





'''simple docstring'''
from math import factorial

class      snake_case     :




 """simple docstring"""



 def __init__(       self       :							List[str]							,	__A       :							Any							,	__A       :							Tuple	):
        __UpperCamelCase       =  real
        if isinstance(__A							,	__A	):
               __UpperCamelCase       =  [1] * rank
        else:
               __UpperCamelCase       =  rank






 def __repr__(       self       :							Any	):
        return (
            f'''{self.real}+'''
            f'''{'+'.join(str(__A	)+'E'+str(n+1	)for n,dual in enumerate(self.duals	)	)}'''
        )






 def        _lowerCamelCase					(       self       :							str	):
        __UpperCamelCase       =  self.duals.copy()
        while cur[-1] == 0:
               cur.pop(-1	)
        return Dual(self.real							,	__A	)






 def __add__(       self       :							List[Any]							,	__A       :							Any	):
        if not isinstance(__A							,	__A	):
               return Dual(self.real + other							,	self.duals	)
        __UpperCamelCase       =  self.duals.copy()
        __UpperCamelCase       =  other.duals.copy()
        if len(__A	) > len(__A	):
               o_dual.extend([1] * (len(__A	) - len(__A	))	)
        elif len(__A	) < len(__A	):
               s_dual.extend([1] * (len(__A	) - len(__A	))	)
        __UpperCamelCase       =  []
        for i in range(len(__A	)	):
               new_duals.append(s_dual[i] + o_dual[i]	)
        return Dual(self.real + other.real							,	__A	)

 SCREAMING_SNAKE_CASE_	:					Tuple					=__add__






 def __sub__(       self       :							List[str]							,	__A       :							List[Any]	):
        return self + other * -1






 def __mul__(       self       :							Tuple							,	__A       :							List[str]	):
        if not isinstance(__A							,	__A	):
               __UpperCamelCase       =  []
               for i in self.duals:
                      new_duals.append(i * other	)
               return Dual(self.real * other							,	__A	)
        __UpperCamelCase       =  [0] * (len(self.duals	) + len(other.duals	) + 1)
        for i, item in enumerate(self.duals	):
               for j, jtem in enumerate(other.duals	):
                      new_duals[i + j + 1] += item * jtem
        for k in range(len(self.duals	)	):
               new_duals[k] += self.duals[k] * other.real
        for index in range(len(other.duals	)	):
               new_duals[index] += other.duals[index] * self.real
        return Dual(self.real * other.real							,	__A	)

 SCREAMING_SNAKE_CASE_	:					Optional[Any]					=__mul__






 def __truediv__(       self       :							int							,	__A       :							List[str]	):
        if not isinstance(__A							,	__A	):
               __UpperCamelCase       =  []
               for i in self.duals:
                      new_duals.append(i / other	)
               return Dual(self.real / other							,	__A	)
        raise ValueError






 def __floordiv__(       self       :							Any							,	__A       :							List[Any]	):
        if not isinstance(__A							,	__A	):
               __UpperCamelCase       =  []
               for i in self.duals:
                      new_duals.append(i // other	)
               return Dual(self.real // other							,	__A	)
        raise ValueError






 def __pow__(       self       :							str							,	__A       :							Optional[int]	):
        if n < 0 or isinstance(__A							,	__A	):
               raise ValueError('power must be a positive integer'	)
        if n == 0:
               return 1
        if n == 1:
               return self
        __UpperCamelCase       =  self
        for _ in range(n - 1	):
               x *= self
        return x






def 				lowercase__   (   __lowercase						:  str				,  __lowercase						:  Optional[int]				,  __lowercase						:  List[str]     ) ->      Dict:



       """simple docstring"""






       if not callable(__lowercase     ):
              raise ValueError('differentiate() requires a function as input for func'     )
       if not isinstance(__lowercase				,  (float, int)     ):
              raise ValueError('differentiate() requires a float as input for position'     )
       if not isinstance(__lowercase				,  __lowercase     ):
              raise ValueError('differentiate() requires an int as input for order'     )
       __UpperCamelCase       =  Dual(__lowercase				,  1     )
       __UpperCamelCase       =  func(__lowercase     )
       if order == 0:
              return result.real
       return result.duals[order - 1] * factorial(__lowercase     )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    def 				lowercase__   (   __lowercase						:  Optional[int]     ) ->      List[Any]:



