Class: Polynomials::Polynomial

Inherits:
Object
  • Object
show all
Includes:
Analyzable
Defined in:
lib/polynomials/polynomial.rb

Constant Summary

Constants included from Analyzable

Analyzable::AfterExtremaCurvatureMapping, Analyzable::MinimumOrMaximum

Instance Attribute Summary collapse

Class Method Summary collapse

Instance Method Summary collapse

Methods included from Analyzable

#curvature_behaviour, #inflection_points, #local_extrema, #strives_for

Constructor Details

#initialize(*args) ⇒ Polynomial

Returns a new instance of Polynomial.



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# File 'lib/polynomials/polynomial.rb', line 16

def initialize(*args)
  self.terms = Hash.new { |hash, key| hash[key] = Term.new(key) }
  unless args.empty?
    args.reverse.each.with_index do |coefficient,exponent|
      self.terms[exponent].coefficient += coefficient
    end
  end
end

Instance Attribute Details

#terms ⇒ Object

Returns the value of attribute terms.



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# File 'lib/polynomials/polynomial.rb', line 5

def terms
  @terms
end

Class Method Details

.parse(string) ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 7

def self.parse(string)
  polynomial = self.new
  string.split(/(?=[-+])/).each do |term|
    parsed = Term.parse(term)
    polynomial.terms[parsed.exponent].coefficient += parsed.coefficient
  end
  return polynomial
end

Instance Method Details

#==(other) ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 69

def ==(other)
  delete_zeros = proc{ |_,t| t.coefficient.zero? }
  self.terms.delete_if(&delete_zeros) == other.terms.delete_if(&delete_zeros)
end

#calculate(x) ⇒ Object Also known as: call 



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# File 'lib/polynomials/polynomial.rb', line 25

def calculate(x)
  self.terms.values.inject(0.0) do |acc,t|
    acc + (t.coefficient.to_f * (x**t.exponent))
  end
end

#degree ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 58

def degree
  self.terms.keys.max || 0
end

#derivative ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 32

def derivative
  new_function = self.alter do |nf, term|
    (nf.terms[term.exponent - 1].coefficient += term.exponent * term.coefficient) unless term.exponent.zero?
  end

end

#grouped_pointset(start, stop, step = 0.1, grouped) ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 92

def grouped_pointset(start,stop,step=0.1,grouped)
  Hash[grouped.map do |key,intervals|
    intervals = intervals.reject { |s,e| e < start || s > stop }
    intervals = intervals.map do |s,e|
      self.pointset([s,start].max, [e,stop].min, step)
    end
    [key,intervals]
  end]
end

#gt ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 74

def gt
  self.terms[self.degree]
end

#lt ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 78

def lt
  self.terms[self.terms.reject { |_,t| t.coefficient.zero? }.min_by{ |_,t| t.exponent}.first]
end

#pointset(start, stop, step = 0.1) ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 82

def pointset(start,stop,step=0.1)
  data = []
  x = start
  while x < stop
    data << [x,self.(x)]
    x += step
  end
  data << [stop,self.(stop)]
end

#roots ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 39

def roots
  if !terms.empty? and (terms.keys.none?(&:zero?) || terms[0].coefficient.zero?)
    self.alter { |nf, term| nf.terms[term.exponent-self.lt.exponent].coefficient = term.coefficient }.roots << Root.new(0.0)
  else
    case self.degree
    when 1
      Set[-self.terms[0].coefficient / self.terms[1].coefficient]
    when 2
      Formulas.roots_of_quadratic_function(*coefficients_till(2))
    when 3
      Formulas.roots_of_cubic_function(*coefficients_till(3))
    when 4
      Formulas.roots_of_quartic_function(*coefficients_till(4))
    else
      Set[]
    end.map { |x| Root.new(x) }.to_set
  end
end

#to_s ⇒ Object 



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# File 'lib/polynomials/polynomial.rb', line 62

def to_s
  terms.sort_by { |_,t| -t.exponent }.inject("") do |string,(_,term)|
    string << term.to_s unless term.coefficient.zero? && !term.exponent.zero?
  string
  end.strip.sub(/\A\+\s/, '')
end