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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 PURPSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
# This contains rules for computing/converting properties between a matroid and its dual.
object Matroid {
# @category Duality
# The dual matroid.
property DUAL : self : twin;
rule DUAL.N_ELEMENTS = N_ELEMENTS;
rule DUAL.LABELS = LABELS;
rule DUAL.RANK : N_ELEMENTS, RANK {
$this->DUAL->RANK = $this->N_ELEMENTS - $this->RANK;
}
weight 0.1;
rule DUAL.BASES : BASES, N_ELEMENTS {
$this->DUAL->BASES = dual_bases_from_bases($this->N_ELEMENTS, $this->BASES);
}
weight 1.10;
rule DUAL.NON_BASES : NON_BASES, N_ELEMENTS {
$this->DUAL->NON_BASES = dual_bases_from_bases($this->N_ELEMENTS, $this->NON_BASES);
}
weight 1.10;
rule DUAL.CIRCUITS : BASES, N_ELEMENTS {
$this->DUAL->CIRCUITS = dual_circuits_from_bases($this->N_ELEMENTS, $this->BASES);
}
weight 4.10;
rule BASES : DUAL.CIRCUITS, N_ELEMENTS {
$this->BASES = bases_from_dual_circuits($this->N_ELEMENTS, $this->DUAL->CIRCUITS);
}
weight 4.10;
rule BASES : DUAL.CIRCUITS, RANK, N_ELEMENTS {
$this->BASES = bases_from_dual_circuits_and_rank($this->N_ELEMENTS, $this->RANK, $this->DUAL->CIRCUITS);
}
weight 3.10;
rule DUAL.VECTORS : VECTORS {
$this->DUAL->VECTORS = transpose(null_space(transpose($this->VECTORS)));
}
weight 3.10;
precondition : RANK, N_ELEMENTS {
$this->RANK < $this->N_ELEMENTS;
}
rule DUAL.VECTORS : VECTORS, N_ELEMENTS {
$this->DUAL->VECTORS = new Matrix<Rational>($this->N_ELEMENTS, $this->VECTORS->cols != 0);
}
weight 0.10;
precondition : RANK, N_ELEMENTS {
$this->RANK == $this->N_ELEMENTS;
}
rule MATROID_HYPERPLANES : DUAL.CIRCUITS, N_ELEMENTS {
my $total = sequence(0,$this->N_ELEMENTS);
$this->MATROID_HYPERPLANES = [ map { $total - $_} @{$this->DUAL->CIRCUITS}];
}
weight 1.10;
rule DUAL.CIRCUITS : MATROID_HYPERPLANES, N_ELEMENTS {
my $total = sequence(0,$this->N_ELEMENTS);
$this->DUAL->CIRCUITS = [ map { $total - $_} @{$this->MATROID_HYPERPLANES}];
}
weight 1.10;
rule SPARSE_PAVING : PAVING, DUAL.PAVING {
$this->SPARSE_PAVING = $this->PAVING && $this->DUAL->PAVING;
}
weight 0.1;
rule IDENTICALLY_SELF_DUAL : CIRCUITS, DUAL.CIRCUITS {
$this->IDENTICALLY_SELF_DUAL = defined(find_permutation($this->CIRCUITS, $this->DUAL->CIRCUITS));
}
weight 2.10;
precondition : N_ELEMENTS, RANK {
2*$this->RANK == $this->N_ELEMENTS;
}
rule SELF_DUAL : CIRCUITS, DUAL.CIRCUITS {
$this->SELF_DUAL = defined(find_row_col_permutation(new IncidenceMatrix($this->CIRCUITS), new IncidenceMatrix($this->DUAL->CIRCUITS)));
}
weight 5.10;
precondition : N_ELEMENTS, RANK {
2*$this->RANK == $this->N_ELEMENTS;
}
rule CONNECTED_COMPONENTS : DUAL.CIRCUITS, N_ELEMENTS{
$this->CONNECTED_COMPONENTS = connected_components_from_circuits($this->DUAL->CIRCUITS, $this->N_ELEMENTS);
}
weight 1.10;
rule SELF_DUAL, IDENTICALLY_SELF_DUAL : {
$this->SELF_DUAL = 0;
$this->IDENTICALLY_SELF_DUAL = 0;
}
weight 0.1;
precondition : N_ELEMENTS, RANK {
2*$this->RANK != $this->N_ELEMENTS;
}
rule SELF_DUAL : IDENTICALLY_SELF_DUAL {
$this->SELF_DUAL = 1;
}
weight 0.1;
precondition : IDENTICALLY_SELF_DUAL;
rule IDENTICALLY_SELF_DUAL : BASES, DUAL.BASES {
$this->IDENTICALLY_SELF_DUAL = defined(find_permutation($this->BASES, $this->DUAL->BASES));
}
weight 2.10;
precondition : N_ELEMENTS, RANK {
2 * $this->RANK == $this->N_ELEMENTS;
}
rule SELF_DUAL : BASES, DUAL.BASES {
$this->SELF_DUAL = defined(find_row_col_permutation(new IncidenceMatrix($this->BASES), new IncidenceMatrix($this->DUAL->BASES)));
}
weight 5.10;
precondition : N_ELEMENTS, RANK {
2*$this->RANK == $this->N_ELEMENTS;
}
rule SPLIT : {
$this->SPLIT=1;
}
precondition : PAVING || DUAL.PAVING;
weight 0.10;
# @category Advanced properties
# Whether the dual of the matroid is transversal,
# i.e. same as [[DUAL.TRANSVERSAL]]
user_method COTRANSVERSAL {
return $_[0]->DUAL->TRANSVERSAL;
}
# @category Advanced properties
# Alias for [[COTRANSVERSAL]]
user_method STRICT_GAMMOID {
return $_[0]->COTRANSVERSAL();
}
}
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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