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# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://polymake.org
#
# This program 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 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program 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.
#-------------------------------------------------------------------------------
# @category Producing a matroid from scratch
# Create the matroid corresponding to Pappus' Theorem.
# Realizable if and only if the size of the field is not 2,3 or 5.
# An excluded minor for the field with 5 elements.
# @return Matroid
user_function pappus_matroid() {
my $m = new Matroid(BASES=> [[0, 1, 3], [0, 1, 4], [0, 1, 5], [0, 1, 6], [0, 1, 7], [0, 1, 8], [0, 2, 3], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 3, 4], [0, 3, 5], [0, 3, 6], [0, 3, 7], [0, 3, 8], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 5, 6], [0, 5, 8], [0, 6, 7], [0, 6, 8], [0, 7, 8], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 5, 7], [1, 5, 8], [1, 6, 7], [1, 6, 8], [1, 7, 8], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 8], [2, 4, 5], [2, 4, 7], [2, 4, 8], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 6, 7], [2, 6, 8], [2, 7, 8], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 6, 7], [3, 6, 8], [3, 7, 8], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 6, 7], [4, 6, 8], [4, 7, 8], [5, 6, 7], [5, 6, 8], [5, 7, 8]],
N_ELEMENTS=>9,
RANK=>3);
$m->name="Pappus matroid";
$m->description="Matroid corresponding to Pappus' Theorem";
return $m;
}
# @category Producing a matroid from scratch
# Create the matroid encoding the violation of Pappus' Theorem. Not realizable over any field.
# An excluded minor for all finite fields with more than four elements.
# Algebraic over all field that do not have characteristic 0.
# @return Matroid
user_function non_pappus_matroid() {
my $m = new Matroid(BASES=> [[0, 1, 3], [0, 1, 4], [0, 1, 5], [0, 1, 6], [0, 1, 7], [0, 1, 8], [0, 2, 3], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 3, 4], [0, 3, 5], [0, 3, 6], [0, 3, 7], [0, 3, 8], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 5, 6], [0, 5, 8], [0, 6, 7], [0, 6, 8], [0, 7, 8], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 4, 5], [1, 4, 6], [1, 4, 7], [1, 4, 8], [1, 5, 7], [1, 5, 8], [1, 6, 7], [1, 6, 8], [1, 7, 8], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 8], [2, 4, 5], [2, 4, 7], [2, 4, 8], [2, 5, 6], [2, 5, 7], [2, 5, 8], [2, 6, 7], [2, 6, 8], [2, 7, 8], [3, 4, 5], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 6, 7], [3, 6, 8], [3, 7, 8], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 6, 7], [4, 6, 8], [4, 7, 8], [5, 6, 7], [5, 6, 8], [5, 7, 8]],
N_ELEMENTS=>9,
RANK=>3);
$m->name="Non-Pappus matroid";
$m->description="Matroid encoding the violation of Pappus' Theorem";
return $m;
}
# @category Producing a matroid from scratch
# A regular matroid that's not graphical nor cographical.
# Algebraic over all fields.
# @return Matroid
user_function r10_matroid() {
my $m = new Matroid(VECTORS=> [[1,0,0,0,0],[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[-1,1,0,0,1],[1,-1,1,0,0],[0,1,-1,1,0],[0,0,1,-1,1],[1,0,0,1,-1]]);
$m->name="R10 matroid";
$m->description="A regular matroid that's not graphical nor cographical";
return $m;
}
# @category Producing a matroid from scratch
# A minimal non-representable matroid.
# An excluded minor for all finite fields with more than four elements.
# Non-algebraic.
# @return Matroid
user_function vamos_matroid() {
my $m = new Matroid(BASES=> [[0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 6], [0, 1, 5, 7], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 6, 7], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="Vamos matroid";
$m->description="The Vamos matroid, a minimal non-representable matroid";
return $m;
}
# @category Producing a matroid from scratch
# A matroid related to the Vamos matroid (see [Oxley:matroid theory (2nd ed.) page 72])
# @return Matroid
user_function non_vamos_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 6], [0, 1, 5, 7], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 6, 7], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="Non-Vamos matroid";
$m->description="The Non-Vamos matroid, a matroid related to the Vamos matroid (see Oxley: Matroid theory (2nd ed.), page 72)";
return $m;
}
# @category Producing a matroid from scratch
# The only other ternary 3-spike apart from the non-Fano matroid.
# Non binary. Algebraic over all fields.
# @return Matroid
user_function p7_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2], [0, 1, 3], [0, 1, 5], [0, 1, 6], [0, 2, 3], [0, 2, 4], [0, 2, 6], [0, 3, 4], [0, 3, 5], [0, 4, 5], [0, 4, 6], [0, 5, 6], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 4, 5], [1, 4, 6], [1, 5, 6], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 4, 5], [2, 4, 6], [2, 5, 6], [3, 4, 6], [3, 5, 6], [4, 5, 6]],
N_ELEMENTS=>7,
RANK=>3);
$m->name="P7 matroid";
$m->description="The only other ternary 3-spike apart from the non-Fano matroid";
return $m;
}
# @category Producing a matroid from scratch
# The repesentation over the reals is obtained from a 3-cube where one face is rotated by 45°.
# Non-representable if and only if the characeristic of the field is 2. Algebraic over all fields.
# @return Matroid
user_function p8_matroid() {
my $m = new Matroid(TERNARY_VECTORS=>[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[0,1,1,2],[1,0,1,1],[1,1,0,1],[2,1,1,0]],
BASES=>[[0,1,2,3],[0,1,2,4],[0,1,2,5],[0,1,2,6],[0,1,3,4],[0,1,3,5],[0,1,3,7],[0,1,4,5],[0,1,4,6],[0,1,4,7],[0,1,5,6],[0,1,5,7],[0,1,6,7],[0,2,3,4],[0,2,3,6],[0,2,3,7],[0,2,4,5],[0,2,4,6],[0,2,4,7],[0,2,5,6],[0,2,5,7],[0,2,6,7],[0,3,4,5],[0,3,4,6],[0,3,5,6],[0,3,5,7],[0,3,6,7],[0,4,5,7],[0,4,6,7],[0,5,6,7],[1,2,3,5],[1,2,3,6],[1,2,3,7],[1,2,4,5],[1,2,4,6],[1,2,4,7],[1,2,5,7],[1,2,6,7],[1,3,4,5],[1,3,4,6],[1,3,4,7],[1,3,5,6],[1,3,5,7],[1,3,6,7],[1,4,5,6],[1,4,6,7],[1,5,6,7],[2,3,4,5],[2,3,4,6],[2,3,4,7],[2,3,5,6],[2,3,5,7],[2,3,6,7],[2,4,5,6],[2,4,5,7],[2,5,6,7],[3,4,5,6],[3,4,5,7],[3,4,6,7],[4,5,6,7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="P8 matroid";
$m->description="The repesentation over the reals is obtained from a 3-cube where one face is rotated by 45°.";
return $m;
}
# @category Producing a matroid from scratch
# Obtained from [[p8_matroid]] by relaxing its only pair of disjoint circuit-hyperplanes.
# @return Matroid
user_function non_p8_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3, 7], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 6], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 6, 7], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 6, 7], [2, 4, 5, 6], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [4, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="Non-P8 matroid";
$m->description="Obtained from the P8 matroid by relaxing its only pair of disjoint circuit-hyperplanes";
return $m;
}
# @category Producing a matroid from scratch
# An excluded minor for some properties (see [Oxley:matroid theory (2nd ed.) page 650]).
# Non binary. Algebraic over all fields.
# @return Matroid
user_function j_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 7], [0, 1, 3, 4], [0, 1, 3, 6], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 5, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 5, 6], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="J-matroid";
$m->description="An excluded minor for some properties (see Oxley: Matroid theory (2nd ed.), page 650)";
return $m;
}
# @category Producing a matroid from scratch
# The 4-point planes are the six faces of the cube an the two twisted plannes.
# Identically self-dual. Representable over all field with more then 4 elements and algebraic over all fields.
# @return Matroid
user_function l8_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 6, 7], [0, 4, 5, 6], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7], [4, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="L8 matroid";
$m->description="The 4-point planes are the six faces of the cube an the two twisted plannes.
