Regina 7.1 Calculation Engine
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Represents a torus bundle over the circle. More...
#include <manifold/torusbundle.h>
Public Member Functions | |
TorusBundle () | |
Creates a new trivial torus bundle over the circle. More... | |
TorusBundle (const Matrix2 &newMonodromy) | |
Creates a new torus bundle over the circle using the given monodromy. More... | |
TorusBundle (long mon00, long mon01, long mon10, long mon11) | |
Creates a new torus bundle over the circle using the given monodromy. More... | |
TorusBundle (const TorusBundle &)=default | |
Creates a new copy of the given torus bundle. More... | |
const Matrix2 & | monodromy () const |
Returns the monodromy describing how the upper and lower torus boundaries are identified. More... | |
TorusBundle & | operator= (const TorusBundle &)=default |
Sets this to be a copy of the given torus bundle. More... | |
void | swap (TorusBundle &other) noexcept |
Swaps the contents of this and the given torus bundle. More... | |
bool | operator== (const TorusBundle &compare) const |
Determines whether this and the given object contain precisely the same presentations of the same torus bundle. More... | |
bool | operator!= (const TorusBundle &compare) const |
Determines whether this and the given object do not contain precisely the same presentations of the same torus bundle. More... | |
AbelianGroup | homology () const override |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | isHyperbolic () const override |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | writeName (std::ostream &out) const override |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. More... | |
std::ostream & | writeTeXName (std::ostream &out) const override |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
std::string | name () const |
Returns the common name of this 3-manifold as a human-readable string. More... | |
std::string | texName () const |
Returns the common name of this 3-manifold in TeX format. More... | |
std::string | structure () const |
Returns details of the structure of this 3-manifold that might not be evident from its common name. More... | |
virtual Triangulation< 3 > | construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
bool | operator< (const Manifold &compare) const |
Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold. More... | |
virtual std::ostream & | writeStructure (std::ostream &out) const |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More... | |
void | writeTextShort (std::ostream &out) const |
Writes a short text representation of this object to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const |
Writes a detailed text representation of this object to the given output stream. More... | |
std::string | str () const |
Returns a short text representation of this object. More... | |
std::string | utf8 () const |
Returns a short text representation of this object using unicode characters. More... | |
std::string | detail () const |
Returns a detailed text representation of this object. More... | |
Represents a torus bundle over the circle.
This is expressed as the product of the torus and the interval, with the two torus boundaries identified according to some specified monodromy.
The monodromy is described by a 2-by-2 matrix M as follows. Let a and b be generating curves of the upper torus boundary, and let p and q be the corresponding curves on the lower torus boundary (so that a and p are parallel and b and q are parallel). Then we identify the torus boundaries so that, in additive terms:
[a] [p] [ ] = M * [ ] [b] [q]
All optional Manifold routines except for construct() are implemented for this class.
This class supports copying but does not implement separate move operations, since its internal data is so small that copying is just as efficient. It implements the C++ Swappable requirement via its own member and global swap() functions, for consistency with the other manifold classes.
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inline |
Creates a new trivial torus bundle over the circle.
In other words, this routine creates a torus bundle with the identity monodromy.
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inline |
Creates a new torus bundle over the circle using the given monodromy.
newMonodromy | describes precisely how the upper and lower torus boundaries are identified. See the class notes for details. |
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inline |
Creates a new torus bundle over the circle using the given monodromy.
The four elements of the monodromy matrix are passed separately. They combine to give the full monodromy matrix M as follows:
[ mon00 mon01 ] M = [ ] [ mon10 mon11 ]
mon00 | the (0,0) element of the monodromy matrix. |
mon01 | the (0,1) element of the monodromy matrix. |
mon10 | the (1,0) element of the monodromy matrix. |
mon11 | the (1,1) element of the monodromy matrix. |
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default |
Creates a new copy of the given torus bundle.
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virtualinherited |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
For details of which types of 3-manifolds have implemented this routine, see the class notes for each corresponding subclasses of Manifold.
The default implemention of this routine just throws a NotImplemented exception.
