Exercise 1: decorators and generators for the solution of ODEs

The file hints/ex1.py contains a generator function that solves the ODE using explicit Euler method:

1. Implement a decorator step_counter that counts how many values are yielded from the generator, i.e., how many steps the method has performed.
2. Apply the decorator to the explicit_euler function.
3. Create a generator with and .
4. Consume exactly 10 steps from the generator and print each value.

Exercise 2: Polynomial class (1/2)

Starting from hints/ex2.py, implement a Polynomial class with the following features:

1. Constructor and string representation:

   • Accept variable coefficients: Polynomial(1, 2, 3) represents .
   • Implement __repr__ to print: "1 + 2x + 3x^2".

2. Operator overloading:

   • Implement __add__ for polynomial addition.
   • Test: Polynomial(1, 2) + Polynomial(3, 4) → "4 + 6x".

3. Inheritance and polymorphism:

   • Create abstract method evaluate(self, x) (x can be a single point or a list).
   • Subclass StandardPolynomialEvaluator: implements standard evaluation.
   • Subclass HornerPolynomialEvaluator: implements Horner's rule.

Exercise 2: Polynomial class (2/2)

4. Decorator and performance:
   • Implement a @measure_time decorator.
   • Compare performance on 10000 points between standard and Horner methods.
   • Verify that results match.

Hints:

• Use time.time() or time.perf_counter() in the decorator.
• Standard evaluation: .
• Horner's rule: .

Exercise 3: modular data processing package (1/2)

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

1. Refactor the code into a modular package dataprocessor

dataprocessor/
├── __init__.py      # Package entry point.
├── operations.py    # Data processing functions.
└── data_analysis.py # DataAnalyzer class.

• __init__.py: Import and export necessary functions and classes. Define __all__ to control what the package exports with from dataprocessor import *. In particular, it should export process_data, additional_operation, DataAnalyzer, pd.

Exercise 3: modular data processing package (2/2)

• operations.py: Contains functions for data processing:

  • process_data(df, column1, column2, result_column): Adds values from two columns.
  • additional_operation(df, column1, column2, additional_column1, other_column2): Performs multiplication and division operations.

• data_analysis.py: Contains a class DataAnalyzer, replacing DataProcessor, that encapsulates data analysis functionality:

  • Constructor accepts the name of the column to analyze.
  • Method analyze_data(df) returns mean and max values.

2. In a separate folder, create a main_dataprocess.py script that demonstrates the package usage.