";
return $m;
}
# @category Producing a matroid from scratch
# An excluded minor for the dyadic matroids (see [Oxley:matroid theory (2nd ed.) page 558]).
# @return Matroid
user_function n1_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3, 4], [0, 1, 2, 3, 5], [0, 1, 2, 3, 6], [0, 1, 2, 3, 7], [0, 1, 2, 3, 8], [0, 1, 2, 4, 7], [0, 1, 2, 4, 8], [0, 1, 2, 4, 9], [0, 1, 2, 5, 7], [0, 1, 2, 5, 8], [0, 1, 2, 5, 9], [0, 1, 2, 6, 7], [0, 1, 2, 6, 8], [0, 1, 2, 6, 9], [0, 1, 2, 7, 9], [0, 1, 2, 8, 9], [0, 1, 3, 4, 6], [0, 1, 3, 4, 7], [0, 1, 3, 4, 9], [0, 1, 3, 5, 6], [0, 1, 3, 5, 7], [0, 1, 3, 5, 9], [0, 1, 3, 6, 7], [0, 1, 3, 6, 8], [0, 1, 3, 6, 9], [0, 1, 3, 7, 8], [0, 1, 3, 7, 9], [0, 1, 3, 8, 9], [0, 1, 4, 6, 7], [0, 1, 4, 6, 8], [0, 1, 4, 6, 9], [0, 1, 4, 7, 8], [0, 1, 4, 8, 9], [0, 1, 5, 6, 7], [0, 1, 5, 6, 8], [0, 1, 5, 6, 9], [0, 1, 5, 7, 8], [0, 1, 5, 8, 9], [0, 1, 6, 7, 8], [0, 1, 6, 7, 9], [0, 1, 7, 8, 9], [0, 2, 3, 4, 5], [0, 2, 3, 4, 6], [0, 2, 3, 4, 9], [0, 2, 3, 5, 6], [0, 2, 3, 5, 7], [0, 2, 3, 5, 8], [0, 2, 3, 5, 9], [0, 2, 3, 6, 7], [0, 2, 3, 6, 8], [0, 2, 3, 6, 9], [0, 2, 3, 7, 9], [0, 2, 3, 8, 9], [0, 2, 4, 5, 7], [0, 2, 4, 5, 8], [0, 2, 4, 5, 9], [0, 2, 4, 6, 7], [0, 2, 4, 6, 8], [0, 2, 4, 6, 9], [0, 2, 4, 7, 9], [0, 2, 4, 8, 9], [0, 2, 5, 6, 7], [0, 2, 5, 6, 8], [0, 2, 5, 6, 9], [0, 2, 6, 7, 9], [0, 2, 6, 8, 9], [0, 3, 4, 5, 6], [0, 3, 4, 5, 7], [0, 3, 4, 5, 9], [0, 3, 4, 6, 7], [0, 3, 4, 6, 9], [0, 3, 4, 7, 9], [0, 3, 5, 6, 8], [0, 3, 5, 7, 8], [0, 3, 5, 8, 9], [0, 3, 6, 7, 8], [0, 3, 6, 8, 9], [0, 3, 7, 8, 9], [0, 4, 5, 6, 7], [0, 4, 5, 6, 8], [0, 4, 5, 6, 9], [0, 4, 5, 7, 8], [0, 4, 5, 8, 9], [0, 4, 6, 7, 8], [0, 4, 6, 7, 9], [0, 4, 6, 8, 9], [0, 4, 7, 8, 9], [0, 5, 6, 7, 8], [0, 5, 6, 8, 9], [0, 6, 7, 8, 9], [1, 2, 3, 4, 5], [1, 2, 3, 4, 8], [1, 2, 3, 4, 9], [1, 2, 3, 5, 6], [1, 2, 3, 5, 7], [1, 2, 3, 5, 9], [1, 2, 3, 6, 8], [1, 2, 3, 6, 9], [1, 2, 3, 7, 8], [1, 2, 3, 7, 9], [1, 2, 3, 8, 9], [1, 2, 4, 5, 7], [1, 2, 4, 5, 8], [1, 2, 4, 5, 9], [1, 2, 4, 7, 8], [1, 2, 4, 7, 9], [1, 2, 5, 6, 7], [1, 2, 5, 6, 8], [1, 2, 5, 6, 9], [1, 2, 5, 7, 8], [1, 2, 5, 7, 9], [1, 2, 5, 8, 9], [1, 2, 6, 7, 8], [1, 2, 6, 7, 9], [1, 2, 7, 8, 9], [1, 3, 4, 5, 6], [1, 3, 4, 5, 7], [1, 3, 4, 5, 9], [1, 3, 4, 6, 8], [1, 3, 4, 6, 9], [1, 3, 4, 7, 8], [1, 3, 4, 7, 9], [1, 3, 4, 8, 9], [1, 3, 5, 6, 7], [1, 3, 5, 7, 9], [1, 3, 6, 7, 8], [1, 3, 6, 7, 9], [1, 3, 7, 8, 9], [1, 4, 5, 6, 7], [1, 4, 5, 6, 8], [1, 4, 5, 6, 9], [1, 4, 5, 7, 8], [1, 4, 5, 8, 9], [1, 4, 6, 7, 8], [1, 4, 6, 7, 9], [1, 4, 7, 8, 9], [1, 5, 6, 7, 8], [1, 5, 6, 7, 9], [1, 5, 7, 8, 9], [2, 3, 4, 5, 6], [2, 3, 4, 5, 8], [2, 3, 4, 5, 9], [2, 3, 4, 6, 8], [2, 3, 4, 6, 9], [2, 3, 4, 8, 9], [2, 3, 5, 6, 7], [2, 3, 5, 6, 8], [2, 3, 5, 7, 8], [2, 3, 5, 7, 9], [2, 3, 5, 8, 9], [2, 3, 6, 7, 8], [2, 3, 6, 7, 9], [2, 3, 6, 8, 9], [2, 3, 7, 8, 9], [2, 4, 5, 6, 7], [2, 4, 5, 6, 8], [2, 4, 5, 6, 9], [2, 4, 5, 7, 8], [2, 4, 5, 7, 9], [2, 4, 5, 8, 9], [2, 4, 6, 7, 8], [2, 4, 6, 7, 9], [2, 4, 7, 8, 9], [2, 5, 6, 7, 8], [2, 5, 6, 7, 9], [2, 5, 6, 8, 9], [2, 6, 7, 8, 9], [3, 4, 5, 6, 7], [3, 4, 5, 6, 8], [3, 4, 5, 7, 8], [3, 4, 5, 7, 9], [3, 4, 5, 8, 9], [3, 4, 6, 7, 8], [3, 4, 6, 7, 9], [3, 4, 6, 8, 9], [3, 4, 7, 8, 9], [3, 5, 6, 7, 8], [3, 5, 7, 8, 9], [3, 6, 7, 8, 9], [4, 5, 6, 7, 9], [4, 5, 6, 8, 9], [4, 5, 7, 8, 9], [4, 6, 7, 8, 9], [5, 6, 7, 8, 9]],
N_ELEMENTS=>10,
RANK=>5);
$m->name="N1 matroid";
$m->description="An excluded minor for the dyadic matroids";
return $m;
