From af197de3f2f5581ccfbd1810074dbddd2b3a86a0 Mon Sep 17 00:00:00 2001 From: Ulli Kehrle Date: Thu, 8 Nov 2018 12:46:35 +0100 Subject: Make documentation more verbose --- gap/subgroupladders.autodoc | 31 +++++++++++++++++++++++++++++++ gap/subgroupladders.gd | 5 ++--- 2 files changed, 33 insertions(+), 3 deletions(-) create mode 100644 gap/subgroupladders.autodoc (limited to 'gap') diff --git a/gap/subgroupladders.autodoc b/gap/subgroupladders.autodoc new file mode 100644 index 0000000..0e9c8d2 --- /dev/null +++ b/gap/subgroupladders.autodoc @@ -0,0 +1,31 @@ +@AutoDocPlainText +@Chapter Introduction + +This package provides an algorithm that computes a subgroup ladder from a permutation group up to the parent symmetric group. +The algorithm was described by Bernd Schmalz in [1, Theorem 3.1.1]. + +Solutions of some problems in group theory can relatively easy be transferred to a sub- or supergroup if the index is small. +Let G be a permutation group on the set \{1,...,n\}. +So one might try to find a series of subgroups G = H_0,...,H_k = S_n of the symmetric group S_n such that H_{{i-1}} is a subgroup of H_i for every i and transfer the solution of a problem for the symmetric group step by step to G. + +Sometimes it is not possible to find such a series with small indices between consecutive subgroups. +This is where subgroup ladders may make sense: +A subgroup ladder is series of subgroups G = H_0,...,H_k = S_n of the symmetric group such that for every 1 \leq i \leq k, H_i is a subgroup of H_{{i-1}} or H_{{i-1}} is a subgroup of H_i. +So we sometimes go up to a larger group in order to keep the indices small. + +If G is a Young subgroup of S_n, the algorithm in this repository can find a subgroup ladder of G such that the indices are at most the degree of the permutation group. + +@Chapter subgroupladders +@Section subgroupladders + +@Chapter License + +subgroupladders is free software you can redistribute it and/or modify it under +the terms of the GNU General Public License as published by the Free Software +Foundation; either version 3 of the License, or (at your option) any later +version. For details, see the file LICENSE distributed as part of this package +or see the FSF's own site. + +@Chapter References +[1] B. Schmalz. Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. Bayreuther Mathematische Schriften, 31, S.109--143, 1990. +@EndAutoDocPlainText diff --git a/gap/subgroupladders.gd b/gap/subgroupladders.gd index 59b9325..b663821 100644 --- a/gap/subgroupladders.gd +++ b/gap/subgroupladders.gd @@ -4,14 +4,12 @@ # Declarations # -#! @Chapter subgroup-ladders -#! @Section subgroup-ladders - #! @Description #! Given a list of lists part of positive integers, this will compute #! the Young subgroup corresponding to this partition. #! @Returns a group #! @Arguments part +#! @ChapterInfo subgroupladders, subgroupladders DeclareGlobalFunction( "YoungGroupFromPartition" ); #! @Description #! Given a permutation group G, this will compute a subgroup ladder @@ -26,4 +24,5 @@ DeclareGlobalFunction( "YoungGroupFromPartition" ); #! At this step, the index may be larger than the degree. #! @Returns a list of groups #! @Arguments G +#! @ChapterInfo subgroupladders, subgroupladders DeclareGlobalFunction( "SubgroupLadder"); -- cgit v1.2.3-24-g4f1b From 9470f7a21bde04823c8fa421be5de617ff551b2a Mon Sep 17 00:00:00 2001 From: Ulli Kehrle Date: Thu, 8 Nov 2018 12:57:50 +0100 Subject: doc: mention that YoungGroupFromPartition does not checker whether the input is valid. --- gap/subgroupladders.gd | 1 + 1 file changed, 1 insertion(+) (limited to 'gap') diff --git a/gap/subgroupladders.gd b/gap/subgroupladders.gd index b663821..2291eb7 100644 --- a/gap/subgroupladders.gd +++ b/gap/subgroupladders.gd @@ -7,6 +7,7 @@ #! @Description #! Given a list of lists part of positive integers, this will compute #! the Young subgroup corresponding to this partition. +#! This function does not check whether the supplied lists are actually disjoint. #! @Returns a group #! @Arguments part #! @ChapterInfo subgroupladders, subgroupladders -- cgit v1.2.3-24-g4f1b