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|
Help on instancemethod in module regina.engine:
boundaryComponents(...)
boundaryComponents(self: regina.Triangulation6) -> <internal>.ListView[regina.BoundaryComponent6]
Returns an object that allows iteration through and random access to
all boundary components of this triangulation.
Note that, in Regina's standard dimensions, each ideal vertex forms
its own boundary component, and some invalid vertices do also. See the
BoundaryComponent class notes for full details on what constitutes a
boundary component in standard and non-standard dimensions.
The object that is returned is lightweight, and can be happily copied
by value. The C++ type of the object is subject to change, so C++
users should use ``auto`` (just like this declaration does).
The returned object is guaranteed to be an instance of ListView, which
means it offers basic container-like functions and supports range-
based ``for`` loops. Note that the elements of the list will be
pointers, so your code might look like:
```
for (BoundaryComponent<dim>* b : tri.boundaryComponents()) { ... }
```
The object that is returned will remain up-to-date and valid for as
long as the triangulation exists. In contrast, however, remember that
the individual boundary components _within_ this list will be deleted
and replaced each time the triangulation changes. Therefore it is best
to treat this object as temporary only, and to call
boundaryComponents() again each time you need it.
Returns:
access to the list of all boundary components.
Help on instancemethod in module regina.engine:
components(...)
components(self: regina.Triangulation6) -> <internal>.ListView[regina.Component6]
Returns an object that allows iteration through and random access to
all components of this triangulation.
The object that is returned is lightweight, and can be happily copied
by value. The C++ type of the object is subject to change, so C++
users should use ``auto`` (just like this declaration does).
The returned object is guaranteed to be an instance of ListView, which
means it offers basic container-like functions and supports range-
based ``for`` loops. Note that the elements of the list will be
pointers, so your code might look like:
```
for (Component<dim>* c : tri.components()) { ... }
```
The object that is returned will remain up-to-date and valid for as
long as the triangulation exists. In contrast, however, remember that
the individual component objects _within_ this list will be deleted
and replaced each time the triangulation changes. Therefore it is best
to treat this object as temporary only, and to call components() again
each time you need it.
Returns:
access to the list of all components.
Help on instancemethod in module regina.engine:
faces(...)
faces(self: regina.Triangulation6, arg0: int) -> Union[<internal>.ListView[regina.Vertex6], <internal>.ListView[regina.Edge6], <internal>.ListView[regina.Triangle6], <internal>.ListView[regina.Tetrahedron6], <internal>.ListView[regina.Pentachoron6], <internal>.ListView[regina.Face6_5]]
Returns an object that allows iteration through and random access to
all *subdim*-faces of this triangulation, in a way that is optimised
for Python programmers.
C++ users should not use this routine. The return type must be fixed
at compile time, and so it is a std::variant that can hold any of the
lightweight return types from the templated faces<subdim>() function.
This means that the return value will still need compile-time
knowledge of *subdim* to extract and use the appropriate face objects.
However, once you know *subdim* at compile time, you are much better
off using the (simpler and faster) routine faces<subdim>() instead.
For Python users, this routine is much more useful: the return type
can be chosen at runtime, and so this routine returns a Python list of
Face<dim, subdim> objects (holding all the *subdim*-faces of the
triangulation), which you can use immediately.
Exception ``InvalidArgument``:
The face dimension *subdim* is outside the supported range (i.e.,
negative, or greater than or equal to *dim*).
Parameter ``subdim``:
the face dimension; this must be between 0 and *dim*-1 inclusive.
Returns:
access to the list of all *subdim*-faces.
Help on instancemethod in module regina.engine:
face(...)
face(self: regina.Triangulation6, arg0: int, arg1: int) -> Union[regina.Vertex6, regina.Edge6, regina.Triangle6, regina.Tetrahedron6, regina.Pentachoron6, regina.Face6_5]
Returns the requested *subdim*-face of this triangulation, in a way
that is optimised for Python programmers.
For C++ users, this routine is not very useful: since precise types
must be know at compile time, this routine returns a std::variant *v*
that could store a pointer to any class Face<dim, ...>. This means you
cannot access the face directly: you will still need some kind of
compile-time knowledge of *subdim* before you can extract and use an
appropriate Face<dim, subdim> object from *v*. However, once you know
*subdim* at compile time, you are better off using the (simpler and
faster) routine face<subdim>() instead.
For Python users, this routine is much more useful: the return type
can be chosen at runtime, and so this routine simply returns a
Face<dim, subdim> object of the appropriate face dimension that you
can use immediately.
The specific return type for C++ programmers will be
std::variant<Face<dim, 0>*, ..., Face<dim, dim-1>*>.
Exception ``InvalidArgument``:
The face dimension *subdim* is outside the supported range (i.e.,
negative, or greater than or equal to *dim*).
Parameter ``subdim``:
the face dimension; this must be between 0 and *dim*-1 inclusive.
Parameter ``index``:
the index of the desired face, ranging from 0 to
countFaces<subdim>()-1 inclusive.
Returns:
the requested face.
Help on instancemethod in module regina.engine:
simplices(...)
simplices(self: regina.Triangulation6) -> <internal>.ListView[regina.Simplex6]
Returns an object that allows iteration through and random access to
all top-dimensional simplices in this triangulation.
The object that is returned is lightweight, and can be happily copied
by value. The C++ type of the object is subject to change, so C++
users should use ``auto`` (just like this declaration does).
