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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, Ben Burton *
* For further details contact Ben Burton (bab@debian.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 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* 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. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program. If not, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
/*! \file enumerate/hilbertcd.h
* \brief Provides a modified Contejean-Devie algorithm for Hilbert basis
* enumeration.
*/
#ifndef __REGINA_HILBERTCD_H
#ifndef __DOXYGEN
#define __REGINA_HILBERTCD_H
#endif
#include "regina-core.h"
#include "maths/matrix.h"
#include "maths/vector.h"
#include <iterator>
#include <list>
#include <vector>
namespace regina {
class ValidityConstraints;
/**
* Implements a modified Contejean-Devie algorithm for enumerating Hilbert
* bases. This is based on the stack-based algorithm described in
* "An efficient incremental algorithm for solving systems of linear
* Diophantine equations", Inform. and Comput. 113 (1994), 143-172,
* and has been modified to allow for additional constraints (such as
* the quadrilateral constraints from normal surface theory).
*
* All routines of interest within this class are static; no object of
* this class should ever be created.
*
* \warning For normal surface theory, the Contejean-Devie algorithm is
* extremely slow, even when modified to incorporate admissibility
* constraints. Consider using the much faster HilbertPrimal or
* HilbertDual instead.
*
* \ingroup enumerate
*/
class HilbertCD {
public:
/**
* Determines the Hilbert basis that generates all integer
* points in the intersection of the <i>n</i>-dimensional
* non-negative orthant with some linear subspace.
* The resulting basis elements will be of the class \a RayClass,
* and will be passed into the given action function one at a time.
*
* The non-negative orthant is an <i>n</i>-dimensional cone with
* its vertex at the origin. The extremal rays of this cone are
* the \a n non-negative coordinate axes. This cone also has \a n
* facets, where the <i>i</i>th facet is the non-negative
* orthant of the plane perpendicular to the <i>i</i>th coordinate
* axis.
*
* This routine takes a linear subspace, defined by the
* intersection of a set of hyperplanes through the origin (this
* subspace is described as a matrix, with each row giving the
* equation for one hyperplane).
*
* The purpose of this routine is to compute the Hilbert basis of
* the set of all integer points in the intersection of the
* original cone with this linear subspace. The resulting list
* of basis vectors will contain no duplicates or redundancies.
*
* The parameter \a constraints may contain a set of validity
* constraints, in which case this routine will only return _valid_
* basis elements. Each validity constraint is of the form "at
* most one of these coordinates may be non-zero"; see the
* ValidityConstraints class for details. These contraints have the
* important property that, although validity is not preserved under
* addition, _invalidity_ is.
*
* For each of the resulting basis elements, this routine will call
* \a action (which must be a function or some other callable object).
* This action should return \c void, and must take exactly one
* argument, which will be the basis element stored using \a RayClass.
* The argument will be passed as an rvalue; a typical \a action
* would take it as an rvalue reference (RayClass&&) and move its
* contents into some other more permanent storage.
*
* \pre The template argument RayClass is derived from (or equal to)
* Vector<T>, where \a T is one of Regina's arbitrary-precision
* integer classes (Integer or LargeInteger).
*
* \warning For normal surface theory, the Contejean-Devie algorithm is
* extremely slow, even when modified to incorporate admissibility
* constraints. Consider using the much faster HilbertPrimal or
* HilbertDual instead.
*
* \python There are two versions of this function available
* in Python. The first version is the same as the C++ function;
* here you must pass \a action, which may be a pure Python function.
* The second form does not have an \a action argument; instead you
* call `enumerate(subspace, constraints)`,
* and it returns a Python list containing all Hilbert basis elements.
* In both versions, the argument \a RayClass is fixed as VectorInt.
*
* \param action a function (or other callable object) that will be
* called for each basis element. This function must take a single
* argument, which will be passed as an rvalue of type RayClass.
* \param subspace a matrix defining the linear subspace to intersect
* with the given cone. Each row of this matrix is the equation
* for one of the hyperplanes whose intersection forms this linear
* subspace. The number of columns in this matrix must be the
* dimension of the overall space in which we are working.
* \param constraints a set of validity constraints as described above,
* or ValidityConstraints::none if none should be imposed.
*/
template <class RayClass, typename Action>
static void enumerate(Action&& action,
const MatrixInt& subspace, const ValidityConstraints& constraints);
// Mark this class as non-constructible.
HilbertCD() = delete;
private:
/**
* A helper class for Hilbert basis enumeration, describing a
* single candidate basis vector.
*
* The coordinates of the vector are inherited through the
* Vector superclass.
*
* The \a BitmaskType template argument is used to store one bit
* per coordinate, which is \c false if the coordinate is zero
* or \c true if the coordinate is non-zero.
*
* \tparam IntegerType the integer type used to store and manipulate
* vectors; this must be one of Regina's own integer types.
*
* \tparam BitmaskType the bitmask type used to indicate zero/non-zero
* coordinates; this must be one of Regina's own bitmask types, such as
* Bitmask, Bitmask1 or Bitmask2.
*/
template <class IntegerType, class BitmaskType>
struct VecSpec : public Vector<IntegerType> {
BitmaskType mask_;
/**< A bitmask indicating which coordinates are zero
(\c false) and which are non-zero (\c true). */
/**
* Creates the zero vector.
*
* \param dim the total dimension of the space (and
* therefore the toatl length of this vector).
*/
inline VecSpec(size_t dim);
/**
* Creates a new clone of the given vector.
*/
VecSpec(const VecSpec&) = default;
/**
* Sets this to be a clone of the given vector.
*/
VecSpec& operator = (const VecSpec&) = default;
};
/**
* Identical to the public routine enumerate(),
* except that there is an extra template parameter \a BitmaskType.
* This describes what type should be used for bitmasks that
* assign flags to individual coordinate positions.
*
* All arguments to this function are identical to those for the
* public routine enumerate().
*
* \pre The bitmask type is one of Regina's bitmask types, such
* as Bitmask, Bitmask1 or Bitmask2.
* \pre The type \a BitmaskType can handle at least \a n bits,
* where \a n is the dimension of the Euclidean space (i.e., the
* number of columns in \a subspace).
*/
template <class RayClass, class BitmaskType, typename Action>
static void enumerateUsingBitmask(Action&& action,
const MatrixInt& subspace, const ValidityConstraints& constraints);
};
// Inline functions for HilbertCD::VecSpec
template <class IntegerType, class BitmaskType>
inline HilbertCD::VecSpec<IntegerType, BitmaskType>::VecSpec(size_t dim) :
Vector<IntegerType>(dim), mask_(dim) {
// All vector elements are initialised to zero thanks to the default
// constructors in Regina's integer classes.
}
} // namespace regina
// Template definitions
#include "enumerate/hilbertcd-impl.h"
#endif
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