           """simple docstring"""






           return y**2 * y**4


    print(differentiate(f, 9, 2))



import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)







class   __lowercase      (unittest.TestCase ):
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						List[str]					=					Vector([1, 2, 3]					)
       self.assertEqual(x.component(0					)      ,							1					)
       self.assertEqual(x.component(2					)      ,							3					)
       __lowerCAmelCase					:						Dict					=					Vector()
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Vector([0, 0, 0, 0, 0, 1]					)
       self.assertEqual(str(A_					)      ,							'''(0,0,0,0,0,1)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Union[str, Any]					=					Vector([1, 2, 3, 4]					)
       self.assertEqual(len(A_					)      ,							4					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Dict					=					Vector([1, 2]					)
       __lowerCAmelCase					:						Optional[int]					=					Vector([1, 2, 3, 4, 5]					)
       __lowerCAmelCase					:						Optional[Any]					=					Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]					)
       __lowerCAmelCase					:						str					=					Vector([1, -1, 1, -1, 2, -3, 4, -5]					)
       self.assertAlmostEqual(x.euclidean_length()      ,							2.236      ,							3					)
       self.assertAlmostEqual(y.euclidean_length()      ,							7.416      ,							3					)
       self.assertEqual(z.euclidean_length()      ,							0					)
       self.assertAlmostEqual(w.euclidean_length()      ,							7.616      ,							3					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						List[str]					=					Vector([1, 1, 1]					)
       self.assertEqual((x + y).component(0					)      ,							2					)
       self.assertEqual((x + y).component(1					)      ,							3					)
       self.assertEqual((x + y).component(2					)      ,							4					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						List[str]					=					Vector([1, 1, 1]					)
       self.assertEqual((x - y).component(0					)      ,							0					)
       self.assertEqual((x - y).component(1					)      ,							1					)
       self.assertEqual((x - y).component(2					)      ,							2					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						str					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						List[Any]					=					Vector([2, -1, 4]					)  # for test of dot product
       __lowerCAmelCase					:						Optional[int]					=					Vector([1, -2, -1]					)
       self.assertEqual(str(x * 3.0					)      ,							'''(3.0,6.0,9.0)'''					)
       self.assertEqual((a * b)      ,							0					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       self.assertEqual(str(zero_vector(10					)					).count('''0'''					)      ,							10					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       self.assertEqual(str(unit_basis_vector(3      ,							1					)					)      ,							'''(0,1,0)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						str					=					Vector([1, 2, 3]					)
       __lowerCAmelCase					:						Any					=					Vector([1, 0, 1]					)
       self.assertEqual(str(axpy(2      ,							A_      ,							A_					)					)      ,							'''(3,4,7)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Vector([1, 0, 0, 0, 0, 0]					)
       __lowerCAmelCase					:						Optional[Any]					=					x.copy()
       self.assertEqual(str(A_					)      ,							str(A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						List[str]					=					Vector([1, 0, 0]					)
       x.change_component(0      ,							0					)
       x.change_component(1      ,							1					)
       self.assertEqual(str(A_					)      ,							'''(0,1,0)'''					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Union[str, Any]					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       self.assertEqual('''|1,2,3|\n|2,4,5|\n|6,7,8|\n'''      ,							str(A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						List[Any]					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						str					=					[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
       for x in range(a.height()					):
             for y in range(a.width()					):
                   self.assertEqual(minors[x][y]      ,							a.minor(A_      ,							A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Optional[int]					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						Tuple					=					[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
       for x in range(a.height()					):
             for y in range(a.width()					):
                   self.assertEqual(cofactors[x][y]      ,							a.cofactor(A_      ,							A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Dict					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       self.assertEqual(-5      ,							a.determinant()					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]      ,							3      ,							3					)
       __lowerCAmelCase					:						Union[str, Any]					=					Vector([1, 2, 3]					)
       self.assertEqual('''(14,32,50)'''      ,							str(a * x					)					)
       self.assertEqual('''|2,4,6|\n|8,10,12|\n|14,16,18|\n'''      ,							str(a * 2					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       a.change_component(0      ,							2      ,							5					)
       self.assertEqual('''|1,2,5|\n|2,4,5|\n|6,7,8|\n'''      ,							str(A_					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Tuple					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       self.assertEqual(7      ,							a.component(2      ,							1					)      ,							0.01					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Any					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						Dict					=					Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]      ,							3      ,							3					)
       self.assertEqual('''|2,4,10|\n|4,8,10|\n|12,14,18|\n'''      ,							str(a + b					)					)
 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       __lowerCAmelCase					:						Dict					=					Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]      ,							3      ,							3					)
       __lowerCAmelCase					:						str					=					Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]      ,							3      ,							3					)
       self.assertEqual('''|0,0,-4|\n|0,0,0|\n|0,0,-2|\n'''      ,							str(a - b					)					)





 def 	UpperCamelCase__  (							self					)					->None:



       '''simple docstring'''





       self.assertEqual(
           '''|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n'''      ,							str(square_zero_matrix(5					)					)      ,							)


if __name__ == "__main__":
 unittest.main()