}
# @category Producing a matroid from scratch
# An excluded minor for the dyadic matroids (see [Oxley:matroid theory (2nd ed.) page 558]).
# @return Matroid
user_function n2_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 6], [0, 1, 2, 3, 4, 7], [0, 1, 2, 3, 4, 8], [0, 1, 2, 3, 4, 9], [0, 1, 2, 3, 4, 11], [0, 1, 2, 3, 5, 6], [0, 1, 2, 3, 5, 10], [0, 1, 2, 3, 5, 11], [0, 1, 2, 3, 6, 7], [0, 1, 2, 3, 6, 8], [0, 1, 2, 3, 6, 9], [0, 1, 2, 3, 6, 10], [0, 1, 2, 3, 7, 10], [0, 1, 2, 3, 7, 11], [0, 1, 2, 3, 8, 10], [0, 1, 2, 3, 8, 11], [0, 1, 2, 3, 9, 10], [0, 1, 2, 3, 9, 11], [0, 1, 2, 3, 10, 11], [0, 1, 2, 4, 5, 8], [0, 1, 2, 4, 5, 9], [0, 1, 2, 4, 5, 10], [0, 1, 2, 4, 6, 8], [0, 1, 2, 4, 6, 9], [0, 1, 2, 4, 6, 10], [0, 1, 2, 4, 7, 8], [0, 1, 2, 4, 7, 9], [0, 1, 2, 4, 7, 10], [0, 1, 2, 4, 8, 10], [0, 1, 2, 4, 8, 11], [0, 1, 2, 4, 9, 10], [0, 1, 2, 4, 9, 11], [0, 1, 2, 4, 10, 11], [0, 1, 2, 5, 6, 8], [0, 1, 2, 5, 6, 9], [0, 1, 2, 5, 6, 10], [0, 1, 2, 5, 8, 10], [0, 1, 2, 5, 8, 11], [0, 1, 2, 5, 9, 10], [0, 1, 2, 5, 9, 11], [0, 1, 2, 5, 10, 11], [0, 1, 2, 6, 7, 8], [0, 1, 2, 6, 7, 9], [0, 1, 2, 6, 7, 10], [0, 1, 2, 7, 8, 10], [0, 1, 2, 7, 8, 11], [0, 1, 2, 7, 9, 10], [0, 1, 2, 7, 9, 11], [0, 1, 2, 7, 10, 11], [0, 1, 3, 4, 5, 7], [0, 1, 3, 4, 5, 8], [0, 1, 3, 4, 5, 11], [0, 1, 3, 4, 6, 7], [0, 1, 3, 4, 6, 8], [0, 1, 3, 4, 6, 11], [0, 1, 3, 4, 7, 8], [0, 1, 3, 4, 7, 9], [0, 1, 3, 4, 7, 11], [0, 1, 3, 4, 8, 9], [0, 1, 3, 4, 9, 11], [0, 1, 3, 5, 6, 7], [0, 1, 3, 5, 6, 8], [0, 1, 3, 5, 6, 11], [0, 1, 3, 5, 7, 10], [0, 1, 3, 5, 7, 11], [0, 1, 3, 5, 8, 10], [0, 1, 3, 5, 8, 11], [0, 1, 3, 5, 10, 11], [0, 1, 3, 6, 7, 8], [0, 1, 3, 6, 7, 9], [0, 1, 3, 6, 7, 10], [0, 1, 3, 6, 7, 11], [0, 1, 3, 6, 8, 9], [0, 1, 3, 6, 8, 10], [0, 1, 3, 6, 8, 11], [0, 1, 3, 6, 9, 11], [0, 1, 3, 6, 10, 11], [0, 1, 3, 7, 8, 10], [0, 1, 3, 7, 8, 11], [0, 1, 3, 7, 9, 10], [0, 1, 3, 7, 9, 11], [0, 1, 3, 7, 10, 11], [0, 1, 3, 8, 9, 10], [0, 1, 3, 8, 9, 11], [0, 1, 3, 9, 10, 11], [0, 1, 4, 5, 7, 8], [0, 1, 4, 5, 7, 9], [0, 1, 4, 5, 7, 10], [0, 1, 4, 5, 8, 9], [0, 1, 4, 5, 8, 10], [0, 1, 4, 5, 8, 11], [0, 1, 4, 5, 9, 11], [0, 1, 4, 5, 10, 11], [0, 1, 4, 6, 7, 8], [0, 1, 4, 6, 7, 9], [0, 1, 4, 6, 7, 10], [0, 1, 4, 6, 8, 9], [0, 1, 4, 6, 8, 10], [0, 1, 4, 6, 8, 11], [0, 1, 4, 6, 9, 11], [0, 1, 4, 6, 10, 11], [0, 1, 4, 7, 8, 9], [0, 1, 4, 7, 8, 10], [0, 1, 4, 7, 8, 11], [0, 1, 4, 7, 9, 10], [0, 1, 4, 7, 9, 11], [0, 1, 4, 7, 10, 11], [0, 1, 4, 8, 9, 10], [0, 1, 4, 8, 9, 11], [0, 1, 4, 9, 10, 11], [0, 1, 5, 6, 7, 8], [0, 1, 5, 6, 7, 9], [0, 1, 5, 6, 7, 10], [0, 1, 5, 6, 8, 9], [0, 1, 5, 6, 8, 10], [0, 1, 5, 6, 8, 11], [0, 1, 5, 6, 9, 11], [0, 1, 5, 6, 10, 11], [0, 1, 5, 7, 8, 10], [0, 1, 5, 7, 8, 11], [0, 1, 5, 7, 9, 10], [0, 1, 5, 7, 9, 11], [0, 1, 5, 7, 10, 11], [0, 1, 5, 8, 9, 10], [0, 1, 5, 8, 9, 11], [0, 1, 5, 9, 10, 11], [0, 1, 6, 7, 8, 9], [0, 1, 6, 7, 8, 10], [0, 1, 6, 7, 8, 11], [0, 1, 6, 7, 9, 11], [0, 1, 6, 7, 10, 11], [0, 1, 7, 8, 9, 10], [0, 1, 7, 8, 9, 11], [0, 1, 7, 9, 10, 11], [0, 2, 3, 4, 5, 6], [0, 2, 3, 4, 5, 7], [0, 2, 3, 4, 5, 11], [0, 2, 3, 4, 6, 8], [0, 2, 3, 4, 6, 9], [0, 2, 3, 4, 7, 8], [0, 2, 3, 4, 7, 9], [0, 2, 3, 4, 8, 11], [0, 2, 3, 4, 9, 11], [0, 2, 3, 5, 6, 7], [0, 2, 3, 5, 6, 10], [0, 2, 3, 5, 7, 10], [0, 2, 3, 5, 7, 11], [0, 2, 3, 5, 10, 11], [0, 2, 3, 6, 7, 8], [0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 8, 10], [0, 2, 3, 6, 9, 10], [0, 2, 3, 7, 8, 10], [0, 2, 3, 7, 8, 11], [0, 2, 3, 7, 9, 10], [0, 2, 3, 7, 9, 11], [0, 2, 3, 8, 10, 11], [0, 2, 3, 9, 10, 11], [0, 2, 4, 5, 6, 8], [0, 2, 4, 5, 6, 9], [0, 2, 4, 5, 6, 10], [0, 2, 4, 5, 7, 8], [0, 2, 4, 5, 7, 9], [0, 2, 4, 5, 7, 10], [0, 2, 4, 5, 8, 11], [0, 2, 4, 5, 9, 11], [0, 2, 4, 5, 10, 11], [0, 2, 4, 6, 8, 10], [0, 2, 4, 6, 9, 10], [0, 2, 4, 7, 8, 10], [0, 2, 4, 7, 9, 10], [0, 2, 4, 8, 10, 11], [0, 2, 4, 9, 10, 11], [0, 2, 5, 6, 7, 8], [0, 2, 5, 6, 7, 9], [0, 2, 5, 6, 7, 10], [0, 2, 5, 6, 8, 10], [0, 2, 5, 6, 9, 10], [0, 2, 5, 7, 8, 10], [0, 2, 5, 7, 8, 11], [0, 2, 5, 7, 9, 10], [0, 2, 5, 7, 9, 11], [0, 