polymath/nomial/polynomial.rb', line 157

def factor_gcd
  cls = classification
  if cls[:special] == :zero or cls[:len] == :monomial
    return monomials
  end
  @gcd = monomials.reduce(:gcd)
  monomials.map { |monomial|
    monomial / @gcd
  }
end

#homogenize! ⇒ Object

Returns an array of monomials.

Returns:

  • an array of monomials



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# File 'lib/polymath/nomial/polynomial.rb', line 61

def homogenize!
  monomials.each { |monomial| monomial.homogenize!(variable) }
end

#leading_coefficient ⇒ Object

Returns an integer.

Returns:

  • an integer



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# File 'lib/polymath/nomial/polynomial.rb', line 139

def leading_coefficient
  monomials_where_deg(deg).first.cof
end

#modified_expression? ⇒ Boolean

Returns boolean.

Returns:

  • (Boolean) —

    boolean



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# File 'lib/polymath/nomial/polynomial.rb', line 52

def modified_expression?
  homogenized_exp != exp
end

#monomials_where_deg(n) ⇒ Object

Returns an array of monomials with degree == n.

Parameters:

  • n —

    the specified degree

Returns:

  • an array of monomials with degree == n



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# File 'lib/polymath/nomial/polynomial.rb', line 110

def monomials_where_deg(n)
  monomials.select { |monomial| monomial.deg == n }
end

#order ⇒ Object

Returns an array of monomials in descending order.

Returns:

  • an array of monomials in descending order



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# File 'lib/polymath/nomial/polynomial.rb', line 70

def order
  monomials.sort_by { |monomial| -monomial.deg }
end

#to_s ⇒ Object

Returns a string.

Returns:

  • a string



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# File 'lib/polymath/nomial/polynomial.rb', line 218

def to_s
  expression = monomials.collect { |monomial| monomial.to_s }.reduce { |m, t|
    joiner = t[0] == "-" ? "" : "+"
    m += joiner + t
  }
  if @gcd.cof == 1 and @gcd.deg == 0
    expression
  else
    "#{@gcd}(#{expression})"
  end
end