From a420ba3ce2beb1f27aac60faee579f34069e5303 Mon Sep 17 00:00:00 2001
From: Slavasil <subvia@proton.me>
Date: Mon, 13 Apr 2026 13:23:12 +0300
Subject: [PATCH] replace expressions with polynomials, add interpreter command
 class, rewrite parser

---
 lib/ruby_algebra.rb            |   5 +-
 lib/ruby_algebra/command.rb    |  46 ++++
 lib/ruby_algebra/expression.rb | 375 -----------------------------
 lib/ruby_algebra/parser.rb     | 427 +++++++++++++++++++++------------
 lib/ruby_algebra/polynomial.rb |  22 +-
 5 files changed, 343 insertions(+), 532 deletions(-)
 create mode 100644 lib/ruby_algebra/command.rb
 delete mode 100644 lib/ruby_algebra/expression.rb

diff --git a/lib/ruby_algebra.rb b/lib/ruby_algebra.rb
index d017ed9..2664ef9 100644
--- a/lib/ruby_algebra.rb
+++ b/lib/ruby_algebra.rb
@@ -1,9 +1,6 @@
 # frozen_string_literal: true
 
 require_relative 'ruby_algebra/version'
-require_relative 'ruby_algebra/expression'
+require_relative 'ruby_algebra/command'
 require_relative 'ruby_algebra/polynomial'
 require_relative 'ruby_algebra/parser'
-
-module RubyAlgebra
-end
diff --git a/lib/ruby_algebra/command.rb b/lib/ruby_algebra/command.rb
new file mode 100644
index 0000000..167162d
--- /dev/null
+++ b/lib/ruby_algebra/command.rb
@@ -0,0 +1,46 @@
+# frozen_string_literal: true
+
+module RubyAlgebra
+  # Команда интерпретатора
+  class Command
+  end
+
+  # Команда присвоения
+  class AssignmentCommand < Command
+    attr_reader :lhs, :operation, :operand1, :operand2
+
+    def initialize(lhs, operation, operand1, operand2)
+      @lhs = lhs
+      @operation = operation
+      @operand1 = operand1
+      @operand2 = operand2
+    end
+
+    def to_s
+      result = @lhs.is_a?(Array) ? @lhs.join(', ') : @lhs.to_s
+      result += ' := '
+      result += @operand1.to_s
+      case @operation
+      when :add
+        result += ' + '
+      when :sub
+        result += ' - '
+      when :mult, :scale
+        result += ' * '
+      when :div
+        result += ' / '
+      end
+      result += @operand2.to_s if @operation != :assign
+      result
+    end
+  end
+
+  # Команда вывода на экран
+  class DisplayCommand < Command
+    attr_reader :polynomial
+
+    def initialize(polynomial)
+      @polynomial = polynomial
+    end
+  end
+end
diff --git a/lib/ruby_algebra/expression.rb b/lib/ruby_algebra/expression.rb
deleted file mode 100644
index 4307a1f..0000000
--- a/lib/ruby_algebra/expression.rb
+++ /dev/null
@@ -1,375 +0,0 @@
-# frozen_string_literal: true
-
-module RubyAlgebra
-  class Expression
-    def to_s
-      raise NotImplementedError
-    end
-
-    def type
-      raise NotImplementedError
-    end
-
-    def op_priority
-      raise NotImplementedError
-    end
-
-    def op_assoc_type
-      raise NotImplementedError
-    end
-
-    def diff(v)
-      raise NotImplementedError, "#{self.class}#diff not implemented"
-    end
-
-    def evaluate
-      raise NotImplementedError, "#{self.class}#evaluate not implemented"
-    end
-
-    def constant?
-      raise NotImplementedError, "#{self.class}#constant? not implemented"
-    end
-  end
-
-  class Addition < Expression
-    attr_reader :lhs, :rhs
-
-    def initialize(lhs, rhs)
-      raise ArgumentError unless lhs.is_a?(Expression) && rhs.is_a?(Expression)
-
-      @lhs = lhs
-      @rhs = rhs
-    end
-
-    def to_s
-      need_parentheses_left = lhs.op_priority < op_priority || (lhs.op_priority == op_priority && op_assoc_type == :right)
-      need_parentheses_right = rhs.op_priority < op_priority || (rhs.op_priority == op_priority && op_assoc_type == :left)
-
-      result = need_parentheses_left ? "(#{lhs}) + " : "#{lhs} + "
-      result + (need_parentheses_right ? "(#{rhs})" : rhs.to_s)
-    end
-
