Regina Calculation Engine
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Represents a torus bundle over the circle. More...
#include <manifold/ntorusbundle.h>
Public Member Functions | |
NTorusBundle () | |
Creates a new trivial torus bundle over the circle. More... | |
NTorusBundle (const NMatrix2 &newMonodromy) | |
Creates a new torus bundle over the circle using the given monodromy. More... | |
NTorusBundle (long mon00, long mon01, long mon10, long mon11) | |
Creates a new torus bundle over the circle using the given monodromy. More... | |
NTorusBundle (const NTorusBundle &cloneMe) | |
Creates a clone of the given torus bundle. More... | |
const NMatrix2 & | getMonodromy () const |
Returns the monodromy describing how the upper and lower torus boundaries are identified. More... | |
NAbelianGroup * | getHomologyH1 () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. More... | |
bool | isHyperbolic () const |
Returns whether or not this is a finite-volume hyperbolic manifold. More... | |
std::ostream & | writeName (std::ostream &out) const |
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 |
Writes the common name of this 3-manifold in TeX format to the given output stream. More... | |
std::string | getName () const |
Returns the common name of this 3-manifold as a human-readable string. More... | |
std::string | getTeXName () const |
Returns the common name of this 3-manifold in TeX format. More... | |
std::string | getStructure () const |
Returns details of the structure of this 3-manifold that might not be evident from its common name. More... | |
virtual NTriangulation * | construct () const |
Returns a triangulation of this 3-manifold, if such a construction has been implemented. More... | |
bool | operator< (const NManifold &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... | |
virtual void | writeTextShort (std::ostream &out) const |
Writes this object in short text format to the given output stream. More... | |
virtual void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. More... | |
Input and Output | |
std::string | str () const |
Returns the output from writeTextShort() as a string. More... | |
std::string | toString () const |
A deprecated alias for str(), which returns the output from writeTextShort() as a string. More... | |
std::string | detail () const |
Returns the output from writeTextLong() as a string. More... | |
std::string | toStringLong () const |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string. 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 NManifold routines except for construct() are implemented for this class.
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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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inline |
Creates a clone of the given torus bundle.
cloneMe | the torus bundle to clone. |
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inlinevirtualinherited |
Returns a triangulation of this 3-manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3-manifold (for instance, if this 3-manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3-manifolds have construction routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.
Reimplemented in regina::NSFSpace, regina::NSnapPeaCensusManifold, regina::NLensSpace, and regina::NSimpleSurfaceBundle.
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inherited |
Returns the output from writeTextLong() as a string.
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virtual |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
Reimplemented from regina::NManifold.
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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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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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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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inlinevirtual |
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::NManifold.
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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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inherited |
Returns the output from writeTextShort() as a string.
__str__()
function.
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inlineinherited |
A deprecated alias for str(), which returns the output from writeTextShort() as a string.
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inlineinherited |
A deprecated alias for detail(), which returns the output from writeTextLong() as a string.
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virtual |
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::NManifold.
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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::NSFSpace, and regina::NSnapPeaCensusManifold.
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virtual |
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::NManifold.
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inlinevirtualinherited |
Writes this object in long text format to the given output stream.
The output should provide the user with all the information they could want. The output should be human-readable, should not contain extremely long lines (so users can read the output in a terminal), and should end with a final newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out | the output stream to which to write. |
Reimplemented from regina::ShareableObject.
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inlinevirtualinherited |
Writes this object in short text format to the given output stream.
The output should be human-readable, should fit on a single line, and should not end with a newline.
out | the output stream to which to write. |
Implements regina::ShareableObject.