implement interpreter and demo + bug fixes

- implement interpreter and demo
- replace StandardError with appropriate subclasses
- implement division
- rewrite Polynomial.simplify()

lib/ruby_algebra/polynomial.rb

@@ -17,7 +17,7 @@ module RubyAlgebra
 
     def to_s
       if @terms.empty?
-        result = ''
+        result = '0'
       else
         result = @terms[-1].to_s
         i = @terms.length - 2
@@ -37,7 +37,7 @@ module RubyAlgebra
       raise NotImplementedError
     end
 
-    def evaluate(values)
+    def substitute(values)
       result = 0
       @terms.each do |term|
         # ...
@@ -67,6 +67,50 @@ module RubyAlgebra
       end
     end
 
+    def /(other)
+      raise StandardError, "cannot divide by zero" if other.zero?
+      return [Polynomial.new, Polynomial.new] if self.zero?
+
+      # Сначала проверить, что оба многочлена от одной и той же переменной
+      t = if @terms.empty? || @terms[-1].variables.empty? then other.terms[-1] else @terms[-1] end
+      unless t.variables.empty?
+        only_variable = t.variables.keys[0]
+        @terms.each do |term|
+          next if term.variables.empty?
+          unless term.variables.length == 1 && term.variables.keys[0] == only_variable
+            raise StandardError, "cannot divide polynomials with different variables"
+          end
+        end
+        other.terms.each do |term|
+          next if term.variables.empty?
+          unless term.variables.length == 1 && term.variables.keys[0] == only_variable
+            raise StandardError, "cannot divide polynomials with different variables"
+          end
+        end
+      end
+
+      quotient = Polynomial.new
+      remainder = self
+      divisor_power = unless other.terms.last.variables.empty? then other.terms.last.variables.first[1] else 0 end
+      loop do
+        break if remainder.zero?
+
+        dividend_power = unless remainder.terms.last.variables.empty? then remainder.terms.last.variables.first[1] else 0 end
+        break if dividend_power < divisor_power
+
+        result_power = dividend_power - divisor_power
+        result_coeff = remainder.terms.last.coeff.to_f / other.terms.last.coeff
+        if result_power > 0
+          q = Term.new(result_coeff, {only_variable => result_power})
+        else
+          q = Term.new(result_coeff, {})
+        end
+        quotient += q
+        remainder -= other * q
+      end
+      [quotient, remainder]
+    end
+
     def **(other)
       result = Polynomial.new([Term.new(1)])
       other.times do
@@ -91,50 +135,40 @@ module RubyAlgebra
       @terms == other.terms
     end
 
-    def simplify
+    def _simplify
       i = 0
       new_terms = @terms.filter { |t| !t.zero? }
       while i < new_terms.length
         j = i + 1
+        annihilated = false
         while j < new_terms.length
           if new_terms[i].similar_to?(new_terms[j])
             new_terms[i] += new_terms[j]
+            new_terms.delete_at(j)
             if new_terms[i].zero?
               new_terms.delete_at(i)
-              i -= 1
-              j -= 1
+              annihilated = true
+              break
             end
-            new_terms.delete_at(j)
-            j -= 1
+          else
+            j += 1
           end
-          j += 1
         end
-        i += 1
+        i += 1 unless annihilated
       end
-      Polynomial.new(new_terms.sort_by { |t| t.total_power })
+      new_terms.sort_by { |t| t.total_power }
+    end
+
+    def simplify
+      Polynomial.new(_simplify)
     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 }
+      @terms = _simplify
+    end
+
+    def zero?
+      @terms.all? { |t| t.zero? }
     end
   end
 
@@ -160,7 +194,7 @@ module RubyAlgebra
       raise NotImplementedError
     end
 
-    def evaluate(values)
+    def substitute(values)
       raise NotImplementedError
     end
 
@@ -186,6 +220,11 @@ module RubyAlgebra
       Term.new(@coeff * other.coeff, new_variables)
     end
 
+    def /(other)
+      raise StandardError, "cannot divide by zero" if other.zero?
+
+    end
+
     def +@
       Term.new(@coeff, @variables)
     end
@@ -203,7 +242,13 @@ module RubyAlgebra
     end
 
     def to_s
-      result = @coeff != 1 ? @coeff.to_s : ''
+      if @coeff == 1 && !@variables.empty?
+        result = ''
+      elsif @coeff == -1 && !@variables.empty?
+        result = '-'
+      else
+        result = @coeff.to_s
+      end
       unless @variables.empty?
         first = true
         @variables.each do |var, power|