-    def type
-      :add
-    end
-
-    def op_priority
-      10
-    end
-
-    def op_assoc_type
-      :left
-    end
-
-    def ==(other)
-      return false if other.type != type
-
-      lhs == other.lhs && rhs == other.rhs
-    end
-
-    def diff(v)
-      Addition.new(@lhs.diff(v), @rhs.diff(v))
-    end
-
-    def evaluate
-      lhs_val = @lhs.evaluate
-      rhs_val = @rhs.evaluate
-      return nil if lhs_val.nil? || rhs_val.nil?
-
-      lhs_val + rhs_val
-    end
-
-    def constant?
-      @lhs.constant? && @rhs.constant?
-    end
-  end
-
-  class Subtraction < Addition
-    attr_reader :lhs, :rhs
-
-    def to_s
-      need_parentheses_left = lhs.op_priority < op_priority || (lhs.op_priority == op_priority && op_assoc_type == :right)
-      need_parentheses_right = rhs.op_priority < op_priority || (rhs.op_priority == op_priority && op_assoc_type == :left)
-
-      result = need_parentheses_left ? "(#{lhs}) - " : "#{lhs} - "
-      result + (need_parentheses_right ? "(#{rhs})" : rhs.to_s)
-    end
-
-    def type
-      :sub
-    end
-
-    def diff(v)
-      Subtraction.new(@lhs.diff(v), @rhs.diff(v))
-    end
-
-    def evaluate
-      lhs_val = @lhs.evaluate
-      rhs_val = @rhs.evaluate
-      return nil if lhs_val.nil? || rhs_val.nil?
-
-      lhs_val - rhs_val
-    end
-
-    def constant?
-      @lhs.constant? && @rhs.constant?
-    end
-  end
-
-  class Multiplication < Expression
-    attr_reader :lhs, :rhs
-
-    def initialize(lhs, rhs)
-      raise ArgumentError unless lhs.is_a?(Expression) && rhs.is_a?(Expression)
-
-      @lhs = lhs
-      @rhs = rhs
-    end
-
-    def to_s
-      need_parentheses_left = lhs.op_priority < op_priority || (lhs.op_priority == op_priority && op_assoc_type == :right)
-      need_parentheses_right = rhs.op_priority < op_priority || (rhs.op_priority == op_priority && op_assoc_type == :left)
-
-      if lhs.type == :constant && lhs.value == 1
-        need_parentheses_right ? "(#{rhs})" : rhs.to_s
-      elsif lhs.type == :constant && lhs.value == -1
-        need_parentheses_right ? "-(#{rhs})" : "-#{rhs}"
-      elsif (need_parentheses_right || rhs.type == :variable) && (need_parentheses_left || lhs.type == :mult || lhs.type == :constant)
-        result = need_parentheses_left ? "(#{lhs})" : lhs.to_s
-        result += ' ' if lhs.type == :variable && rhs.type == :variable && lhs.single_letter? && rhs.single_letter?
-        result + (need_parentheses_right ? "(#{rhs})" : rhs.to_s)
-      else
-        result = need_parentheses_left ? "(#{lhs}) * " : "#{lhs} * "
-        result + (need_parentheses_right ? "(#{rhs})" : rhs.to_s)
-      end
-    end
-
-    def type
-      :mult
-    end
-
-    def op_priority
-      20
-    end
-
-    def op_assoc_type
-      :left
-    end
-
-    def ==(other)
-      return false if other.type != type
-
-      lhs == other.lhs && rhs == other.rhs
-    end
-
-    def diff(v)
-      u_prime = @lhs.diff(v)
-      v_prime = @rhs.diff(v)
-      term1 = Multiplication.new(u_prime, @rhs)
-      term2 = Multiplication.new(@lhs, v_prime)
-      Addition.new(term1, term2)
-    end
-
-    def evaluate
-      lhs_val = @lhs.evaluate
-      rhs_val = @rhs.evaluate
-      return nil if lhs_val.nil? || rhs_val.nil?
-
-      lhs_val * rhs_val
-    end
-
-    def constant?
-      @lhs.constant? && @rhs.constant?
-    end
-  end
-
-  class Division < Multiplication
-    def to_s
-      need_parentheses_left = lhs.op_priority < op_priority || (lhs.op_priority == op_priority && op_assoc_type == :right)
-      need_parentheses_right = rhs.op_priority < op_priority || (rhs.op_priority == op_priority && op_assoc_type == :left)
-
-      result = need_parentheses_left ? "(#{lhs}) / " : "#{lhs} / "
