original_docstring: 
      Given a linear equation system's matrix LU decomposition and
      its system vector, it uses forward and backward substitution
      to compute the system's solution.
  
      :param lower_matrix:
      :param upper_matrix:
      :param sys_vector:
      :return: vector, system's solution
      
docstring: Given a linear equation system's matrix LU decomposition and
  its system vector, it uses forward and backward substitution
  to compute the system's solution.
docstring_tokens: Given a linear equation system ' s matrix LU decomposition and its system vector it uses forward and backward substitution to compute the system ' s solution .
code: def lu_system_solve(
          lower_matrix: Matrix,
          upper_matrix: Matrix,
          sys_vector: Vector
  ) -> Vector:
      """
      Given a linear equation system's matrix LU decomposition and
      its system vector, it uses forward and backward substitution
      to compute the system's solution.
  
      :param lower_matrix:
      :param upper_matrix:
      :param sys_vector:
      :return: vector, system's solution
      """
      low_solution = solve_lower_sys(lower_matrix, sys_vector)
      return solve_upper_sys(upper_matrix, low_solution)
code_tokens: def lu_system_solve ( lower_matrix : Matrix , upper_matrix : Matrix , sys_vector : Vector ) -> Vector : low_solution = solve_lower_sys ( lower_matrix , sys_vector ) return solve_upper_sys ( upper_matrix , low_solution )
short_docstring: Given a linear equation system's matrix LU decomposition and
  its system vector, it uses forward and backward substitution
  to compute the system's solution.
short_docstring_tokens: Given a linear equation system ' s matrix LU decomposition and its system vector it uses forward and backward substitution to compute the system ' s solution .
comment: """
      Given a linear equation system's matrix LU decomposition and
      its system vector, it uses forward and backward substitution
      to compute the system's solution.
  
      :param lower_matrix:
      :param upper_matrix:
      :param sys_vector:
      :return: vector, system's solution
      """