Description
linear_algebra/src/polynom_for_points.py::points_to_polynomial crashes with ZeroDivisionError for valid inputs that include a point with x = 0. It solves the interpolation system with Gaussian elimination without pivoting, so a zero on the diagonal divides by zero:
for count in range(x):
for number in range(x):
if count == number:
continue
fraction = matrix[number][count] / matrix[count][count] # /0 when matrix[count][count] == 0
...matrix[count][count] = coordinates[count][0] ** (x - (count + 1)). When an x-coordinate is 0, that diagonal entry is 0 ** positive = 0, so the very first elimination step divides by zero. The input passes every validation in the function (non-empty, all pairs length-2, distinct points, distinct x-values) — it is a genuinely fittable set — and then crashes in the solver.
Steps to reproduce (verified)
from linear_algebra.src.polynom_for_points import points_to_polynomial
points_to_polynomial([[0, 1], [1, 2], [2, 5]]) # f(x) = x^2 + 1 passes through these
# -> ZeroDivisionError: division by zero
points_to_polynomial([[0, 0], [1, 1], [2, 4]]) # f(x) = x^2
# -> ZeroDivisionError: division by zero
The existing doctests only use x-values 1, 2, 3, so the x = 0 case is uncovered.
Expected behavior
For [[0, 1], [1, 2], [2, 5]] it should return the fitting polynomial (f(x)=x^2*1.0+x^1*0.0+x^0*1.0), not crash. Any set of points with distinct x-values has a unique interpolating polynomial.
Actual behavior
ZeroDivisionError whenever any point has x = 0 (and generally whenever a zero pivot appears on the diagonal during elimination).
Suggested fix
Use partial pivoting: before each elimination step, swap in a row whose matrix[r][count] is non-zero (largest magnitude). This removes the zero-pivot crash and also improves numerical stability. A doctest with an x = 0 point (e.g. points_to_polynomial([[0, 1], [1, 2], [2, 5]])) should be added to cover it.
Description
linear_algebra/src/polynom_for_points.py::points_to_polynomialcrashes withZeroDivisionErrorfor valid inputs that include a point withx = 0. It solves the interpolation system with Gaussian elimination without pivoting, so a zero on the diagonal divides by zero:matrix[count][count] = coordinates[count][0] ** (x - (count + 1)). When an x-coordinate is0, that diagonal entry is0 ** positive = 0, so the very first elimination step divides by zero. The input passes every validation in the function (non-empty, all pairs length-2, distinct points, distinct x-values) — it is a genuinely fittable set — and then crashes in the solver.Steps to reproduce (verified)
The existing doctests only use x-values
1, 2, 3, so thex = 0case is uncovered.Expected behavior
For
[[0, 1], [1, 2], [2, 5]]it should return the fitting polynomial (f(x)=x^2*1.0+x^1*0.0+x^0*1.0), not crash. Any set of points with distinct x-values has a unique interpolating polynomial.Actual behavior
ZeroDivisionErrorwhenever any point hasx = 0(and generally whenever a zero pivot appears on the diagonal during elimination).Suggested fix
Use partial pivoting: before each elimination step, swap in a row whose
matrix[r][count]is non-zero (largest magnitude). This removes the zero-pivot crash and also improves numerical stability. A doctest with anx = 0point (e.g.points_to_polynomial([[0, 1], [1, 2], [2, 5]])) should be added to cover it.