2, 5, 7, 10, 11], [0, 2, 5, 8, 10, 11], [0, 2, 5, 9, 10, 11], [0, 2, 6, 7, 8, 10], [0, 2, 6, 7, 9, 10], [0, 2, 7, 8, 10, 11], [0, 2, 7, 9, 10, 11], [0, 3, 4, 5, 6, 7], [0, 3, 4, 5, 6, 8], [0, 3, 4, 5, 6, 11], [0, 3, 4, 5, 7, 8], [0, 3, 4, 5, 7, 11], [0, 3, 4, 5, 8, 11], [0, 3, 4, 6, 7, 8], [0, 3, 4, 6, 7, 9], [0, 3, 4, 6, 8, 9], [0, 3, 4, 6, 8, 11], [0, 3, 4, 6, 9, 11], [0, 3, 4, 7, 8, 9], [0, 3, 4, 7, 8, 11], [0, 3, 4, 7, 9, 11], [0, 3, 4, 8, 9, 11], [0, 3, 5, 6, 7, 8], [0, 3, 5, 6, 7, 10], [0, 3, 5, 6, 7, 11], [0, 3, 5, 6, 8, 10], [0, 3, 5, 6, 10, 11], [0, 3, 5, 7, 8, 10], [0, 3, 5, 7, 8, 11], [0, 3, 5, 7, 10, 11], [0, 3, 5, 8, 10, 11], [0, 3, 6, 7, 8, 9], [0, 3, 6, 7, 8, 10], [0, 3, 6, 7, 8, 11], [0, 3, 6, 7, 9, 10], [0, 3, 6, 7, 9, 11], [0, 3, 6, 8, 9, 10], [0, 3, 6, 8, 10, 11], [0, 3, 6, 9, 10, 11], [0, 3, 7, 8, 9, 10], [0, 3, 7, 8, 9, 11], [0, 3, 7, 8, 10, 11], [0, 3, 7, 9, 10, 11], [0, 3, 8, 9, 10, 11], [0, 4, 5, 6, 7, 8], [0, 4, 5, 6, 7, 9], [0, 4, 5, 6, 7, 10], [0, 4, 5, 6, 8, 9], [0, 4, 5, 6, 8, 10], [0, 4, 5, 6, 8, 11], [0, 4, 5, 6, 9, 11], [0, 4, 5, 6, 10, 11], [0, 4, 5, 7, 8, 9], [0, 4, 5, 7, 8, 10], [0, 4, 5, 7, 8, 11], [0, 4, 5, 7, 9, 11], [0, 4, 5, 7, 10, 11], [0, 4, 5, 8, 9, 11], [0, 4, 5, 8, 10, 11], [0, 4, 6, 7, 8, 10], [0, 4, 6, 7, 9, 10], [0, 4, 6, 8, 9, 10], [0, 4, 6, 8, 10, 11], [0, 4, 6, 9, 10, 11], [0, 4, 7, 8, 9, 10], [0, 4, 7, 8, 10, 11], [0, 4, 7, 9, 10, 11], [0, 4, 8, 9, 10, 11], [0, 5, 6, 7, 8, 9], [0, 5, 6, 7, 8, 11], [0, 5, 6, 7, 9, 10], [0, 5, 6, 7, 9, 11], [0, 5, 6, 7, 10, 11], [0, 5, 6, 8, 9, 10], [0, 5, 6, 8, 10, 11], [0, 5, 6, 9, 10, 11], [0, 5, 7, 8, 9, 10], [0, 5, 7, 8, 9, 11], [0, 5, 7, 8, 10, 11], [0, 5, 7, 9, 10, 11], [0, 5, 8, 9, 10, 11], [0, 6, 7, 8, 9, 10], [0, 6, 7, 8, 10, 11], [0, 6, 7, 9, 10, 11], [0, 7, 8, 9, 10, 11], [1, 2, 3, 4, 5, 6], [1, 2, 3, 4, 5, 9], [1, 2, 3, 4, 5, 10], [1, 2, 3, 4, 5, 11], [1, 2, 3, 4, 6, 7], [1, 2, 3, 4, 6, 8], [1, 2, 3, 4, 6, 9], [1, 2, 3, 4, 6, 10], [1, 2, 3, 4, 6, 11], [1, 2, 3, 4, 7, 9], [1, 2, 3, 4, 7, 10], [1, 2, 3, 4, 7, 11], [1, 2, 3, 4, 8, 9], [1, 2, 3, 4, 8, 10], [1, 2, 3, 4, 8, 11], [1, 2, 3, 4, 9, 10], [1, 2, 3, 4, 10, 11], [1, 2, 3, 5, 6, 9], [1, 2, 3, 5, 6, 10], [1, 2, 3, 5, 6, 11], [1, 2, 3, 5, 9, 10], [1, 2, 3, 5, 9, 11], [1, 2, 3, 6, 7, 9], [1, 2, 3, 6, 7, 10], [1, 2, 3, 6, 7, 11], [1, 2, 3, 6, 8, 9], [1, 2, 3, 6, 8, 10], [1, 2, 3, 6, 8, 11], [1, 2, 3, 6, 9, 11], [1, 2, 3, 6, 10, 11], [1, 2, 3, 7, 9, 10], [1, 2, 3, 7, 9, 11], [1, 2, 3, 8, 9, 10], [1, 2, 3, 8, 9, 11], [1, 2, 3, 9, 10, 11], [1, 2, 4, 5, 6, 8], [1, 2, 4, 5, 6, 9], [1, 2, 4, 5, 6, 10], [1, 2, 4, 5, 8, 9], [1, 2, 4, 5, 8, 10], [1, 2, 4, 5, 8, 11], [1, 2, 4, 5, 9, 10], [1, 2, 4, 5, 9, 11], [1, 2, 4, 5, 10, 11], [1, 2, 4, 6, 7, 8], [1, 2, 4, 6, 7, 9], [1, 2, 4, 6, 7, 10], [1, 2, 4, 6, 8, 9], [1, 2, 4, 6, 8, 10], [1, 2, 4, 6, 8, 11], [1, 2, 4, 6, 9, 11], [1, 2, 4, 6, 10, 11], [1, 2, 4, 7, 8, 9], [1, 2, 4, 7, 8, 10], [1, 2, 4, 7, 8, 11], [1, 2, 4, 7, 9, 10], [1, 2, 4, 7, 9, 11], [1, 2, 4, 7, 10, 11], [1, 2, 4, 8, 9, 10], [1, 2, 4, 8, 9, 11], [1, 2, 4, 9, 10, 11], [1, 2, 5, 6, 8, 9], [1, 2, 5, 6, 8, 10], [1, 2, 5, 6, 8, 11], [1, 2, 5, 6, 9, 11], [1, 2, 5, 6, 10, 11], [1, 2, 5, 8, 9, 10], [1, 2, 5, 8, 9, 11], [1, 2, 5, 9, 10, 11], [1, 2, 6, 7, 8, 9], [1, 2, 6, 7, 8, 10], [1, 2, 6, 7, 8, 11], [1, 2, 6, 7, 9, 11], [1, 2, 6, 7, 10, 11], [1, 2, 7, 8, 9, 10], [1, 2, 7, 8, 9, 11], [1, 2, 7, 9, 10, 11], [1, 3, 4, 5, 6, 7], [1, 3, 4, 5, 6, 8], [1, 3, 4, 5, 6, 11], [1, 3, 4, 5, 7, 9], [1, 3, 4, 5, 7, 10], [1, 3, 4, 5, 7, 11], [1, 3, 4, 5, 8, 9], [1, 3, 4, 5, 8, 10], [1, 3, 4, 5, 8, 11], [1, 3, 4, 5, 9, 11], [1, 3, 4, 5, 10, 11], [1, 3, 4, 6, 7, 8], [1, 3, 4, 6, 7, 9], [1, 3, 4, 6, 7, 10], [1, 3, 4, 6, 8, 9], [1, 3, 4, 6, 8, 10], [1, 3, 4, 6, 8, 11], [1, 3, 4, 6, 9, 11], [1, 3, 4, 6, 10, 11], [1, 3, 4, 7, 8, 9], [1, 3, 4, 7, 8, 10], [1, 3, 4, 7, 8, 11], [1, 3, 4, 7, 9, 10], [1, 3, 4, 7, 9, 11], [1, 3, 4, 7, 10, 11], [1, 3, 4, 8, 9, 10], [1, 3, 4, 8, 9, 11], [1, 3, 4, 9, 10, 11], [1, 3, 5, 6, 7, 9], [1, 3, 5, 6, 