Regina Calculation Engine
Classes | Typedefs | Functions
Splitting Surfaces

Splitting surfaces in triangulations. More...

Classes

class  regina::SigCensus
 A utility class used by formSigCensus(). More...
 
class  regina::SigPartialIsomorphism
 Represents a partial isomorphism between two splitting surface signatures. More...
 
class  regina::Signature
 Represents a signature of a splitting surface in a closed 3-manifold triangulation. More...
 

Typedefs

typedef std::list< SigPartialIsomorphism * > regina::SigIsoList
 A list of partial isomorphisms on splitting surface signatures. More...
 
typedef void(* regina::UseSignature) (const Signature &, const SigIsoList &, void *)
 A routine used to do arbitrary processing upon a splitting surface signature and its automorphisms. More...
 
typedef SigCensus regina::NSigCensus
 Deprecated typedef for backward compatibility. More...
 
typedef SigIsoList regina::NSigIsoList
 Deprecated typedef for backward compatibility. More...
 
typedef SigPartialIsomorphism regina::NSigPartialIsomorphism
 Deprecated typedef for backward compatibility. More...
 
typedef Signature regina::NSignature
 Deprecated typedef for backward compatibility. More...
 

Functions

unsigned long regina::formSigCensus (unsigned order, UseSignature use, void *useArgs=0)
 Forms a census of all splitting surface signatures of the given order. More...
 

Detailed Description

Splitting surfaces in triangulations.

Typedef Documentation

◆ NSigCensus

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
The class NSigCensus has now been renamed to SigCensus.

◆ NSigIsoList

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
The typedef NSigIsoList has now been renamed to SigIsoList.

◆ NSignature

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.

◆ NSigPartialIsomorphism

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
The class NSigPartialIsomorphism has now been renamed to SigPartialIsomorphism.

◆ SigIsoList

A list of partial isomorphisms on splitting surface signatures.

◆ UseSignature

typedef void(* regina::UseSignature) (const Signature &, const SigIsoList &, void *)

A routine used to do arbitrary processing upon a splitting surface signature and its automorphisms.

Such routines are used to process signatures found when running a signature census.

The first parameter passed should be a splitting surface signature. The second parameter should be a list of all automorphisms of this signature. The third parameter may contain arbitrary data as passed to formSigCensus().

Function Documentation

◆ formSigCensus()

unsigned long regina::formSigCensus ( unsigned  order,
UseSignature  use,
void *  useArgs = 0 
)

Forms a census of all splitting surface signatures of the given order.

The order of a signature is the number of quads in the corresponding splitting surface.

Each signature will be produced precisely once up to equivalence. Signatures are considered equivalent if they are related by some combination of:

  • relabelling symbols;
  • rotating an individual cycle;
  • inverting an individual cycle (i.e., reversing the cycle and changing the case of each symbol in the cycle);
  • reversing all cycles without changing the case of any symbols.

Each signature produced will have its cycles ordered by decreasing length. Each cycle will have at least half of its symbols lower-case.

For each signature that is generated, routine use (as passed to this function) will be called with that signature and its automorphisms as arguments.

Warning
Currently upper-case symbols in signatures are not supported by this routine; only signatures whose symbols are all lower-case will be produced.
Todo:
Feature: Add support for symbols of differing case.
Python:
Not present.
Parameters
orderthe order of signatures to generate.
usethe function to call upon each signature that is found. The first parameter passed to this function will be a splitting surface signature. The second parameter will be a list of all its automorphisms. The third parameter will be parameter useArgs as was passed to this routine.
useArgsthe pointer to pass as the final parameter for the function use which will be called upon each signature found.
Returns
the total number of non-equivalent signatures that were found.

Copyright © 1999-2016, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).