RubyAlgebra/lib/ruby_algebra/polynomial.rb

# frozen_string_literal: true

module RubyAlgebra
  # Многочлен - сумма одночленов
  class Polynomial
    # одночлены
    attr_reader :terms

    def initialize(terms = [])
      @terms = if terms.is_a? Term
                 [terms]
               else
                 terms
               end
      simplify!
    end

    def to_s
      if @terms.empty?
        result = ''
      else
        result = @terms[-1].to_s
        i = @terms.length - 2
        while i >= 0
          result += if @terms[i].coeff > 0
                      " + #{@terms[i]}"
                    else
                      " - #{-@terms[i]}"
                    end
          i -= 1
        end
      end
      result
    end

    def diff
      raise NotImplementedError
    end

    def evaluate(values)
      result = 0
      @terms.each do |term|
        # ...
      end
      result
    end

    def +(other)
      if other.is_a? Polynomial
        Polynomial.new(@terms + other.terms).simplify
      elsif other.is_a? Term
        Polynomial.new(@terms + [other]).simplify
      else
        Polynomial.new(@terms + [Term.new(other)]).simplify
      end
    end

    def *(other)
      if other.is_a? Polynomial
        result = Polynomial.new
        other.terms.each do |term|
          result += self * term
        end
        result
      else
        Polynomial.new(@terms.map { |term| term * other })
      end
    end

    def **(other)
      result = Polynomial.new([Term.new(1)])
      other.times do
        result *= self
      end
      result
    end

    def -(other)
      self + -other
    end

    def +@
      self
    end

    def -@
      self * -1
    end

    def ==(other)
      @terms == other.terms
    end

    def simplify
      i = 0
      new_terms = @terms.filter { |t| !t.zero? }
      while i < new_terms.length
        j = i + 1
        while j < new_terms.length
          if new_terms[i].similar_to?(new_terms[j])
            new_terms[i] += new_terms[j]
            if new_terms[i].zero?
              new_terms.delete_at(i)
              i -= 1
              j -= 1
            end
            new_terms.delete_at(j)
            j -= 1
          end
          j += 1
        end
        i += 1
      end
      Polynomial.new(new_terms.sort_by { |t| t.total_power })
    end

    def simplify!
      i = 0
      new_terms = @terms.filter { |t| !t.zero? }
      while i < new_terms.length
        j = i + 1
        while j < new_terms.length
          if new_terms[i].similar_to?(new_terms[j])
            new_terms[i] += new_terms[j]
            if new_terms[i].zero?
              new_terms.delete_at(i)
              i -= 1
              j -= 1
            end
            new_terms.delete_at(j)
            j -= 1
          end
          j += 1
        end
        i += 1
      end
      @terms = new_terms.sort_by { |t| t.total_power }
    end
  end

  # Одночлен в форме a_n * x_1^k_1 * ... * x_n^k_n
  class Term
    attr_reader :coeff, :variables

    def initialize(coeff = 0, variables = {})
      @coeff = coeff
      @variables = {}
      variables.each do |var, power|
        next if power.zero?

        if @variables[var].nil?
          @variables[var] = power
        else
          @variables[var] += power
        end
      end
    end

    def diff(var)
      raise NotImplementedError
    end

    def evaluate(values)
      raise NotImplementedError
    end

    def +(other)
      raise NotImplementedError, 'addition of non-similar terms is not implemented' unless similar_to?(other)

      Term.new(@coeff + other.coeff, @variables)
    end

    def *(other)
      return Term.new if @coeff.zero? || other.coeff.zero?

      new_variables = @variables.clone
      other.variables.each do |symbol, power|
        if new_variables[symbol].nil?
          new_variables[symbol] = power
        else
          new_variables[symbol] += power
        end
      end
      Term.new(@coeff * other.coeff, new_variables)
    end

    def +@
      Term.new(@coeff, @variables)
    end

    def -@
      Term.new(-@coeff, @variables)
    end

    def ==(other)
      @coeff == other.coeff && @variables == other.variables
    end

    def total_power
      @variables.values.sum
    end

    def to_s
      result = coeff.to_s
      unless @variables.empty?
        first = true
        @variables.each do |var, power|
          result += if first
                      "#{var}^#{power}"
                    else
                      " * #{var}^#{power}"
                    end
          first = false
        end
      end
      result
    end

    def similar_to?(other)
      return false if @variables.length != other.variables.length

      other.variables.each do |var, power|
        return false if @variables[var] != power
      end
      true
    end

    def zero?
      @coeff.zero?
    end
  end
end