добавил производную

lib/ruby_algebra/expression.rb

@@ -17,6 +17,9 @@ module RubyAlgebra
     def op_assoc_type
       raise NotImplementedError
     end
+    def diff(v)
+      raise NotImplementedError, "#{self.class}#diff not implemented"
+    end
   end
 
   class Addition < Expression
@@ -47,6 +50,9 @@ module RubyAlgebra
     def op_assoc_type
       :left
     end
+    def diff(v)
+      Addition.new(@lhs.diff(v), @rhs.diff(v))
+    end
   end
 
   class Subtraction < Addition
@@ -63,6 +69,9 @@ module RubyAlgebra
     def type
       :sub
     end
+    def diff(v)
+      Subtraction.new(@lhs.diff(v), @rhs.diff(v))
+    end
   end
 
   class Multiplication < Expression
@@ -105,6 +114,13 @@ module RubyAlgebra
     def op_assoc_type
       :left
     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
   end
 
   class Division < Multiplication
@@ -119,6 +135,17 @@ module RubyAlgebra
     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
   end
 
   class Power < Expression
@@ -149,6 +176,18 @@ module RubyAlgebra
     def op_assoc_type
       :right
     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
   end
 
   class Constant < Expression
@@ -173,6 +212,9 @@ module RubyAlgebra
     def op_assoc_type
       nil
     end
+    def diff(v)
+      Constant.new(0)
+    end
   end
 
   class Variable < Expression
@@ -202,5 +244,8 @@ module RubyAlgebra
     def single_letter?
       @is_single_letter
     end
+    def diff(v)
+      @symbol == v ? Constant.new(1) : Constant.new(0)
+    end
   end
 end