-      result + (need_parentheses_right ? "(#{rhs})" : rhs.to_s)
-    end
-
-    def type
-      :div
-    end
-
-    def diff(v)
-      u_prime = @lhs.diff(v)
-      v_prime = @rhs.diff(v)
-
-      numerator = Subtraction.new(
-        Multiplication.new(u_prime, @rhs),
-        Multiplication.new(@lhs, v_prime)
-      )
-      denominator = Power.new(@rhs, Constant.new(2))
-      Division.new(numerator, denominator)
-    end
-
-    def evaluate
-      lhs_val = @lhs.evaluate
-      rhs_val = @rhs.evaluate
-      return nil if lhs_val.nil? || rhs_val.nil?
-      return nil if rhs_val == 0
-
-      lhs_val.to_f / rhs_val
-    end
-
-    def constant?
-      @lhs.constant? && @rhs.constant?
-    end
-  end
-
-  class Power < Expression
-    attr_reader :base, :exponent
-
-    def initialize(base, exponent)
-      raise ArgumentError unless base.is_a?(Expression) && exponent.is_a?(Expression)
-
-      @base = base
-      @exponent = exponent
-    end
-
-    def to_s
-      need_parentheses_left = base.op_priority < op_priority || (base.op_priority == op_priority && op_assoc_type == :right)
-      need_parentheses_right = exponent.op_priority < op_priority || (exponent.op_priority == op_priority && op_assoc_type == :left)
-
-      result = need_parentheses_left ? "(#{base}) ^ " : "#{base} ^ "
-      result + (need_parentheses_right ? "(#{exponent})" : exponent.to_s)
-    end
-
-    def type
-      :pow
-    end
-
-    def op_priority
-      30
-    end
-
-    def op_assoc_type
-      :right
-    end
-
-    def ==(other)
-      return false if other.type != type
-
-      base == other.base && exponent == other.exponent
-    end
-
-    def diff(v)
-      unless @exponent.is_a?(Constant)
-        raise NotImplementedError, 'Дифференцирование степени с неконстантным показателем не реализовано'
-      end
-
-      n = @exponent.value
-      # (u^n)' = n * u^(n-1) * u'
-      base_diff = @base.diff(v)
-      new_power = Power.new(@base, Constant.new(n - 1))
-      coeff = Constant.new(n)
-      Multiplication.new(coeff, Multiplication.new(new_power, base_diff))
-    end
-
-    def evaluate
-      base_val = @base.evaluate
-      exp_val = @exponent.evaluate
-      return nil if base_val.nil? || exp_val.nil?
-
-      base_val**exp_val
-    end
-
-    def constant?
-      @base.constant? && @exponent.constant?
-    end
-  end
-
-  class Constant < Expression
-    attr_reader :value
-
-    def initialize(value)
-      @value = value
-    end
-
-    def to_s
-      @value.to_s
-    end
-
-    def type
-      :constant
-    end
-
-    def op_priority
-      1000
-    end
-
-    def op_assoc_type
-      nil
-    end
-
-    def ==(other)
-      return false if other.type != type
-
-      value == other.value
-    end
-
-    def diff(v)
-      Constant.new(0)
-    end
-
-    def evaluate
-      @value
-    end
-
-    def constant?
-      true
-    end
-  end
-
-  class Variable < Expression
-    attr_reader :symbol
-
-    def initialize(symbol)
-      @symbol = symbol
-      @is_single_letter = symbol.length == 1
-    end
-
-    def to_s
-      @symbol
-    end
-
-    def type
-      :variable
-    end
-
-    def op_priority
-      1000
-    end
-
-    def op_assoc_type
-      nil
-    end
-
-    def single_letter?
-      @is_single_letter
-    end
-
-    def ==(other)
-      return false if other.type != type
-
-      symbol == other.symbol
-    end
-
-    def diff(v)
-      @symbol == v ? Constant.new(1) : Constant.new(0)
-    end
-
-    def evaluate
-      nil
-    end
-
-    def constant?
-      false
-    end
-  end
-end
diff --git a/lib/ruby_algebra/parser.rb b/lib/ruby_algebra/parser.rb
index 77e4b8b..bc6ccbc 100644
--- a/lib/ruby_algebra/parser.rb
+++ b/lib/ruby_algebra/parser.rb
@@ -2,199 +2,332 @@
 
