Artin's method for class field computation

lucas legrand on Fri, 30 Apr 2021 11:16:34 +0200

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Artin's method for class field computation

To: "pari-dev@pari.math.u-bordeaux.fr" <pari-dev@pari.math.u-bordeaux.fr>
Subject: Artin's method for class field computation
From: lucas legrand <legrand.lucas.pro@hotmail.fr>
Date: Fri, 30 Apr 2021 09:16:32 +0000
Accept-language: fr-FR, en-US
Arc-authentication-results: i=1; mx.microsoft.com 1; spf=none; dmarc=none; dkim=none; arc=none
Arc-message-signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=microsoft.com; s=arcselector9901; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-SenderADCheck; bh=ZQpfyMxegltg2aQHm+K5pdYQ2c2MWm9h0KkyBoEOWNw=; b=VOxyFLN9myzs2Ez8KqIp9XdAS2hMadD5eVNiYKAKtMG0Lr3rAPhz9gIGJGh20Bw84zy9zX/chnTXhzLr7JPzcxEY3uNFgCyS3jVvsJ60H6Boraxy8TufVNUWb5SRzERffGlQCNbvKsvZMSJ7nqS6GFSKT3n+uTlulCq7iUYotdPGmsevCXOrVd9AK6gAwnLxtnLNhsbVelOfcwXxroRmZnIEdJil2O+MsmV6hgS13bbizWjp/BdDyJGn/PQiuxorIqusD3srRe7T0MoVqZqg7byxlpcC/lOQno9VhHRKldGk3DihW5KYg2EbjyhYPtbEM7LcgleNFP8e70RCeDdU7A==
Arc-seal: i=1; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=none; b=KOp7MmD3UWtY8lvv4JS8DmV6t2mh3Jblc1gasxK0OoP4D6JvoHaWBGWQvUApTKSlIEX26/E9AxxZycYjlIEsSxiuc4PvMRTvcO9KBKBxjyN9NeUTjw2uEyj9ybhOPLd7nxLg2Ll/IhykNF8cdlugwNGJKPrqfFRQIX2y6wKnXGxrPmXdyzc+ys9z3AscFQ3eFZE6LfkP4KZG0+yp6iVYGyNjPbf1z+Ktt+wPfF2woGJBQmbISiJKp7kEOJRFejYikCWlHTBoGpTDQbdnTJPqkzZW05DezFUR7EZm4tmRs9k3WyyxDJqnXOtgqpH2QibTdDBQBQ/k7yN4nnkcv/Ayzw==
Delivery-date: Fri, 30 Apr 2021 11:16:34 +0200
Thread-index: AQHXPZTMoDY5U067iUGzSeiaqlpV+Q==
Thread-topic: Artin's method for class field computation

Hi,

Looking at 'kummer.c', I (think I) understand that your current bnrclassfield implementation break the looked for extension into intermediate prime degree extensions and then apply rnfkummer to each of them, following closely Hecke's method in Cohen Vol. 2.

Maybe I'm mistaken, but I can't find anything in sources related to Artin's method which uses Artin reciprocity map and can deal with prime power degree extensions at once. Is there reasons Artin's method is not implemented ? Maybe it's unpublished, or you have plan for this ?

Well this question is just for curiosity, since I'm actually playing around with Artin's method for understanding purposes.

Lucas

Follow-Ups:
- Re: Artin's method for class field computation
  - From: Aurel Page <aurel.page@normalesup.org>
- Re: Artin's method for class field computation
  - From: Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>

Prev by Date: Re: Finding n mod p^(D-1) given A=g^n mod p^D
Next by Date: Re: Artin's method for class field computation
Previous by thread: Re: Finding n mod p^(D-1) given A=g^n mod p^D
Next by thread: Re: Artin's method for class field computation
Index(es):
- Date
- Thread