7, 10], [1, 3, 5, 6, 7, 11], [1, 3, 5, 6, 8, 9], [1, 3, 5, 6, 8, 10], [1, 3, 5, 6, 8, 11], [1, 3, 5, 6, 9, 11], [1, 3, 5, 6, 10, 11], [1, 3, 5, 7, 9, 10], [1, 3, 5, 7, 9, 11], [1, 3, 5, 8, 9, 10], [1, 3, 5, 8, 9, 11], [1, 3, 5, 9, 10, 11], [1, 3, 6, 7, 8, 9], [1, 3, 6, 7, 8, 10], [1, 3, 6, 7, 8, 11], [1, 3, 6, 7, 9, 11], [1, 3, 6, 7, 10, 11], [1, 3, 7, 8, 9, 10], [1, 3, 7, 8, 9, 11], [1, 3, 7, 9, 10, 11], [1, 4, 5, 6, 7, 8], [1, 4, 5, 6, 7, 9], [1, 4, 5, 6, 7, 10], [1, 4, 5, 6, 8, 9], [1, 4, 5, 6, 8, 10], [1, 4, 5, 6, 8, 11], [1, 4, 5, 6, 9, 11], [1, 4, 5, 6, 10, 11], [1, 4, 5, 7, 8, 9], [1, 4, 5, 7, 8, 10], [1, 4, 5, 7, 8, 11], [1, 4, 5, 7, 9, 10], [1, 4, 5, 7, 9, 11], [1, 4, 5, 7, 10, 11], [1, 4, 5, 8, 9, 10], [1, 4, 5, 8, 9, 11], [1, 4, 5, 9, 10, 11], [1, 5, 6, 7, 8, 9], [1, 5, 6, 7, 8, 10], [1, 5, 6, 7, 8, 11], [1, 5, 6, 7, 9, 11], [1, 5, 6, 7, 10, 11], [1, 5, 7, 8, 9, 10], [1, 5, 7, 8, 9, 11], [1, 5, 7, 9, 10, 11], [2, 3, 4, 5, 6, 7], [2, 3, 4, 5, 6, 9], [2, 3, 4, 5, 6, 10], [2, 3, 4, 5, 6, 11], [2, 3, 4, 5, 7, 9], [2, 3, 4, 5, 7, 10], [2, 3, 4, 5, 7, 11], [2, 3, 4, 5, 9, 11], [2, 3, 4, 5, 10, 11], [2, 3, 4, 6, 7, 8], [2, 3, 4, 6, 7, 9], [2, 3, 4, 6, 8, 9], [2, 3, 4, 6, 8, 10], [2, 3, 4, 6, 8, 11], [2, 3, 4, 6, 9, 10], [2, 3, 4, 6, 9, 11], [2, 3, 4, 7, 8, 9], [2, 3, 4, 7, 8, 10], [2, 3, 4, 7, 8, 11], [2, 3, 4, 7, 9, 10], [2, 3, 4, 7, 9, 11], [2, 3, 4, 8, 9, 11], [2, 3, 4, 8, 10, 11], [2, 3, 4, 9, 10, 11], [2, 3, 5, 6, 7, 9], [2, 3, 5, 6, 7, 10], [2, 3, 5, 6, 7, 11], [2, 3, 5, 6, 9, 10], [2, 3, 5, 6, 10, 11], [2, 3, 5, 7, 9, 10], [2, 3, 5, 7, 9, 11], [2, 3, 5, 9, 10, 11], [2, 3, 6, 7, 8, 9], [2, 3, 6, 7, 8, 10], [2, 3, 6, 7, 8, 11], [2, 3, 6, 7, 9, 10], [2, 3, 6, 7, 9, 11], [2, 3, 6, 8, 9, 10], [2, 3, 6, 8, 10, 11], [2, 3, 6, 9, 10, 11], [2, 3, 7, 8, 9, 10], [2, 3, 7, 8, 9, 11], [2, 3, 8, 9, 10, 11], [2, 4, 5, 6, 7, 8], [2, 4, 5, 6, 7, 9], [2, 4, 5, 6, 7, 10], [2, 4, 5, 6, 8, 9], [2, 4, 5, 6, 8, 10], [2, 4, 5, 6, 8, 11], [2, 4, 5, 6, 9, 10], [2, 4, 5, 6, 9, 11], [2, 4, 5, 6, 10, 11], [2, 4, 5, 7, 8, 9], [2, 4, 5, 7, 8, 10], [2, 4, 5, 7, 8, 11], [2, 4, 5, 7, 9, 10], [2, 4, 5, 7, 9, 11], [2, 4, 5, 7, 10, 11], [2, 4, 5, 8, 9, 11], [2, 4, 5, 8, 10, 11], [2, 4, 5, 9, 10, 11], [2, 4, 6, 7, 8, 10], [2, 4, 6, 7, 9, 10], [2, 4, 6, 8, 9, 10], [2, 4, 6, 8, 10, 11], [2, 4, 6, 9, 10, 11], [2, 4, 7, 8, 9, 10], [2, 4, 7, 8, 10, 11], [2, 4, 7, 9, 10, 11], [2, 4, 8, 9, 10, 11], [2, 5, 6, 7, 8, 9], [2, 5, 6, 7, 8, 10], [2, 5, 6, 7, 8, 11], [2, 5, 6, 7, 9, 11], [2, 5, 6, 7, 10, 11], [2, 5, 6, 8, 9, 10], [2, 5, 6, 8, 10, 11], [2, 5, 6, 9, 10, 11], [2, 5, 7, 8, 9, 10], [2, 5, 7, 8, 9, 11], [2, 5, 7, 9, 10, 11], [2, 5, 8, 9, 10, 11], [2, 6, 7, 8, 9, 10], [2, 6, 7, 8, 10, 11], [2, 6, 7, 9, 10, 11], [2, 7, 8, 9, 10, 11], [3, 4, 5, 6, 7, 8], [3, 4, 5, 6, 7, 9], [3, 4, 5, 6, 7, 10], [3, 4, 5, 6, 8, 9], [3, 4, 5, 6, 8, 10], [3, 4, 5, 6, 8, 11], [3, 4, 5, 6, 9, 11], [3, 4, 5, 6, 10, 11], [3, 4, 5, 7, 8, 9], [3, 4, 5, 7, 8, 10], [3, 4, 5, 7, 8, 11], [3, 4, 5, 7, 9, 11], [3, 4, 5, 7, 10, 11], [3, 4, 5, 8, 9, 11], [3, 4, 5, 8, 10, 11], [3, 4, 6, 7, 8, 10], [3, 4, 6, 7, 9, 10], [3, 4, 6, 8, 9, 10], [3, 4, 6, 8, 10, 11], [3, 4, 6, 9, 10, 11], [3, 4, 7, 8, 9, 10], [3, 4, 7, 8, 10, 11], [3, 4, 7, 9, 10, 11], [3, 4, 8, 9, 10, 11], [3, 5, 6, 7, 8, 9], [3, 5, 6, 7, 8, 10], [3, 5, 6, 7, 8, 11], [3, 5, 6, 7, 9, 10], [3, 5, 6, 7, 9, 11], [3, 5, 6, 7, 10, 11], [3, 5, 6, 8, 9, 10], [3, 5, 6, 8, 10, 11], [3, 5, 6, 9, 10, 11], [3, 5, 7, 8, 9, 10], [3, 5, 7, 8, 9, 11], [3, 5, 7, 9, 10, 11], [3, 5, 8, 9, 10, 11], [3, 6, 7, 8, 9, 10], [3, 6, 7, 8, 10, 11], [3, 6, 7, 9, 10, 11], [3, 7, 8, 9, 10, 11], [4, 5, 6, 7, 8, 10], [4, 5, 6, 7, 9, 10], [4, 5, 6, 8, 9, 10], [4, 5, 6, 8, 10, 11], [4, 5, 6, 9, 10, 11], [4, 5, 7, 8, 9, 10], [4, 5, 7, 8, 10, 11], [4, 5, 7, 9, 10, 11], [4, 5, 8, 9, 10, 11], [5, 6, 7, 8, 9, 10], [5, 6, 7, 8, 10, 11], [5, 6, 7, 9, 10, 11], [5, 7, 8, 9, 10, 11]],
N_ELEMENTS=>12,
RANK=>6);
$m->name="N2 matroid";
$m->description="An excluded minor for the dyadic matroids";
return $m;