 module RubyAlgebra
   module Parser
+    # Токен выражения или команды
     class Token
       attr_reader :type
+
+      def initialize; end
     end
 
-    class NumberToken < Token
-      attr_reader :value
-
-      def initialize(value)
-        @type = :num
-        @value = value
+    # Знак сложения
+    class PlusToken < Token
+      def initialize
+        super()
+        @type = :plus
       end
     end
 
-    class IdentifierToken < Token
-      attr_reader :name
-
-      def initialize(name)
-        @type = :id
-        @name = name
+    # Знак вычитания
+    class MinusToken < Token
+      def initialize
+        super()
+        @type = :minus
       end
     end
 
-    class BinaryOperatorToken < Token
-      attr_reader :op
-
-      def initialize(op)
-        @type = :op
-        @op = op
+    # Знак умножения
+    class MultiplyToken < Token
+      def initialize
+        super()
+        @type = :mult
       end
     end
 
-    class UnaryOperatorToken < Token
-      attr_reader :op
-
-      def initialize(op)
-        @type = :unary_op
-        @op = op
+    # Знак деления
+    class DivideToken < Token
+      def initialize
+        super()
+        @type = :div
       end
     end
 
+    # Знак возведения в степень
+    class PowerToken < Token
+      def initialize
+        super()
+        @type = :pow
+      end
+    end
+
+    # Скобка
     class ParenthesisToken < Token
       attr_reader :closing
 
       def initialize(closing)
+        super()
         @type = :paren
         @closing = closing
       end
     end
 
+    # Знак присвоения :=
+    class AssignmentToken < Token
+      def initialize
+        super()
+        @type = :assign
+      end
+    end
+
+    # Запятая
+    class CommaToken < Token
+      def initialize
+        super()
+        @type = :comma
+      end
+    end
+
+    # Имя переменной или функции
+    class IdentifierToken < Token
+      attr_reader :symbol
+
+      def initialize(symbol)
+        super()
+        @type = :id
+        @symbol = symbol
+      end
+
+      def variable?
+        @symbol.match?(/^\p{Ll}/)
+      end
+    end
+
+    # Целое или дробное число
+    class NumberToken < Token
+      attr_reader :value
+
+      def initialize(value)
+        super()
+        @type = :num
+        @value = value
+      end
+    end
+
+    # Специальный токен, означающий конец ввода
     class EndToken < Token
-      def initialize()
+      def initialize
+        super()
         @type = :end
       end
     end
 
