Exercise 1: generators for the solution of ODEs

Solving the differential equation by applying the explicit Euler method results in the recursion:

Starting from hints/ex1.py, given initial value and a given value of the time step , implement a decorator step_counter that counts and prints how many time steps have been performed. Perform 10 steps.

Exercise 2: Polynomial class (1/3)

Starting from hints/ex2.py, you are tasked with implementing a Python class called Polynomial that represents polynomials. The class should have the following features:

1. Constructor: The class should have a custom constructor that takes variable coefficients as arguments. The coefficients should be provided in increasing order of degree ().

2. String representation: Implement the __repr__ method to provide a string representation of the polynomial. The string should display the polynomial in a human-readable form. For example, for the polynomial with coefficients [1, 2, 3], the string representation should be "1 + 2x + 3x^2".

3. Addition and multiplication: Implement the __add__ and __mul__ methods to allow addition and multiplication of polynomials. The methods should return a new polynomial.

Exercise 2: Polynomial class (2/3)

4. Class method to create from string: Implement a @classmethod called from_string that creates a Polynomial object from a string representation. Assume that the input string will be a polynomial in the form of "a + bx + ... + cx^(n-1) + dx^n".

5. The base class Polynomial should be extended by two subclasses:

   • StandardPolynomialEvaluator: Implements the standard polynomial evaluation method:
   • HornerPolynomialEvaluator: Implements Horner's rule for polynomial evaluation:

Exercise 2: Polynomial class (3/3)

6. Implement a measure_time decorator, which measures the time taken by a function to execute.

7. Instantiate objects of both StandardPolynomialEvaluator and HornerPolynomialEvaluator with the same set of coefficients.

8. Apply the measure_time decorator to a function that takes a PolynomialEvaluator object and evaluates it at a given list of points.

9. Evaluate the polynomial at the same 1000 points using both methods and compare the results. Raise an assertion error if the results do not match.

10. Use the decorated function to evaluate the polynomial using both the standard method and Horner's rule, and observe the logged results and execution times.

Exercise 3: modular data processing package

Refactor the existing data processing code provided in hints/ex3.py into a modular package with multiple modules, functions, classes.

1. Refactoring: Refactor the code into a modular package dataprocessor with the following modules:
   • __init__.py: Entry point for the package, import necessary functions, classes, and data. Implement __all__.
   • operations.py: Contains functions for data processing and analysis.
   • data_analysis.py: Introduce a class DataAnalyzer that encapsulates data processing and analysis functionalities.
2. Documentation: Provide docstrings for functions and classes. Explain the purpose and usage of each function and configuration option.
3. Test cases: Create a test main.py script to demonstrate the usage of the package.