|
Karim Belabas on Sat, 12 Oct 2024 18:05:24 +0200
|
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
|
Re: computing all square root modulo a composite
|
- To: Max Alekseyev <maxale@gmail.com>
- Subject: Re: computing all square root modulo a composite
- From: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>
- Date: Sat, 12 Oct 2024 18:05:21 +0200
- Cc: Pari Users <pari-users@pari.math.u-bordeaux.fr>
- Delivery-date: Sat, 12 Oct 2024 18:05:24 +0200
- Dkim-signature: v=1; a=rsa-sha256; c=relaxed/simple; d=math.u-bordeaux.fr; s=2022; t=1728749122; bh=hHwDaFJ7kBOBGPu9cbJPCiguZKxYG8gw2ytK/RRW+mk=; h=Date:From:To:Cc:References:In-Reply-To:From; b=sZuYTnZbhU8Z2r8r+SWAofScnZc/2JG76FuaO3mUzAlJe1LJp+ULj2823FuSIbokc u5cIhHW026gfQUxgOS4w9C2A35Icijrc2ohZViV3JsC7+8dOvHJi+uXKunMIQ+Cd72 K8ugxitDaPur1OMaoCqx8LIhkf6wx2Aa2XeQO15edE6Nst0mwWbWvGrQAvUDCMY7g4 zwKgBDDFtwtry5yv66FKXVtwx5h3+XNFswd+6Ov/kfc9xeGuOWV7GjV8eRcMzgNW81 pN7o7SP6d/1rm6OKKXxZlWfweGGUZibiD8ZctTjW58EGmZGB7qSTEA3Xv01PzJQXfl uFH4bVuMwvwODSCCd20nyimq2Jsdb/UU0PU5qKRPTtWAx3NmGcYqh2SNvjtoChzgZ2 +4KeEsJxoQbeWUUMmf/8sAcayXsvmFBiCVYk5tQpjXTTcjNZ7mWuQ8oOZDjHhbMIHZ bi2G7JVkDGTdynbtfct2xoTdKXZY7cv8z8mMDIJEho2LSZfV0MKuWvG/2t9acO7su2 UoYN5yUi0GixC16IoVaGdTd9wPzCXEKGiCSShEmq8RCARCgbuJqgUC+uab3ii0NskD MCCVGKRWlj09a+WkDwCoBo65IKw2i4/gA7UywpQ/ezxFCvy9zTQOmRjVJLGEzDLK31 LTPqbBSy2kQdr1cjQnptBKQw=
- In-reply-to: <CAJkPp5M8u0a7fP-bZURFDckB+KkcrocpcYSx=NhSD-OaueuxgA@mail.gmail.com>
- Mail-followup-to: Max Alekseyev <maxale@gmail.com>, Pari Users <pari-users@pari.math.u-bordeaux.fr>
- References: <CAJkPp5PxxVZHXM02kNfJf1aV0CYdRoBgZ5YkKNvHbHF4yCXHqw@mail.gmail.com> <ZwqYkqFSUNZekIwn@math.u-bordeaux.fr> <Zwqa0UPT2UxgtaEQ@seventeen> <CAJkPp5M8u0a7fP-bZURFDckB+KkcrocpcYSx=NhSD-OaueuxgA@mail.gmail.com>
* Max Alekseyev [2024-10-12 17:56]:
> As for the name, maybe sqrtall() ?
sqrtmod rather. Also note that function gives you all roots of any
monic quadratic polynomial, not only square roots.
And it has a weird output format, which makes perfect sense if you
think of it (you get the most precise mathematical information). It
does not give you all solutions mod N but modulo M | N, whose
lifts + k (N/M) mod N, 0 <= k < M are the solutions mod N.
I don't think we want that as a GP function.
Cheers,
K.B.
--
Pr. Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77
http://www.math.u-bordeaux.fr/~kbelabas/