-    def self.tokenize(e)
-      i = 0
-      add_implicit_mul = false
-      while i < e.length
-        c = e[i]
-        if c.match?(/\p{Alpha}/)
-          yield BinaryOperatorToken.new(:mult) if add_implicit_mul
-          j = i + 1
-          j += 1 while j < e.length && e[j].match?(/\p{Alnum}/)
-          add_implicit_mul = true
-          yield IdentifierToken.new(e[i...j])
-          i = j
-        elsif c.match?(/[+\-*\/^()]/)
-          yield BinaryOperatorToken.new(:mult) if c == "(" && add_implicit_mul
-          i += 1
-          case c
-          when "+"
-            if add_implicit_mul
-              yield BinaryOperatorToken.new(:add)
-            else
-              yield UnaryOperatorToken.new(:positive)
+    # Класс для разбора выражений на токены
+    class Tokenizer
+      attr_reader :lookahead
+
+      def initialize(expr)
+        @expr = expr
+        @i = 0
+        @lookahead = _next_token
+      end
+
+      def next_token
+        token = @lookahead
+        @lookahead = _next_token unless token.type == :end
+        token
+      end
+
+      def _next_token
+        puts '_next_token'
+
+        loop do
+          return EndToken.new unless @i < @expr.length
+          puts "i = #{@i}"
+          c = @expr[@i]
+          puts "c = #{c}"
+          if c.match?(/\p{Alpha}/)
+            puts 'letter'
+            j = @i + 1
+            j += 1 while j < @expr.length && @expr[j].match?(/\p{Alnum}/)
+            token = IdentifierToken.new(@expr[@i...j])
+            @i = j
+            return token
+          elsif c.match(%r{[+\-*/^():]})
+            puts 'operator'
+            token = nil
+            case c
+            when '+'
+              token = PlusToken.new
+            when '-'
+              token = MinusToken.new
+            when '*'
+              token = MultiplyToken.new
+            when '/'
+              token = DivideToken.new
+            when '^'
+              token = PowerToken.new
+            when '('
+              token = ParenthesisToken.new(false)
+            when ')'
+              token = ParenthesisToken.new(true)
             end
-          when "-"
-            if add_implicit_mul
-              yield BinaryOperatorToken.new(:sub)
-            else
-              yield UnaryOperatorToken.new(:negative)
+            @i += 1
+            if c == ':' && @expr[@i] == '='
+              token = AssignmentToken.new
+              @i += 1
             end
-          when "*"
-            yield BinaryOperatorToken.new(:mult)
-          when "/"
-            yield BinaryOperatorToken.new(:div)
-          when "^"
-            yield BinaryOperatorToken.new(:pow)
-          when "("
-            yield ParenthesisToken.new(false)
-          when ")"
-            yield ParenthesisToken.new(true)
-          end
-          add_implicit_mul = c == ")"
-        elsif c.match?(/\p{Digit}|\./)
-          yield BinaryOperatorToken.new(:mult) if add_implicit_mul
-          j = i + 1
-          j += 1 while j < e.length && e[j].match?(/\p{Digit}|\./)
-          s = e[i...j]
-          fl = s.count "."
-          if fl > 1
-            raise Exception.new
-          end
-          add_implicit_mul = true
-          if fl == 0
-            yield NumberToken.new(s.to_i)
+            return token
+          elsif c.match?(/\p{Digit}|\./)
+            puts 'digit'
+            j = @i + 1
+            j += 1 while j < @expr.length && @expr[j].match?(/\p{Digit}|\./)
+            s = @expr[@i...j]
+            @i = j
+            puts "ssss: #{s}"
+            fl = s.count '.'
+            raise StandardError, 'malformed number' if fl > 1
+            return fl.zero? ? NumberToken.new(s.to_i) : NumberToken.new(s.to_f)
+          elsif c == ' '
+            puts 'whitespace'
+            @i += 1
           else
-            yield NumberToken.new(s.to_f)
+            puts 'unknown'
+            @i += 1
           end
-          i = j
-        elsif c == " "
-          i += 1
-        else
-          i += 1
         end
       end
-      yield EndToken.new
     end
 
