





from math import pi, sqrt, tan

def   a_   (			lowerCAmelCase_				:      float     ):
   if side_length < 0:
      raise ValueError('surface_area_cube() only accepts non-negative values'     )
   return 6 * side_length**2

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if length < 0 or breadth < 0 or height < 0:
      raise ValueError('surface_area_cuboid() only accepts non-negative values'     )
   return 2 * ((length * breadth) + (breadth * height) + (length * height))

def   a_   (			lowerCAmelCase_				:      float     ):
   if radius < 0:
      raise ValueError('surface_area_sphere() only accepts non-negative values'     )
   return 4 * pi * radius**2

def   a_   (			lowerCAmelCase_				:      float     ):
   if radius < 0:
      raise ValueError('surface_area_hemisphere() only accepts non-negative values'     )
   return 3 * pi * radius**2

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if radius < 0 or height < 0:
      raise ValueError('surface_area_cone() only accepts non-negative values'     )
   return pi * radius * (radius + (height**2 + radius**2) ** 0.5)

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if radius_a < 0 or radius_a < 0 or height < 0:
      raise ValueError(
          'surface_area_conical_frustum() only accepts non-negative values'     )
   __lowerCAmelCase							     =     (height**2 + (radius_a - radius_a) ** 2) ** 0.5
   return pi * ((slant_height * (radius_a + radius_a)) + radius_a**2 + radius_a**2)

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if radius < 0 or height < 0:
      raise ValueError('surface_area_cylinder() only accepts non-negative values'     )
   return 2 * pi * radius * (height + radius)

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if torus_radius < 0 or tube_radius < 0:
      raise ValueError('surface_area_torus() only accepts non-negative values'     )
   if torus_radius < tube_radius:
      raise ValueError(
          'surface_area_torus() does not support spindle or self intersecting tori'     )
   return 4 * pow(lowerCAmelCase_,     2     ) * torus_radius * tube_radius

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if length < 0 or width < 0:
      raise ValueError('area_rectangle() only accepts non-negative values'     )
   return length * width

def   a_   (			lowerCAmelCase_				:      float     ):
   if side_length < 0:
      raise ValueError('area_square() only accepts non-negative values'     )
   return side_length**2

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if base < 0 or height < 0:
      raise ValueError('area_triangle() only accepts non-negative values'     )
   return (base * height) / 2

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if sidea < 0 or sidea < 0 or sidea < 0:
      raise ValueError('area_triangle_three_sides() only accepts non-negative values'     )
   elif sidea + sidea < sidea or sidea + sidea < sidea or sidea + sidea < sidea:
      raise ValueError('Given three sides do not form a triangle'     )
   __lowerCAmelCase							     =     (sidea + sidea + sidea) / 2
   __lowerCAmelCase							     =     sqrt(
       semi_perimeter
       * (semi_perimeter - sidea)
       * (semi_perimeter - sidea)
       * (semi_perimeter - sidea)     )
   return area

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if base < 0 or height < 0:
      raise ValueError('area_parallelogram() only accepts non-negative values'     )
   return base * height

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if basea < 0 or basea < 0 or height < 0:
      raise ValueError('area_trapezium() only accepts non-negative values'     )
   return 1 / 2 * (basea + basea) * height

def   a_   (			lowerCAmelCase_				:      float     ):
   if radius < 0:
      raise ValueError('area_circle() only accepts non-negative values'     )
   return pi * radius**2

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if radius_x < 0 or radius_y < 0:
      raise ValueError('area_ellipse() only accepts non-negative values'     )
   return pi * radius_x * radius_y

def   a_   (			lowerCAmelCase_				:      float,     lowerCAmelCase_				:      float     ):
   if diagonal_a < 0 or diagonal_a < 0:
      raise ValueError('area_rhombus() only accepts non-negative values'     )
   return 1 / 2 * diagonal_a * diagonal_a

def   a_   (			lowerCAmelCase_				:      int,     lowerCAmelCase_				:      float     ):
   if not isinstance(lowerCAmelCase_,     lowerCAmelCase_     ) or sides < 3:
      raise ValueError(
          'area_reg_polygon() only accepts integers greater than or \
equal to three as number of sides'     )
   elif length < 0:
      raise ValueError(
          'area_reg_polygon() only accepts non-negative values as \
length of a side'     )
   return (sides * length**2) / (4 * tan(pi / sides     ))
   return (sides * length**2) / (4 * tan(pi / sides     ))


if __name__ == "__main__":
     import doctest

     doctest.testmod(verbose=True)  # verbose so we can see methods missing tests

     print('[DEMO] Areas of various geometric shapes: \n')
     print(F"""Rectangle: {area_rectangle(10, 20) = }""")
     print(F"""Square: {area_square(10) = }""")
     print(F"""Triangle: {area_triangle(10, 10) = }""")
     print(F"""Triangle: {area_triangle_three_sides(5, 12, 13) = }""")
     print(F"""Parallelogram: {area_parallelogram(10, 20) = }""")
     print(F"""Rhombus: {area_rhombus(10, 20) = }""")
     print(F"""Trapezium: {area_trapezium(10, 20, 30) = }""")
     print(F"""Circle: {area_circle(20) = }""")
     print(F"""Ellipse: {area_ellipse(10, 20) = }""")
     print('\nSurface Areas of various geometric shapes: \n')
     print(F"""Cube: {surface_area_cube(20) = }""")
     print(F"""Cuboid: {surface_area_cuboid(10, 20, 30) = }""")
     print(F"""Sphere: {surface_area_sphere(20) = }""")
     print(F"""Hemisphere: {surface_area_hemisphere(20) = }""")
     print(F"""Cone: {surface_area_cone(10, 20) = }""")
     print(F"""Conical Frustum: {surface_area_conical_frustum(10, 20, 30) = }""")
     print(F"""Cylinder: {surface_area_cylinder(10, 20) = }""")
     print(F"""Torus: {surface_area_torus(20, 10) = }""")
     print(F"""Equilateral Triangle: {area_reg_polygon(3, 10) = }""")
     print(F"""Square: {area_reg_polygon(4, 10) = }""")
     print(F"""Reqular Pentagon: {area_reg_polygon(5, 10) = }""")








import mpmath  # for roots of unity
import numpy as np



class     _UpperCAmelCase   :

