add substitution and differentiation

lib/ruby_algebra/polynomial.rb

@@ -33,16 +33,12 @@ module RubyAlgebra
       result
     end
 
-    def diff
-      raise NotImplementedError
+    def diff(variable)
+      Polynomial.new(@terms.map { |term| term.diff(variable) })
     end
 
     def substitute(values)
-      result = 0
-      @terms.each do |term|
-        # ...
-      end
-      result
+      Polynomial.new(@terms.map { |term| term.substitute(values) })
     end
 
     def +(other)
@@ -190,12 +186,28 @@ module RubyAlgebra
       end
     end
 
-    def diff(var)
-      raise NotImplementedError
+    def diff(variable)
+      return Term.new if @variables[variable].nil?
+      new_coeff = @coeff
+      new_variables = @variables.filter { |var, power| var != variable }
+      unless @variables[variable] == 1
+        new_coeff *= @variables[variable]
+        new_variables[variable] = @variables[variable] - 1
+      end
+      Term.new(new_coeff, new_variables)
     end
 
     def substitute(values)
-      raise NotImplementedError
+      new_coeff = @coeff
+      new_variables = {}
+      @variables.each do |var, pow|
+        if values[var].nil?
+          new_variables[var] = pow
+        else
+          new_coeff *= values[var] ** pow
+        end
+      end
+      Term.new(new_coeff, new_variables)
     end
 
     def +(other)