-    def self.parse(expr)
-      operators = []
-      out_stack = []
-      tokenize(expr) do |token|
-        if token.type == :num
-          out_stack.push(Constant.new(token.value))
-        elsif token.type == :end
-          _parse_make_op(operators, out_stack) until operators.empty?
-        elsif token.type == :op || token.type == :unary_op
-          p = _parse_op_prio token
-          while operators.length != 0 && (operators.last.type == :op || operators.last.type == :unary_op) && (_parse_op_prio(operators.last) > p || (_parse_op_prio(operators.last) == p && token.op != :pow && token.op != :positive && token.op != :negative))
-            _parse_make_op(operators, out_stack)
-          end
-          operators.push(token)
-        elsif token.type == :paren
-          if token.closing
-            until operators.empty? || (operators.last.type == :paren && !operators.last.closing)
-              _parse_make_op(operators, out_stack)
-            end
-            if operators.empty? || operators.last.type != :paren || operators.last.closing
-              raise Exception.new
-            else
-              operators.pop
-            end
+    def self.parse_command(expr)
+      tokenizer = Tokenizer.new(expr)
+      n = tokenizer.lookahead
+      if n.type == :id && !n.variable?
+        parse_assignment_command(tokenizer)
+      else
+        parse_display_command(tokenizer)
+      end
+    end
+
+    def self.parse_assignment_command(tokenizer)
+      left_hand_side = tokenizer.next_token
+      n = tokenizer.next_token
+      if n.type == :assign
+        operand1 = tokenizer.lookahead
+        unless operand1.type == :id && !operand1.variable?
+          return AssignmentCommand.new(left_hand_side.symbol, :assign, parse_polynomial(tokenizer), nil)
+        end
+        tokenizer.next_token
+        operator = tokenizer.next_token
+        raise StandardError, "unexpected token #{operator.type}, expected +, -, * or /" unless [:plus, :minus, :mult, :div].include?(operator.type)
+
+        operand2 = tokenizer.next_token
+        unless ([:plus, :minus, :mult].include?(operator.type) && operand2.type == :id && !operand2.variable?) ||
+               ([:mult, :div].include?(operator.type) && operand2.type == :num)
+          raise StandardError, 'unsupported operation or invalid syntax'
+        end
+        if operand2.type == :num
+          if operator.type == :mult
+            return AssignmentCommand.new(left_hand_side.symbol, :scale, operand1.symbol, operand2.value)
           else
-            operators.push token
+            return AssignmentCommand.new(left_hand_side.symbol, :scale, operand1.symbol, 1.0 / operand2.value)
+          end
+        elsif operand2.type == :id
+          case operator.type
+          when :plus
+            return AssignmentCommand.new(left_hand_side.symbol, :add, operand1.symbol, operand2.symbol)
+          when :minus
+            return AssignmentCommand.new(left_hand_side.symbol, :sub, operand1.symbol, operand2.symbol)
+          when :mult
+            return AssignmentCommand.new(left_hand_side.symbol, :mult, operand1.symbol, operand2.symbol)
           end
-        elsif token.type == :id
-          out_stack.push(Variable.new(token.name))
         end
-      end
-      out_stack[0]
-    end
-
-    def self._parse_make_op(operators, out_stack)
-      oper = operators.pop
-      unless (oper.type == :op && out_stack.length >= 2) || (oper.type == :unary_op && out_stack.length >= 1)
-        raise Exception.new
-      end
-      b = out_stack.pop if oper.type == :op
-      a = out_stack.pop
-
-      case oper.op
-      when :add
-        out_stack.push Addition.new(a, b)
-      when :sub
-        out_stack.push Subtraction.new(a, b)
-      when :mult
-        out_stack.push Multiplication.new(a, b)
-      when :div
-        out_stack.push Division.new(a, b)
-      when :pow
-        out_stack.push Power.new(a, b)
-      when :positive
-        out_stack.push a
-      when :negative
-        if a.type == :constant
-          out_stack.push Constant.new(-a.value)
-        else
-          out_stack.push Multiplication.new(Constant.new(-1), a)
+      elsif n.type == :comma
+        second_lhs = tokenizer.next_token
+        unless second_lhs.type == :id && !second_lhs.variable?
+          raise StandardError, "unexpected token #{second_lhs.type}, expected polynomial variable"
         end
+        unless tokenizer.next_token.type == :assign
+          raise StandardError, "unexpected token, expected :="
+        end
+        operand1 = tokenizer.next_token
+        unless operand1.type == :id && !operand1.variable?
+          raise StandardError, "unexpected token #{operand1.type}, expected polynomial variable"
+        end
+        unless tokenizer.next_token.type == :div
+          raise StandardError, "unexpected token, expected /"
+        end
+        operand2 = tokenizer.next_token
+        unless operand2.type == :id && !operand2.variable?
+          raise StandardError, "unexpected token #{operand2.type}, expected polynomial variable"
+        end
+        return AssignmentCommand.new([left_hand_side.symbol, second_lhs.symbol], :div, operand1.symbol)
+      else
+        raise StandardError, "unexpected token #{n.type}, expected ':=' or ','"
       end
     end
 