  """simple docstring"""


  def __init__(    self			:		List[Any] ,  lowerCAmelCase_			:		Dict=None ,  lowerCAmelCase_			:		str=None					)							->						List[Any]:
     # Input as list
     __lowerCAmelCase							     =     list(poly_a or [0]					)[:]
     __lowerCAmelCase							     =     list(poly_b or [0]					)[:]

     # Remove leading zero coefficients
     while self.polyA[-1] == 0:
        self.polyA.pop()
     __lowerCAmelCase							     =     len(self.polyA					)

     while self.polyB[-1] == 0:
        self.polyB.pop()
     __lowerCAmelCase							     =     len(self.polyB					)

     # Add 0 to make lengths equal a power of 2
     __lowerCAmelCase							     =     int(
         2 ** np.ceil(np.loga(len(self.polyA					) + len(self.polyB					) - 1					)					)					)

     while len(self.polyA					) < self.c_max_length:
        self.polyA.append(0					)
     while len(self.polyB					) < self.c_max_length:
        self.polyB.append(0					)
     # A complex root used for the fourier transform
     __lowerCAmelCase							     =     complex(mpmath.root(x=1 ,  n=self.c_max_length ,  k=1					)					)

     # The product
     __lowerCAmelCase							     =     self.__multiply()






  def     lowercase		(    self			:		Optional[int] ,  lowerCAmelCase_			:		str					)							->						Optional[int]:
     __lowerCAmelCase							     =     [[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
     # Corner case
     if len(lowerCAmelCase_					) <= 1:
        return dft[0]
     #
     __lowerCAmelCase							     =     self.c_max_length // 2
     while next_ncol > 0:
        __lowerCAmelCase							     =     [[] for i in range(lowerCAmelCase_					)]
        __lowerCAmelCase							     =     self.root**next_ncol

        # First half of next step
        __lowerCAmelCase							     =     1
        for j in range(self.c_max_length // (next_ncol * 2)					):
           for i in range(lowerCAmelCase_					):
              new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]					)
           current_root *= root
        # Second half of next step
        __lowerCAmelCase							     =     1
        for j in range(self.c_max_length // (next_ncol * 2)					):
           for i in range(lowerCAmelCase_					):
              new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]					)
           current_root *= root
        # Update
        __lowerCAmelCase							     =     new_dft
        __lowerCAmelCase							     =     next_ncol // 2
     return dft[0]






  def     lowercase		(    self			:		Optional[int]					)							->						Any:
     __lowerCAmelCase							     =     self.__dft('A'					)
     __lowerCAmelCase							     =     self.__dft('B'					)
     __lowerCAmelCase							     =     [[dft_a[i] * dft_b[i] for i in range(self.c_max_length					)]]
     del dft_a
     del dft_b

     # Corner Case
     if len(inverce_c[0]					) <= 1:
        return inverce_c[0]
     # Inverse DFT
     __lowerCAmelCase							     =     2
     while next_ncol <= self.c_max_length:
        __lowerCAmelCase							     =     [[] for i in range(lowerCAmelCase_					)]
        __lowerCAmelCase							     =     self.root ** (next_ncol // 2)
        __lowerCAmelCase							     =     1
        # First half of next step
        for j in range(self.c_max_length // next_ncol					):
           for i in range(next_ncol // 2					):
              # Even positions
              new_inverse_c[i].append(
                  (
                      inverce_c[i][j]
                      + inverce_c[i][j + self.c_max_length // next_ncol]
                  )
                  / 2					)
              # Odd positions
              new_inverse_c[i + next_ncol // 2].append(
                  (
                      inverce_c[i][j]
                      - inverce_c[i][j + self.c_max_length // next_ncol]
                  )
                  / (2 * current_root)					)
           current_root *= root
        # Update
        __lowerCAmelCase							     =     new_inverse_c
        next_ncol *= 2
     # Unpack
     __lowerCAmelCase							     =     [round(x[0].real ,  8					) + round(x[0].imag ,  8					) * 1J for x in inverce_c]

     # Remove leading 0's
     while inverce_c[-1] == 0:
        inverce_c.pop()
     return inverce_c






  def __str__(    self			:		Dict					)							->						int:
     __lowerCAmelCase							     =     'A = ' + ' + '.join(
         f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyA[: self.len_A]					)					)
     __lowerCAmelCase							     =     'B = ' + ' + '.join(
         f"""{coef}*x^{i}""" for coef, i in enumerate(self.polyB[: self.len_B]					)					)
     __lowerCAmelCase							     =     'A*B = ' + ' + '.join(
         f"""{coef}*x^{i}""" for coef, i in enumerate(self.product					)					)

     return f"""{a}\n{b}\n{c}"""


# Unit tests
if __name__ == "__main__":
     import doctest

     doctest.testmod()