}
# @category Producing a matroid from scratch
# The complement of the rank-3 whirl in PG(2,3).
# Non binary. Algebraic over all fields.
# @return Matroid
user_function o7_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2], [0, 1, 3], [0, 1, 5], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 3, 4], [0, 3, 5], [0, 3, 6], [0, 4, 5], [0, 5, 6], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 3, 4], [1, 3, 6], [1, 4, 5], [1, 5, 6], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 4, 5], [2, 4, 6], [3, 4, 5], [3, 4, 6], [3, 5, 6], [4, 5, 6]],
N_ELEMENTS=>7,
RANK=>3);
$m->name="O7 matroid";
$m->description="The complement of the rank-3 whirl in PG(2,3)";
return $m;
}
# @category Producing a matroid from scratch
# Configuration of all points in the affine 3-space AG(3,2) or the binary affine cube.
# @return Matroid
user_function ag32_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 6], [0, 1, 5, 7], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 6, 7], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="AG(3,2)";
$m->description="Configuration of all points in the affine 3-space AG(3,2)";
return $m;
}
# @category Producing a matroid from scratch
# The unique relaxation of [[ag32_matroid]].
# @return Matroid
user_function ag32_prime_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 4, 5, 6], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7], [4, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="AG(3,2)'";
$m->description="The unique relaxation of AG(3,2)";
return $m;
}
# @category Producing a matroid from scratch
# The real affine cube.
# @return Matroid
user_function r8_matroid() {
my $m = new Matroid(VECTORS=> [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1],[-1,1,1,1],[1,-1,1,1],[1,1,-1,1],[1,1,1,-1]]);
$m->name="R8 matroid";
$m->description="The real affine cube";
return $m;
}
# @category Producing a matroid from scratch
# A minimal non-representable matroid.
# Non-algebraic.
# @return Matroid
user_function f8_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 4, 5, 6], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7], [4, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="F8 matroid";
$m->description="A minimal non-representable matroid. Not algebraic.";
return $m;
}
# @category Producing a matroid from scratch
# A minimal non-representable matroid.
# An excluded minor for fields that are not of characteristic 2 or have 3 elements. Non-algebraic.
# @return Matroid
user_function q8_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 5, 6], [0, 3, 5, 7], [0, 4, 5, 6], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 5], [1, 2, 3, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 6, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7], [4, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="Q8 matroid";
$m->description="A minimal non-representable matroid. An excluded minor for fields that are not of characteristic 2 or have 3 elements. Non-algebraic.";
return $m;
}
# @category Producing a matroid from scratch
# Representable if and only if the field has characteristic 3.
# An excluded minor for fields that are not of characteristic 2 or 3.
# @return Matroid
user_function t8_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 3, 4], [0, 1, 3, 5], [0, 1, 3, 7], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 5, 6], [0, 1, 5, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 6, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 6, 7], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 5], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 5, 6], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 5, 6], [2, 3, 5, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="T8 matroid";
$m->description="Representable if and only if the field has characteristic 3. An excluded minor for fields that are not of characteristic 2 or 3.";
return $m;
}
# @category Producing a matroid from scratch
# The rank-4 wheel.
# @return Matroid
user_function wheel4_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 6], [0, 1, 2, 7], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 5, 6], [0, 1, 5, 7], [0, 1, 6, 7], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 4, 6], [0, 2, 4, 7], [0, 2, 5, 6], [0, 2, 5, 7], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 5, 6], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 6, 7], [0, 5, 6, 7], [1, 2, 3, 4], [1, 2, 3, 7], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 6, 7], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 5, 7], [1, 3, 6, 7], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 6, 7], [1, 5, 6, 7], [2, 3, 4, 5], [2, 3, 4, 7], [2, 3, 5, 7], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 6, 7], [2, 5, 6, 7], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 5, 6, 7]],
N_ELEMENTS=>8,
RANK=>4);
$m->name="Wheel(4) matroid";
$m->description="The rank-4 wheel";
return $m;
}
# @category Producing a matroid from scratch
# Configuration of the 9 points in the affine plane AG(2,3).
# @return Matroid
user_function ag23_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 1, 5], [0, 1, 6], [0, 1, 7], [0, 2, 3], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 3, 4], [0, 3, 5], [0, 3, 7], [0, 3, 8], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 4, 8], [0, 5, 6], [0, 5, 8], [0, 6, 7], [0, 6, 8], [0, 7, 8], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 8], [1, 3, 4], [1, 3, 6], [1, 3, 7], [1, 3, 8], [1, 4, 5], [1, 4, 7], [1, 4, 8], [1, 5, 6], [1, 5, 7], [1, 5, 8], [1, 6, 7], [1, 6, 8], [1, 7, 8], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 7], [2, 4, 5], [2, 4, 6], [2, 4, 7], [2, 4, 8], [2, 5, 7], [2, 5, 8], [2, 6, 7], [2, 6, 8], [2, 7, 8], [3, 4, 5], [3, 4, 6], [3, 4, 8], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 6, 7], [3, 6, 8], [3, 7, 8], [4, 5, 6], [4, 5, 7], [4, 6, 7], [4, 6, 8], [4, 7, 8], [5, 6, 7], [5, 6, 8], [5, 7, 8]],
N_ELEMENTS=>9,
RANK=>3);
$m->name="AG(2,3)";
$m->description="Configuration of the 9 points in the affine plane AG(2,3)";
return $m;
}
# @category Producing a matroid from scratch
# The rank-3-ternary Dowling Geometry.
# Representable if and only if the field has not characteristic 2.
# @return Matroid
user_function q3_gf3_star_matroid() {
my $m = new Matroid(VECTORS=> transpose(new Matrix([[1,-1,1,1,0,0,1,1,0],[0,0,2,0,0,1,1,1,1],[1,1,1,0,1,1,0,1,0]])));
$m->name="Q3(GF(3)*)";
$m->description="The rank-3-ternary Dowling Geometry";
return $m;
