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/**************************************************************************
* *
* Regina  A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 19992016, 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, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 021101301, USA. *
* *
**************************************************************************/
/*! \file split/signature.h
* \brief Deals with signatures of splitting surfaces.
*/
#ifndef __SIGNATURE_H
#ifndef __DOXYGEN
#define __SIGNATURE_H
#endif
#include "reginacore.h"
#include "output.h"
#include "triangulation/forward.h"
#include <boost/noncopyable.hpp>
namespace regina {
class SigCensus;
class SigPartialIsomorphism;
/**
* \addtogroup split Splitting Surfaces
* Splitting surfaces in triangulations.
* @{
*/
/**
* Represents a signature of a splitting surface in a closed 3manifold
* triangulation.
*
* A <i>splitting surface</i> is (for these purposes) a compact normal surface
* consisting of precisely one quad per tetrahedron and no other normal
* (or almost normal) discs.
*
* A <i>signature</i> of order <i>n</i> is a string consisting of 2<i>n</i>
* letters arranged into cycles, where <i>n</i> is the number of quads in the
* splitting surface. From a signature, the corresponding splitting
* surface and then the entire 3manifold triangulation can be recreated.
*
* A signature of order <i>n</i> uses the first <i>n</i> letters of the
* alphabet, each precisely twice. Case is important; the meaning of a
* letter changes according to whether it appears in uppercase or
* lowercase.
*
* Each letter represents an individual quadrilateral (the two
* occurrences of the letter representing the quadrilateral's two sides).
* Each cycle represents a chain of quadrilaterals joined together in the
* splitting surface. The case of a letter represents in which direction
* a quadrilateral is traversed within a cycle.
*
* Cycles are arranged into <i>cycle groups</i>, where a cycle group
* consists of a series of consecutive cycles all of the same length.
*
* An example of a signature is <tt>(abc)(a)(b)(c)</tt>. This signature
* is of order 3 and contains two cycle groups, the first being
* <tt>(abc)</tt> and the second being <tt>(a)(b)(c)</tt>.
*
* A signature cannot represent a splitting surface with more than 26
* quadrilaterals.
*
* For further details on splitting surfaces and their signatures, consult
* <i>Minimal triangulations and normal surfaces</i>, Burton, PhD thesis,
* available from the Regina website.
*/
class REGINA_API Signature :
public ShortOutput<Signature>,
public boost::noncopyable {
private:
unsigned order_;
/**< The number of quads in this splitting surface. */
unsigned* label;
/**< The 2<i>n</i> letters making up this signature from
start to finish; letters A,B,... are represented by
integers 0,1,... . */
bool* labelInv;
/**< <tt>labelInv[i]</tt> stores the case of the letter
corresponding to <tt>label[i]</tt>. In this case
\c false represents lowercase and \c true represents
uppercase. */
unsigned nCycles;
/**< The number of cycles in this signature. */
unsigned* cycleStart;
/**< The starting position of each cycle; an additional
element is appended to the end of this array storing
the length of the entire signature. */
unsigned nCycleGroups;
/**< The number of cycle groups in this signature. */
unsigned* cycleGroupStart;
/**< The starting cycle for each cycle group; an additional
element is appended to the end of this array storing
the total number of cycles. */
public:
/**
* Creates a new signature that is a clone of the given signature.
*
* @param sig the signature to clone.
*/
Signature(const Signature& sig);
/**
* Destroys this signature.
*/
~Signature();
/**
* Returns the order of this signature. The order is the number
* of quads in the corresponding splitting surface.
*
* @return the order of this signature.
*/
unsigned order() const;
/**
* Parses the given signature string.
*
* Punctuation characters in the given string will be interpreted
* as separating cycles. All whitespace will be ignored.
*
* Examples of valid signatures are <tt>"(ab)(bC)(Ca)"</tt> and
* <tt>"AAbbcC"</tt>. See the class notes for further details
* on what constitutes a valid signature.
*
* \pre The given string contains at least one letter.
*
* @param sig a string representation of a splitting surface
* signature.
* @return a corresponding newly created signature, or 0 if the
* given string was invalid.
*/
static Signature* parse(const std::string& sig);
/**
* Returns a newly created 3manifold triangulation corresponding to
* this splitting surface signature.
*
* @return the corresponding triangulation.
*/
Triangulation<3>* triangulate() const;
/**
* Lexicographically compares the results of transformations upon
* two given cycles. Even if transformations are specified, the
* underlying signatures will not be changed.
*
* This comparison is \e not casesensitive.
*
* \pre The two specified cycles have the same length.
*
* \ifacespython Not present.