NotImplemented | explicit construction has not yet been implemented for this particular 3-manifold. |
FileError | the construction needs to be read from file (as opposed to computed on the fly), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its triangulations from the SnapPea census databases that are installed with Regina. |
Reimplemented in regina::SnapPeaCensusManifold, regina::SimpleSurfaceBundle, regina::SFSpace, regina::LensSpace, and regina::Handlebody.
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inherited |
Returns a detailed text representation of this object.
This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.
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overridevirtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
For details of which types of 3-manifolds have implemented this routine, see the class notes for each corresponding subclasses of Manifold.
The default implemention of this routine just throws a NotImplemented exception.
NotImplemented | homology calculation has not yet been implemented for this particular 3-manifold. |
FileError | the homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its results from the SnapPea census databases that are installed with Regina. |
Reimplemented from regina::Manifold.
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inlineoverridevirtual |
Returns whether or not this is a finite-volume hyperbolic manifold.
true
if this is a finite-volume hyperbolic manifold, or false
if not. Implements regina::Manifold.
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inline |
Returns the monodromy describing how the upper and lower torus boundaries are identified.
See the class notes for details.
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inherited |
Returns the common name of this 3-manifold as a human-readable string.
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inline |
Determines whether this and the given object do not contain precisely the same presentations of the same torus bundle.
This routine does not test for homeomorphism; instead it compares the specific monodromies. If you have two objects that represent same torus bundle using two different monodromies, they will be treated as not equal by this routine.
compare | the presentation with which this will be compared. |
true
if and only if this and the given object do not contain identical presentations of the same torus bundle.
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inherited |
Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold.
The ordering imposed on 3-manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.
The ordering also depends on the particular representation of the 3-manifold that is used. As an example, different representations of the same Seifert fibred space might well be ordered differently.
All that this routine really offers is a well-defined way of ordering 3-manifold representations.
compare | the 3-manifold representation with which this will be compared. |
true
if and only if this is "smaller" than the given 3-manifold representation.
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default |
Sets this to be a copy of the given torus bundle.
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inline |
Determines whether this and the given object contain precisely the same presentations of the same torus bundle.
This routine does not test for homeomorphism; instead it compares the specific monodromies. If you have two objects that represent same torus bundle using two different monodromies, they will be treated as not equal by this routine.
compare | the presentation with which this will be compared. |
true
if and only if this and the given object contain identical presentations of the same torus bundle.
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inherited |
Returns a short text representation of this object.
This text should be human-readable, should use plain ASCII characters where possible, and should not contain any newlines.
Within these limits, this short text ouptut should be as information-rich as possible, since in most cases this forms the basis for the Python str()
and repr()
functions.
str()
will use precisely this function, and for most classes the Python repr()
function will incorporate this into its output.
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inherited |
Returns details of the structure of this 3-manifold that might not be evident from its common name.
For instance, for an orbit space S^3/G this routine might return the full Seifert structure.
This routine may return the empty string if no additional details are deemed necessary.
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inlinenoexcept |
Swaps the contents of this and the given torus bundle.
other | the torus bundle whose contents should be swapped with this. |
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inherited |
Returns the common name of this 3-manifold in TeX format.
No leading or trailing dollar signs will be included.
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inherited |
Returns a short text representation of this object using unicode characters.
Like str(), this text should be human-readable, should not contain any newlines, and (within these constraints) should be as information-rich as is reasonable.
Unlike str(), this function may use unicode characters to make the output more pleasant to read. The string that is returned will be encoded in UTF-8.
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overridevirtual |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
out | the output stream to which to write. |
Implements regina::Manifold.
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inlinevirtualinherited |
Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.
For instance, for an orbit space S^3/G this routine might write the full Seifert structure.
This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.
out | the output stream to which to write. |
Reimplemented in regina::SnapPeaCensusManifold, and regina::SFSpace.
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overridevirtual |
Writes the common name of this 3-manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
out | the output stream to which to write. |
Implements regina::Manifold.
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inlineinherited |
Writes a detailed text representation of this object to the given output stream.
Subclasses must not override this routine. They should override writeName() and writeStructure() instead.
out | the output stream to which to write. |
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inlineinherited |
Writes a short text representation of this object to the given output stream.
Subclasses must not override this routine. They should override writeName() instead.
out | the output stream to which to write. |