}
# @category Producing a matroid from scratch
# Not representable over any field.
# Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html
# @return Matroid
user_function r9a_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 2, 8], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 3, 8], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 4, 8], [0, 1, 5, 6], [0, 1, 5, 7], [0, 1, 6, 7], [0, 1, 6, 8], [0, 1, 7, 8], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 4, 8], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 5, 8], [0, 2, 6, 7], [0, 2, 6, 8], [0, 2, 7, 8], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 4, 8], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 5, 8], [0, 3, 6, 8], [0, 3, 7, 8], [0, 4, 5, 6], [0, 4, 5, 8], [0, 4, 6, 7], [0, 4, 6, 8], [0, 4, 7, 8], [0, 5, 6, 7], [0, 5, 6, 8], [0, 5, 7, 8], [0, 6, 7, 8], [1, 2, 3, 4], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 4, 8], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 7, 8], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 6, 7], [1, 3, 6, 8], [1, 4, 5, 6], [1, 4, 5, 7], [1, 4, 5, 8], [1, 4, 6, 7], [1, 4, 7, 8], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 7, 8], [1, 6, 7, 8], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4, 8], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5, 8], [2, 3, 6, 7], [2, 3, 6, 8], [2, 3, 7, 8], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5, 8], [2, 4, 6, 7], [2, 4, 6, 8], [2, 5, 6, 7], [2, 5, 6, 8], [2, 5, 7, 8], [2, 6, 7, 8], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 6, 7], [3, 4, 6, 8], [3, 4, 7, 8], [3, 5, 6, 7], [3, 5, 6, 8], [3, 5, 7, 8], [3, 6, 7, 8], [4, 5, 6, 7], [4, 5, 6, 8], [4, 5, 7, 8], [4, 6, 7, 8]],
N_ELEMENTS=>9,
RANK=>4);
$m->name="R9_a";
$m->description="Not representable over any field. Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html";
return $m;
}
# @category Producing a matroid from scratch
# Not representable over any field.
# Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html
# @return Matroid
user_function r9b_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 2, 3], [0, 1, 2, 4], [0, 1, 2, 5], [0, 1, 2, 6], [0, 1, 2, 8], [0, 1, 3, 5], [0, 1, 3, 6], [0, 1, 3, 7], [0, 1, 3, 8], [0, 1, 4, 5], [0, 1, 4, 6], [0, 1, 4, 7], [0, 1, 4, 8], [0, 1, 5, 6], [0, 1, 5, 7], [0, 1, 5, 8], [0, 1, 6, 7], [0, 1, 7, 8], [0, 2, 3, 4], [0, 2, 3, 5], [0, 2, 3, 6], [0, 2, 3, 7], [0, 2, 3, 8], [0, 2, 4, 5], [0, 2, 4, 7], [0, 2, 4, 8], [0, 2, 5, 6], [0, 2, 5, 7], [0, 2, 5, 8], [0, 2, 6, 7], [0, 2, 6, 8], [0, 2, 7, 8], [0, 3, 4, 5], [0, 3, 4, 6], [0, 3, 4, 7], [0, 3, 4, 8], [0, 3, 5, 6], [0, 3, 5, 7], [0, 3, 6, 7], [0, 3, 6, 8], [0, 3, 7, 8], [0, 4, 5, 6], [0, 4, 5, 7], [0, 4, 5, 8], [0, 4, 6, 7], [0, 4, 6, 8], [0, 5, 6, 7], [0, 5, 6, 8], [0, 5, 7, 8], [0, 6, 7, 8], [1, 2, 3, 4], [1, 2, 3, 6], [1, 2, 3, 7], [1, 2, 3, 8], [1, 2, 4, 5], [1, 2, 4, 6], [1, 2, 4, 7], [1, 2, 5, 6], [1, 2, 5, 7], [1, 2, 5, 8], [1, 2, 6, 7], [1, 2, 6, 8], [1, 2, 7, 8], [1, 3, 4, 5], [1, 3, 4, 6], [1, 3, 4, 7], [1, 3, 4, 8], [1, 3, 5, 6], [1, 3, 5, 7], [1, 3, 5, 8], [1, 3, 6, 7], [1, 3, 6, 8], [1, 4, 5, 6], [1, 4, 5, 8], [1, 4, 6, 7], [1, 4, 6, 8], [1, 4, 7, 8], [1, 5, 6, 7], [1, 5, 6, 8], [1, 5, 7, 8], [1, 6, 7, 8], [2, 3, 4, 5], [2, 3, 4, 6], [2, 3, 4, 7], [2, 3, 4, 8], [2, 3, 5, 6], [2, 3, 5, 7], [2, 3, 5, 8], [2, 3, 6, 8], [2, 3, 7, 8], [2, 4, 5, 6], [2, 4, 5, 7], [2, 4, 5, 8], [2, 4, 6, 7], [2, 4, 6, 8], [2, 4, 7, 8], [2, 5, 6, 7], [2, 5, 6, 8], [2, 5, 7, 8], [2, 6, 7, 8], [3, 4, 5, 6], [3, 4, 5, 7], [3, 4, 5, 8], [3, 4, 6, 7], [3, 4, 7, 8], [3, 5, 6, 7], [3, 5, 6, 8], [3, 5, 7, 8], [3, 6, 7, 8], [4, 5, 6, 7], [4, 5, 6, 8], [4, 5, 7, 8], [4, 6, 7, 8]],
N_ELEMENTS=>9,
RANK=>4);
$m->name="R9_b";
$m->description="Not representable over any field. Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html";
return $m;
