Add maths/numerical_analysis/lagrange_interpolation.py

[ltianyi992]

Description

Adds Lagrange polynomial interpolation to the numerical analysis module — a classic method currently missing from the repository.

What it does

Given n+1 data points (x_0, y_0), ..., (x_n, y_n) with distinct x-values, the Lagrange interpolating polynomial is the unique polynomial of degree ≤ n passing through all given points:

P(x) = Σ_i  y_i · L_i(x)

where each basis polynomial is:

L_i(x) = Π_{j ≠ i} (x - x_j) / (x_i - x_j)

Why it complements the existing code

The repo already has newton_forward_interpolation.py, which requires equidistant x-values. Lagrange interpolation works for arbitrarily spaced data — a natural complement.

Example

>>> from maths.numerical_analysis.lagrange_interpolation import lagrange_interpolation

# Interpolate through x^2 data — exact for degree-2 polynomials
>>> lagrange_interpolation([1, 2, 3], [1, 4, 9], 2.5)
6.25

# Four points from x^3, non-grid query
>>> lagrange_interpolation([0, 1, 2, 3], [0, 1, 8, 27], 1.5)
3.375

Checklist

• All functions have type hints
• 9 passing doctests (happy-path + edge cases + error cases)
• ruff check --isolated passes with no violations
• python -m doctest passes with no failures
• References to Wikipedia and Mathworld in docstring

References

• https://en.wikipedia.org/wiki/Lagrange_polynomial
• https://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html