*
* @param sig1 the signature containing the first cycle to examine.
* @param cycle1 specifies which cycle to examine in signature
* \a sig1. This must be less than the total number of cycles in
* \a sig1.
* @param start1 allows the first cycle to be transformed by
* rotation; this parameter is the new starting position of the first
* cycle. This must be between 0 and
* <tt>sig1.getCycleLength(cycle1)1</tt> inclusive.
* @param dir1 allows the first cycle to be transformed by
* reversal; this parameter must be positive to use an unreversed
* cycle or negative to use a reversed cycle.
* @param relabel1 allows the first cycle to be transformed by
* relabelling; this parameter must be an array of size at least
* <tt>sig1.order()</tt> mapping old labels 0,1,...
* (representing letters A,B,...) to new labels (which must also be
* 0,1,..., possibly in a different order). This parameter may
* be 0 if no relabelling is to be used.
*
* @param sig2 the signature containing the second cycle to examine.
* @param cycle2 specifies which cycle to examine in signature
* \a sig2. This must be less than the total number of cycles in
* \a sig2.
* @param start2 allows the second cycle to be transformed by
* rotation; this parameter is the new starting position of the
* second cycle. This must be between 0 and
* <tt>sig2.getCycleLength(cycle2)1</tt> inclusive.
* @param dir2 allows the second cycle to be transformed by
* reversal; this parameter must be positive to use an unreversed
* cycle or negative to use a reversed cycle.
* @param relabel2 allows the second cycle to be transformed by
* relabelling; this parameter must be an array of size at least
* <tt>sig2.order()</tt> mapping old labels 0,1,...
* (representing letters A,B,...) to new labels (which must also be
* 0,1,..., possibly in a different order). This parameter may
* be 0 if no relabelling is to be used.
*
* @return 1, 1 or 0 if the transformed first cycle is
* lexicographically less than, greater than or equal to the
* transformed second cycle respectively.
*/
static int cycleCmp(const Signature& sig1, unsigned cycle1,
unsigned start1, int dir1, unsigned* relabel1,
const Signature& sig2, unsigned cycle2, unsigned start2,
int dir2, unsigned* relabel2);
/**
* Writes a string representation of this signature to the given
* output stream.
*
* \ifacespython The parameter \a out does not exist; standard
* output will be used.
*
* @param out the output stream to which to write.
* @param cycleOpen the text to write at the beginning of a cycle
* (such as <tt>"("</tt>).
* @param cycleClose the text to write at the end of a cycle
* (such as <tt>")"</tt>).
* @param cycleJoin the text to write between two cycles.
*/
void writeCycles(std::ostream& out, const std::string& cycleOpen,
const std::string& cycleClose, const std::string& cycleJoin) const;
/**
* Writes a short text representation of this object to the
* given output stream.
*
* \ifacespython Not present.
*
* @param out the output stream to which to write.
*/
void writeTextShort(std::ostream& out) const;
private:
/**
* Creates a new completely uninitialised signature.
*
* \warning The internal arrays \e must be created before this
* signature is destroyed!
*/
Signature();
/**
* Creates a new signature of the given order. All internal
* arrays will be created but not initialised.
*
* The first elements of the \a cycleStart and \a cycleGroupStart
* arrays will be set to 0.
*
* The newly created signature can be used as a partial
* signature containing no cycles.
*
* @param newOrder the order of the new signature; this must be
* strictly positive.
*/
Signature(unsigned newOrder);
friend class regina::SigPartialIsomorphism;
friend class regina::SigCensus;
};
/**
* Deprecated typedef for backward compatibility. This typedef will
* be removed in a future release of Regina.
*
* \deprecated The class NSignature has now been renamed to Signature.
*/
REGINA_DEPRECATED typedef Signature NSignature;
/*@}*/
// Inline functions for Signature
inline Signature::Signature() {
}
inline Signature::Signature(unsigned newOrder) : order_(newOrder),
label(new unsigned[2 * newOrder]), labelInv(new bool[2 * newOrder]),
nCycles(0), cycleStart(new unsigned[2 * newOrder + 1]),
nCycleGroups(0), cycleGroupStart(new unsigned[2 * newOrder + 1]) {
// Insert sentinels.
cycleStart[0] = cycleGroupStart[0] = 0;
}
inline Signature::~Signature() {
delete[] label;
delete[] labelInv;
delete[] cycleStart;
delete[] cycleGroupStart;
}
inline unsigned Signature::order() const {
return order_;
}
inline void Signature::writeTextShort(std::ostream& out) const {
writeCycles(out, "(", ")", "");
}
} // namespace regina
#endif
