#!/usr/bin/env python3
"""Exact audit retracting the proposed quartic K=3 dual obstruction."""

from fractions import Fraction as Q


def add(*vectors):
    return tuple(sum(entries, Q(0)) for entries in zip(*vectors))


def scale(c, vector):
    return tuple(c * entry for entry in vector)


def main() -> None:
    # Coordinates: t^2 F, t^2 x4*d4F, t^4.
    energy = (Q(1), Q(0), Q(1, 2))
    radial_first_three = (Q(4), Q(-1), Q(0))
    fourth_stationarity = (Q(0), Q(3), Q(-1))

    cancellation = add(
        scale(Q(-12, 7), energy),
        scale(Q(3, 7), radial_first_three),
        scale(Q(1, 7), fourth_stationarity),
    )
    assert cancellation == (Q(0), Q(0), Q(-1))

    print("retraction audit: PASS")
    print("basis: (t^2 F, t^2 x4*d4F, t^4)")
    print("energy:", energy)
    print("cyclic stationarity:", radial_first_three)
    print("fourth stationarity:", fourth_stationarity)
    print("-12/7 energy + 3/7 cyclic + 1/7 fourth =", cancellation)
    print("the proposed leading obstruction is exactly a constraint")


if __name__ == "__main__":
    main()