Theoretical Principles & Computational Physics Guide
Python Tuples: Immutable Physical Constants & Phase Space Pairs
Dr. Alorika Chatterjee & Dr. Anirban Shaw
Science & Physics Learners
Python 3 / NumPy / SciPy
1. Core Principles & Theoretical Framework
Immutability & Integrity: Guarantees that fundamental constants, coordinate pairs, and state vectors are protected from accidental mutation.
Packing & Unpacking: Enables clean multi-variable return statements from ODE functions:
r, v = update(r, v, dt). Memory Efficiency: Tuples have lower memory overhead and faster allocation than dynamic lists.
2. Mathematical Formulation & Algorithmic Pipeline
Phase space coordinate state tuple:
$$ \mathbf{\Gamma} = (x, y, z, p_x, p_y, p_z) \in \mathbb{R}^6 $$
3. Numerical Mechanics & Implementation Logic
- Tuple Packing: Group multiple observables into single return statements:
return (x_new, v_new, energy). - Unpacking Assignment: Assign returned variables cleanly:
pos, vel, e = integrate_step(pos, vel). - Hashable Keys: Use tuples as dictionary keys for 2D/3D discrete grid lookups where lists are prohibited.
4. Relevant Computational Practice Exercises
Exercise 1
Write a 2D projectile function that returns a tuple of state variables $(x, y, v_x, v_y, E_{\text{tot}})$.
Exercise 2
Demonstrate tuple unpacking to swap two phase space variables without an intermediate temporary variable.
Exercise 3
Create an immutable registry of physical constants $(c, G, h, e, m_e)$ using named tuples.
- Hans Petter Langtangen, "A Primer on Scientific Programming with Python", Springer (2016).