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group_examples.hpp
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/******************************************************************************/
/* Copyright (C) 2014 Florent Hivert <[email protected]>, */
/* */
/* Distributed under the terms of the GNU General Public License (GPL) */
/* */
/* This code is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU */
/* General Public License for more details. */
/* */
/* The full text of the GPL is available at: */
/* */
/* http://www.gnu.org/licenses/ */
/******************************************************************************/
#ifndef _GROUP_EXAMPLE
#define _GROUP_EXAMPLE
#include "group.hpp"
namespace IVMPG {
template< class Group = PermutationGroup<> > struct GroupExamples {
static Group S3, g100, g_Borie;
};
/* Symmetric group of order 3
*****************************
G = SymmetricGroup(3)
*****************************/
template< class Group >
Group GroupExamples< Group >::S3("S3", 3, {
{{0,1,2}, {1,0,2}, {2,1,0}},
{{0,1,2}, {0,2,1}},
{{0,1,2}}
});;
/* transitive subgroup of S6 number 100 according to Sage
**********************************************************
G = PermutationGroup([[(3,5),(4,6)], [(1,5),(2,6),(3,4)]])
**********************************************************/
template< class Group >
Group GroupExamples< Group >::g100("Transitive Group (6, 100)", 6,
{{{0, 1, 2, 3, 4, 5},
{1, 0, 3, 2, 5, 4},
{3, 2, 4, 5, 1, 0},
{2, 3, 5, 4, 0, 1},
{5, 4, 1, 0, 2, 3},
{4, 5, 0, 1, 3, 2}},
{{0, 1, 2, 3, 4, 5}},
{{0, 1, 2, 3, 4, 5},
{0, 1, 4, 5, 2, 3}},
{{0, 1, 2, 3, 4, 5}},
{{0, 1, 2, 3, 4, 5}},
{{0, 1, 2, 3, 4, 5}}});
/* N. Borie's favorite faforite subgroup of S16
************************************************************************
G = PermutationGroup([[(1,8,14,12,3,7,13,9,2,5,16,11),(4,6,15,10)],
[(1,13,10),(2,14,12,3,15,9,4,16,11),(5,6),(7,8)]])
************************************************************************/
template< class Group >
Group GroupExamples< Group >::g_Borie("N. Borie's favorite", 16,
{{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{7, 6, 5, 4, 3, 0, 2, 1, 13, 12, 15, 14, 11, 8, 10, 9},
{12, 15, 14, 13, 11, 10, 8, 9, 5, 6, 7, 4, 0, 2, 1, 3},
{13, 14, 15, 12, 10, 11, 9, 8, 7, 4, 5, 6, 1, 3, 0, 2},
{6, 7, 4, 5, 2, 1, 3, 0, 12, 13, 14, 15, 8, 11, 9, 10},
{8, 10, 9, 11, 15, 14, 12, 13, 1, 3, 0, 2, 6, 4, 7, 5},
{9, 11, 8, 10, 13, 12, 14, 15, 2, 0, 3, 1, 5, 7, 4, 6},
{11, 9, 10, 8, 14, 15, 13, 12, 0, 2, 1, 3, 7, 5, 6, 4},
{1, 0, 3, 2, 6, 7, 4, 5, 9, 8, 11, 10, 13, 12, 15, 14},
{3, 2, 1, 0, 5, 4, 7, 6, 10, 11, 8, 9, 14, 15, 12, 13},
{2, 3, 0, 1, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12},
{4, 5, 6, 7, 0, 3, 1, 2, 15, 14, 13, 12, 10, 9, 11, 8},
{5, 4, 7, 6, 1, 2, 0, 3, 14, 15, 12, 13, 9, 10, 8, 11},
{15, 12, 13, 14, 8, 9, 11, 10, 6, 5, 4, 7, 2, 0, 3, 1},
{14, 13, 12, 15, 9, 8, 10, 11, 4, 7, 6, 5, 3, 1, 2, 0},
{10, 8, 11, 9, 12, 13, 15, 14, 3, 1, 2, 0, 4, 6, 5, 7}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 2, 3, 1, 8, 9, 11, 10, 7, 4, 5, 6, 12, 14, 15, 13},
{0, 3, 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 3, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 14}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 5, 4, 7, 6, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 9, 8, 10, 11, 14, 12, 13, 15, 4, 6, 5, 7},
{0, 1, 2, 3, 12, 14, 13, 15, 5, 4, 6, 7, 9, 10, 8, 11},
{0, 1, 2, 3, 6, 7, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 10, 11, 9, 8, 14, 12, 13, 15, 4, 6, 5, 7},
{0, 1, 2, 3, 13, 15, 12, 14, 5, 4, 6, 7, 9, 10, 8, 11},
{0, 1, 2, 3, 11, 10, 8, 9, 14, 12, 13, 15, 4, 6, 5, 7},
{0, 1, 2, 3, 8, 9, 11, 10, 14, 12, 13, 15, 4, 6, 5, 7},
{0, 1, 2, 3, 7, 6, 5, 4, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 15, 13, 14, 12, 5, 4, 6, 7, 9, 10, 8, 11},
{0, 1, 2, 3, 14, 12, 15, 13, 5, 4, 6, 7, 9, 10, 8, 11}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 6, 5, 7, 15, 12, 13, 14, 8, 9, 10, 11},
{0, 1, 2, 3, 4, 7, 5, 6, 14, 12, 13, 15, 8, 9, 10, 11}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 7, 6, 14, 12, 13, 15, 8, 9, 11, 10}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 8, 9, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 12, 14, 15, 13, 8, 9, 10, 11},
{0, 1, 2, 3, 4, 5, 6, 7, 11, 10, 9, 8, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 9, 8, 11, 10, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 14, 12, 13, 15, 8, 9, 10, 11},
{0, 1, 2, 3, 4, 5, 6, 7, 13, 15, 14, 12, 8, 9, 10, 11},
{0, 1, 2, 3, 4, 5, 6, 7, 15, 13, 12, 14, 8, 9, 10, 11}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 9, 10, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 9, 11, 12, 13, 15, 14}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 12, 13, 15, 14}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 12, 15, 14},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 14, 13, 12},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 12, 13}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 13, 14},
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 13}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}},
{{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}}} );
} // namespace IVMPG
#endif