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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.
#-------------------------------------------------------------------------------
# FIXME
# here we need a configure block that checks
# - whether the ntl extension is installed
# - can read the ntl path and appropriate includes from it
# (see ticket #504)
#
# - the current version uses CallPolymakeFunction to access integer_kernel
# and fails with an error if this is not found
# CONFIGURE { }
object NormalToricVariety {
# the methods for the following three rules are implemented in the file class_group.cc
rule RATIONAL_DIVISOR_CLASS_GROUP.PROJECTION, RATIONAL_DIVISOR_CLASS_GROUP.LIFTING : RAYS {
my $class_group_data = rational_divisor_class_group($this);
$this->RATIONAL_DIVISOR_CLASS_GROUP->PROJECTION = $class_group_data->first;
$this->RATIONAL_DIVISOR_CLASS_GROUP->LIFTING = $class_group_data->second;
}
precondition : COMPLETE;
rule EFFECTIVE_CONE.INPUT_RAYS : RATIONAL_DIVISOR_CLASS_GROUP.PROJECTION {
$this->EFFECTIVE_CONE->INPUT_RAYS = $this->RATIONAL_DIVISOR_CLASS_GROUP->PROJECTION;
}
precondition : COMPLETE;
declare $a, $b;
# Computes the nef cone of the toric variety corresponding to the fan ''F''
# given in the input also known as the (closure of the) Kaehler cone dual to
# the Mori cone in the space of the rational divisor class group
#
# algorithm:
# Take the matrix 'proj' of the projection to the rational divisor class
# group. Let C be the cone spanned by the columns of 'proj' with index not
# in the cone a divisor is nef if it lies in all cones C_i
#
# Probably not the most efficient algorithm: involves several ch
# computations maybe better approach:
# Use that a divisor ''D'' is nef if and only if its intersection with all
# T-invariant curves is non-negative i.e. in the polytope ''P_D'' all edge
# lengths of edges defined by codim(1)-faces of ''F'' must be non-negative
rule NEF_CONE.INEQUALITIES, NEF_CONE.EQUATIONS : MAXIMAL_CONES, RATIONAL_DIVISOR_CLASS_GROUP.PROJECTION {
$this->NEF_CONE = List::Util::reduce {
polytope::intersection($a,$b)
} map {
new polytope::Cone(INPUT_RAYS=>$this->RATIONAL_DIVISOR_CLASS_GROUP->PROJECTION->minor(~$_,All))
} @{$this->MAXIMAL_CONES}
}
precondition : COMPLETE;
precondition : POINTED;
precondition : FAN_AMBIENT_DIM {$this->FAN_AMBIENT_DIM > 0};
# dualize a cone
rule MORI_CONE.RAYS, MORI_CONE.LINEALITY_SPACE : NEF_CONE.FACETS, NEF_CONE.LINEAR_SPAN {
$this->MORI_CONE->RAYS = $this->NEF_CONE->FACETS;
$this->MORI_CONE->LINEALITY_SPACE = $this->NEF_CONE->LINEAR_SPAN;
}
precondition : COMPLETE;
}
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