fx.sage

import random

F = GF(97)

points = [
    (F(x), F(y))
    for (x, y) in (
        ( 2, 60),
        ( 3, 2),
        ( 4, 18),
        ( 5, 66),
        ( 6, 9),
        ( 7, 87),
        ( 8, 45),
        ( 9, 83),
        (10, 85),
        (11, 70),
        (12, 75),
        (13, 15),
        (14, 95),
        (15, 26),
        (16, 57),
        (17, 21),
        (18, 24),
        (19, 66),
        (20, 48),
        (21, 21),
        (22, 50),
        (23, 53),
        (24, 28),
        (26, 55),
        (27, 18),
        (28, 78),
        (29, 81),
    )
]
print("Aantal punten:", len(points))

R = F['x']

f_ = R.lagrange_polynomial(points)

def recover(points):
    f = R.lagrange_polynomial(points)
    assert f.degree() == f_.degree(), f"Degree is wrong? {f.degree()}"
    assert f(0) == f_(0), f"Afwijkende oplossing: {f(0)}"
    print("Oplossing:", f(0))

recover(points)

for i in range(100):
    sample = random.sample(points, 26)
    recover(sample)