-    def self._parse_op_prio(op_token)
-      case op_token.op
-      when :add, :sub
-        1
-      when :mult, :div
-        2
-      when :pow, :positive, :negative
-        3
+    def self.parse_display_command(tokenizer)
+      DisplayCommand.new(parse_polynomial(tokenizer))
+    end
+
+    def self.parse_polynomial(tokenizer)
+      puts "parse_polynomial <lookahead #{tokenizer.lookahead.type}>"
+      terms = [parse_term(tokenizer)]
+      while [:plus, :minus].include?(tokenizer.lookahead.type)
+        sign = tokenizer.next_token.type == :plus ? +1 : -1
+        terms << parse_term(tokenizer) * sign
       end
+      puts 'parse_polynomial end'
+      Polynomial.new(terms)
+    end
+
+    def self.parse_term(tokenizer)
+      puts "parse_term <lookahead #{tokenizer.lookahead.type}>"
+      n = tokenizer.lookahead
+      unless n.type == :id && n.variable? || n.type == :num
+        raise StandardError, "unexpected token #{n.type}, expected number or variable"
+      end
+      if n.type == :num
+        puts "eat coeff"
+        tokenizer.next_token
+        coeff = n.value
+        variables = {}
+      else
+        coeff = 1
+        v = parse_variable_factor(tokenizer)
+        variables = {v[0] => v[1]}
+      end
+      loop do
+        n = tokenizer.lookahead
+        puts "<lookahead #{n.type}>"
+        unless n.type == :mult || n.type == :id && n.variable?
+          break
+        end
+        v = parse_variable_factor(tokenizer)
+        variables[v[0]] = v[1]
+      end
+      puts 'parse_term end'
+      pp [coeff, variables]
+      Term.new(coeff, variables)
+    end
+
+    def self.parse_variable_factor(tokenizer)
+      puts "parse_term <lookahead #{tokenizer.lookahead.type}>"
+      n = tokenizer.lookahead
+      tokenizer.next_token
+      puts 'eat variable'
+      #n = tokenizer.next_token if n.type == :mult
+      if n.type == :mult
+        n = tokenizer.next_token
+        puts 'eat *'
+      end
+      unless n.type == :id && n.variable?
+        raise StandardError, "unexpected token #{n.type}, expected variable"
+      end
+      variable = n.symbol
+      if tokenizer.lookahead.type == :pow
+        tokenizer.next_token
+        puts 'eat ^'
+        unless tokenizer.lookahead.type == :num
+          raise StandardError, "unexpected token #{n.type}, expected number"
+        end
+        power = tokenizer.next_token.value
+        puts 'eat exponent'
+      else
+        power = 1
+      end
+      puts 'parse_variable_factor end'
+      pp [variable, power]
+      [variable, power]
     end
   end
 end
diff --git a/lib/ruby_algebra/polynomial.rb b/lib/ruby_algebra/polynomial.rb
index 007b1e3..1ddf2a9 100644
--- a/lib/ruby_algebra/polynomial.rb
+++ b/lib/ruby_algebra/polynomial.rb
@@ -171,7 +171,9 @@ module RubyAlgebra
     end
 
     def *(other)
-      return Term.new if @coeff.zero? || other.coeff.zero?
+      return Term.new if zero? || other.zero?
+
+      return Term.new(coeff * other, variables) unless other.is_a? Term
 
       new_variables = @variables.clone
       other.variables.each do |symbol, power|
@@ -205,11 +207,19 @@ module RubyAlgebra
       unless @variables.empty?
         first = true
         @variables.each do |var, power|
-          result += if first
-                      "#{var}^#{power}"
-                    else
-                      " * #{var}^#{power}"
-                    end
+          if first
+            unless power == 1
+              result += "#{var}^#{power}"
+            else
+              result += "#{var}"
+            end
+          else
+            unless power == 1
+              result += " * #{var}^#{power}"
+            else
+              result += " * #{var}"
+            end
+          end
           first = false
         end
       end