What is the paper that is_extra_strong_lucas_prp is referring to?

[haru-44]

The is_extra_strong_lucas_prp is described as follows:

gmpy/src/gmpy_mpz_prp.c

Lines 953 to 959 in ac1e151

	/* *******************************************************************************************
	* mpz_extrastronglucas_prp:
	* Let U_n = LucasU(p,1), V_n = LucasV(p,1), and D=p^2-4.
	* An "extra strong Lucas probable prime" to the base p is a composite n = (2^r)*s+(D/n), where
	* s is odd and (n,2D)=1, such that either U_s == 0 mod n or V_s == +/-2 mod n, or
	* V_((2^t)*s) == 0 mod n for some t with 0 <= t < r-1 [(D/n) is the Jacobi symbol]
	* *******************************************************************************************/

On the other hand, the paper defines extra strong Lucas pseudoprime as follows

An extra strong Lucas pseudoprime ... such that either $U_s \equiv 0 \bmod n$ and $V_s \equiv \pm 2 \bmod n$, or $V_{2^ts} \equiv 0 \bmod n$ ...

The U_s and V_s are and conditions, not or.
The same definition applies to sympy and OEIS.

Is there any references that define extra strong Lucas pseudoprime with or condition? If not, is it a bug?

sympy/sympy#25826

[smichr]

Grammatically, it seems like the statement in the docstring is wrong since a series of or statements would be written as "such that either this, or this, or this" while what is written is "such that either this or this, or this" (suggesting that it is actually "such that either this and this, or this").

[casevh]

It is a bug. The original author of the code published an update that I did not fully merge. I am double-checking the logic in my version of the original code and will have a fix soon. Thanks for the report.

…

On Wed, Oct 25, 2023 at 7:36 AM Christopher Smith ***@***.***> wrote: Grammatically, it seems like the statement in the docstring is wrong since a series of or statements would be written as "such that either this, or this, or this" while what is written is "such that either this or this, or this" (suggesting that it is actually "such that either this and this, or this"). — Reply to this email directly, view it on GitHub <#443 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAMR234LBBWD7THNSCWKSKLYBEPYPAVCNFSM6AAAAAA6PNTNVKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMYTONZZGQZDMNJUGE> . You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[casevh]

I've committed the fix.

[haru-44]

Thank you for the fix.