"""A small exact-arithmetic example; no third-party dependencies."""
from pathlib import Path
import sys
sys.path.insert(0, str(Path(__file__).resolve().parents[1]))
from carry_rank import carry, carry_from_defect, defect_coefficients, exact_rank, old_bound

def main():
    for p, r in [(5, 2), (37, 1), (37, 2), (37, 3), (521, 2)]:
        print(f'p={p}, r={r}: rank={exact_rank(p, r)}, proposed={old_bound(p, r)}')
    p = 37
    x, y = [36, 35], [34, 33]
    direct = carry(x, y, p)
    recovered = carry_from_defect(x, y, p)
    print(f'First carry for x={x}, y={y}: {direct}; defect formula: {recovered}')
    assert direct == recovered
    print('Missing degree at p=37:', [d for d in range(3, p-1, 2)
                                      if defect_coefficients(p)[d] == 0])
    print('p=521,r=2 above is a formula evaluation; the full matrix is not constructed.')

if __name__ == '__main__':
    main()