}
# @category Producing a matroid from scratch
# Configuration of the 13 points in the projective plane PG(2,3).
# @return Matroid
user_function pg23_matroid() {
my $m = new Matroid(BASES=>[[0, 1, 3], [0, 1, 4], [0, 1, 5], [0, 1, 6], [0, 1, 7], [0, 1, 8], [0, 1, 9], [0, 1, 10], [0, 1, 11], [0, 2, 3], [0, 2, 4], [0, 2, 5], [0, 2, 6], [0, 2, 7], [0, 2, 8], [0, 2, 9], [0, 2, 10], [0, 2, 11], [0, 3, 4], [0, 3, 5], [0, 3, 7], [0, 3, 8], [0, 3, 10], [0, 3, 11], [0, 3, 12], [0, 4, 5], [0, 4, 6], [0, 4, 7], [0, 4, 9], [0, 4, 11], [0, 4, 12], [0, 5, 6], [0, 5, 8], [0, 5, 9], [0, 5, 10], [0, 5, 12], [0, 6, 7], [0, 6, 8], [0, 6, 10], [0, 6, 11], [0, 6, 12], [0, 7, 8], [0, 7, 9], [0, 7, 10], [0, 7, 12], [0, 8, 9], [0, 8, 11], [0, 8, 12], [0, 9, 10], [0, 9, 11], [0, 9, 12], [0, 10, 11], [0, 10, 12], [0, 11, 12], [1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 7], [1, 2, 8], [1, 2, 9], [1, 2, 10], [1, 2, 11], [1, 3, 4], [1, 3, 5], [1, 3, 6], [1, 3, 7], [1, 3, 9], [1, 3, 10], [1, 3, 12], [1, 4, 5], [1, 4, 6], [1, 4, 8], [1, 4, 10], [1, 4, 11], [1, 4, 12], [1, 5, 7], [1, 5, 8], [1, 5, 9], [1, 5, 11], [1, 5, 12], [1, 6, 7], [1, 6, 8], [1, 6, 9], [1, 6, 11], [1, 6, 12], [1, 7, 8], [1, 7, 10], [1, 7, 11], [1, 7, 12], [1, 8, 9], [1, 8, 10], [1, 8, 12], [1, 9, 10], [1, 9, 11], [1, 9, 12], [1, 10, 11], [1, 10, 12], [1, 11, 12], [2, 3, 4], [2, 3, 5], [2, 3, 6], [2, 3, 8], [2, 3, 9], [2, 3, 11], [2, 3, 12], [2, 4, 5], [2, 4, 7], [2, 4, 8], [2, 4, 9], [2, 4, 10], [2, 4, 12], [2, 5, 6], [2, 5, 7], [2, 5, 10], [2, 5, 11], [2, 5, 12], [2, 6, 7], [2, 6, 8], [2, 6, 9], [2, 6, 10], [2, 6, 12], [2, 7, 8], [2, 7, 9], [2, 7, 11], [2, 7, 12], [2, 8, 10], [2, 8, 11], [2, 8, 12], [2, 9, 10], [2, 9, 11], [2, 9, 12], [2, 10, 11], [2, 10, 12], [2, 11, 12], [3, 4, 6], [3, 4, 7], [3, 4, 8], [3, 4, 9], [3, 4, 10], [3, 4, 11], [3, 5, 6], [3, 5, 7], [3, 5, 8], [3, 5, 9], [3, 5, 10], [3, 5, 11], [3, 6, 7], [3, 6, 8], [3, 6, 10], [3, 6, 11], [3, 6, 12], [3, 7, 8], [3, 7, 9], [3, 7, 11], [3, 7, 12], [3, 8, 9], [3, 8, 10], [3, 8, 12], [3, 9, 10], [3, 9, 11], [3, 9, 12], [3, 10, 11], [3, 10, 12], [3, 11, 12], [4, 5, 6], [4, 5, 7], [4, 5, 8], [4, 5, 9], [4, 5, 10], [4, 5, 11], [4, 6, 7], [4, 6, 8], [4, 6, 9], [4, 6, 10], [4, 6, 12], [4, 7, 8], [4, 7, 10], [4, 7, 11], [4, 7, 12], [4, 8, 9], [4, 8, 11], [4, 8, 12], [4, 9, 10], [4, 9, 11], [4, 9, 12], [4, 10, 11], [4, 10, 12], [4, 11, 12], [5, 6, 7], [5, 6, 8], [5, 6, 9], [5, 6, 11], [5, 6, 12], [5, 7, 8], [5, 7, 9], [5, 7, 10], [5, 7, 12], [5, 8, 10], [5, 8, 11], [5, 8, 12], [5, 9, 10], [5, 9, 11], [5, 9, 12], [5, 10, 11], [5, 10, 12], [5, 11, 12], [6, 7, 9], [6, 7, 10], [6, 7, 11], [6, 8, 9], [6, 8, 10], [6, 8, 11], [6, 9, 10], [6, 9, 11], [6, 9, 12], [6, 10, 11], [6, 10, 12], [6, 11, 12], [7, 8, 9], [7, 8, 10], [7, 8, 11], [7, 9, 10], [7, 9, 11], [7, 9, 12], [7, 10, 11], [7, 10, 12], [7, 11, 12], [8, 9, 10], [8, 9, 11], [8, 9, 12], [8, 10, 11], [8, 10, 12], [8, 11, 12]],
N_ELEMENTS=>13,
RANK=>3);
$m->name="PG(2,3)";
$m->description="Configuration of the 13 points in the projective plane PG(2,3)";
return $m;
}
# @category Producing a matroid from scratch
# Representable if and only if the field has not characteristic 2.
# The labeling of the elements is similar to those of the Fano matroid.
# @return Matroid
user_function non_fano_matroid() {
my $m = new Matroid(VECTORS=>[[1,1,1],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]]);
$m->name="Non-Fano matroid";
$m->description="The embedding into the reals of the seven points that define the Fano matroid";
return $m;
}
# @category Producing a matroid from scratch
# Creates the Fano plane matroid of rank 3 with 7 elements.
# Representable over a field of characteristic two.
# The labeling of the elements corresponds to the binary encoding of 1,2,...,7 mod 7.
# @return Matroid
user_function fano_matroid() {
my $m = new Matroid(BINARY_VECTORS=>[[1,1,1],[0,0,1],[0,1,0],[0,1,1],[1,0,0],[1,0,1],[1,1,0]],
BASES=>[[0,1,2],[0,1,3],[0,1,4],[0,1,5],[0,2,3],[0,2,4],[0,2,6],[0,3,5],[0,3,6],[0,4,5],[0,4,6],[0,5,6],[1,2,4],[1,2,5],[1,2,6],[1,3,4],[1,3,5],[1,3,6],[1,4,6],[1,5,6],[2,3,4],[2,3,5],[2,3,6],[2,4,5],[2,5,6],[3,4,5],[3,4,6],[4,5,6]],
N_ELEMENTS=>7,
RANK=>3);
$m->name="Fano matroid";
$m->description="The projective plane PG(2,2)";
return $m;
}
# @category Producing a matroid from scratch
# This function can be used to ask for various special matroids, most of which occur in Oxley's book
# [Oxley: Matroid theory (2nd ed.)]. There is a separate function for each of these matroids.
# @param String s The name of the matroid
# @value s 'ag23' Configuration of the 9 points in the affine plane AG(2,3).
# @value s 'ag32' Configuration of all points in the affine 3-space AG(3,2) or the binary affine cube.
# @value s 'ag32_prime' The unique relaxation of [[ag32_matroid]].
# @value s 'fano' The Fano matroid
# @value s 'f8' A minimal non-representable matroid. Also non-algebraic.
# @value s 'j' An excluded minor for some properties (see [Oxley:matroid theory (2nd ed.) page 650]). Not binary. Algebraic over all fields.
# @value s 'l8' The 4-point planes are the six faces of the cube an the two twisted plannes. Identically self-dual. Representable over all field with more then 4 elements and algebraic over all fields.
# @value s 'n1' An excluded minor for the dyadic matroids (see [Oxley:matroid theory (2nd ed.) page 558]).
# @value s 'n2' An excluded minor for the dyadic matroids (see [Oxley:matroid theory (2nd ed.) page 558]).
# @value s 'o7' The complement of the rank-3 whirl in PG(2,3). Non binary. Algebraic over all fields.
# @value s 'p7' The only other ternary 3-spike apart from the non-Fano matroid. Non binary. Algebraic over all fields.
# @value s 'p8' The repesentation over the reals is obtained from a 3-cube where one face is rotated by 45°. Non-representable if and only if the characeristic of the field is 2. Algebraic over all fields.
# @value s 'non_p8' Obtained from [[p8_matroid]] by relaxing its only pair of disjoint circuit-hyperplanes.
# @value s 'pappus' The Pappus matroid
# @value s 'non_pappus' The non-Pappus matroid
# @value s 'pg23' Configuration of the 13 points in the projective plane PG(2,3).
# @value s 'q3_gf3_star' The rank-3-ternary Dowling Geometry. Representable if and only if the field has not characteristic 2.
# @value s 'q8' A minimal non-representable matroid. An excluded minor for fields that are not of characteristic 2 or have 3 elements. Non-algebraic.
# @value s 'r8' The real affine cube.
# @value s 'r9a' Not representable over any field. Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html
# @value s 'r9b' Not representable over any field. Taken from http://doc.sagemath.org/html/en/reference/matroids/sage/matroids/catalog.html
# @value s 'r10' A regular matroid that's not graphical nor cographical. Algebraic over all fields.
# @value s 't8' Representable if and only if the field has characteristic 3. An excluded minor for fields that are not of characteristic 2 or 3.
# @value s 'vamos' The Vamos matroid
# @value s 'non_vamos' The non-Vamos matroid
# @value s 'wheel4' The 4-wheel
# @value s 'non_fano' The non-Fano matroid
user_function special_matroid {
my $s = shift;
return eval($s."_matroid()");
}
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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