Introduction
This is tutorial about a branch developped by Takashi Fukuda, who started working on it in 2018
during the last Atelier in Besançon, and recently merged into the master branch.
PARI already includes many functions and algorithms to determine and work with class groups of
general number fields, notably bnfinit, bnrinit and bnrclassfield. Unconditionally in
small degrees, assuming GRH in moderate degrees, and with little hope of success in huge
degrees (> 150, say).
On the other hand, Iwasawa theory deals with (infinite!) towers of number fields, in particular
cyclotomic Zp-extensions and can give partial information about class groups of number fields of
very high degrees, in particular abelian fields. This tutorial centers on the subcyclopclgp
function which deals with the p-Sylow subgroups of the ideal class group of abelian number fields.
Atelier 2022 (13/01/2022) – p. 2/13