The returned object is guaranteed to be an instance of ListView, which
means it offers basic container-like functions and supports range-
based ``for`` loops. Note that the elements of the list will be
pointers, so your code might look like:
```
for (Simplex<dim>* s : tri.simplices()) { ... }
```
The object that is returned will remain up-to-date and valid for as
long as the triangulation exists: even as simplices are added and/or
removed, it will always reflect the simplices that are currently in
the triangulation. Nevertheless, it is recommended to treat this
object as temporary only, and to call simplices() again each time you
need it.
Returns:
access to the list of all top-dimensional simplices.
Help on instancemethod in module regina.engine:
faces(...)
faces(self: regina.Triangulation4, arg0: int) -> Union[<internal>.ListView[regina.Vertex4], <internal>.ListView[regina.Edge4], <internal>.ListView[regina.Triangle4], <internal>.ListView[regina.Tetrahedron4]]
Returns an object that allows iteration through and random access to
all *subdim*-faces of this triangulation, in a way that is optimised
for Python programmers.
C++ users should not use this routine. The return type must be fixed
at compile time, and so it is a std::variant that can hold any of the
lightweight return types from the templated faces<subdim>() function.
This means that the return value will still need compile-time
knowledge of *subdim* to extract and use the appropriate face objects.
However, once you know *subdim* at compile time, you are much better
off using the (simpler and faster) routine faces<subdim>() instead.
For Python users, this routine is much more useful: the return type
can be chosen at runtime, and so this routine returns a Python list of
Face<dim, subdim> objects (holding all the *subdim*-faces of the
triangulation), which you can use immediately.
Exception ``InvalidArgument``:
The face dimension *subdim* is outside the supported range (i.e.,
negative, or greater than or equal to *dim*).
Parameter ``subdim``:
the face dimension; this must be between 0 and *dim*-1 inclusive.
Returns:
access to the list of all *subdim*-faces.
Help on instancemethod in module regina.engine:
face(...)
face(self: regina.Triangulation4, arg0: int, arg1: int) -> Union[regina.Vertex4, regina.Edge4, regina.Triangle4, regina.Tetrahedron4]
Returns the requested *subdim*-face of this triangulation, in a way
that is optimised for Python programmers.
For C++ users, this routine is not very useful: since precise types
must be know at compile time, this routine returns a std::variant *v*
that could store a pointer to any class Face<dim, ...>. This means you
cannot access the face directly: you will still need some kind of
compile-time knowledge of *subdim* before you can extract and use an
appropriate Face<dim, subdim> object from *v*. However, once you know
*subdim* at compile time, you are better off using the (simpler and
faster) routine face<subdim>() instead.
For Python users, this routine is much more useful: the return type
can be chosen at runtime, and so this routine simply returns a
Face<dim, subdim> object of the appropriate face dimension that you
can use immediately.
The specific return type for C++ programmers will be
std::variant<Face<dim, 0>*, ..., Face<dim, dim-1>*>.
Exception ``InvalidArgument``:
The face dimension *subdim* is outside the supported range (i.e.,
negative, or greater than or equal to *dim*).
Parameter ``subdim``:
the face dimension; this must be between 0 and *dim*-1 inclusive.
Parameter ``index``:
the index of the desired face, ranging from 0 to
countFaces<subdim>()-1 inclusive.
Returns:
the requested face.
Help on instancemethod in module regina.engine:
embeddings(...)
embeddings(self: regina.Vertex6) -> <internal>.ListView[regina.VertexEmbedding6]
Returns an object that allows iteration through and random access to
all of the ways in which this face appears within a top-dimensional
simplex of the underlying triangluation.
The object that is returned is lightweight, and can be happily copied
by value. The C++ type of the object is subject to change, so C++
users should use ``auto`` (just like this declaration does).
The returned object is guaranteed to be an instance of ListView, which
means it offers basic container-like functions and supports range-
based ``for`` loops. The elements of the list will be read-only
objects of type FaceEmbedding<dim, subdim>. For example, your code
might look like:
```
Face<dim, subdim>* face = ...;
for (const auto& emb : face->embeddings()) { ... }
```
In most cases, the ordering of appearances is arbitrary. The exception
is for codimension 2, where these appearances are ordered in a way
that follows the link around the face (which in codimension 2 is
always a path or a cycle).
Using embeddings() is equivalent to iterating over the face itself. It
generates a tiny amount of extra overhead, but also may be considered
more readable. In particular, the code above is equivalent to both of
the following alternatives:
```
Face<dim, subdim>* face = ...;
for (const auto& emb : *face) { ... }
```
```
Face<dim, subdim>* face = ...;
for (size_t i = 0; i < face->degree(); ++i) {
const auto& emb = face->embedding(i);
...
}
```
Returns:
access to the list of all appearances of this face within a top-
dimensional simplex of the underlying triangulation.
Help on instancemethod in module regina.engine:
embeddings(...)
embeddings(self: regina.Vertex3) -> <internal>.ListView[regina.VertexEmbedding3]
Returns an object that allows iteration through and random access to
all of the ways in which this face appears within a top-dimensional
simplex of the underlying triangluation.
The object that is returned is lightweight, and can be happily copied
by value. The C++ type of the object is subject to change, so C++
users should use ``auto`` (just like this declaration does).
The returned object is guaranteed to be an instance of ListView, which
means it offers basic container-like functions and supports range-
based ``for`` loops. The elements of the list will be read-only
objects of type FaceEmbedding<dim, subdim>. For example, your code
might look like:
```
Face<dim, subdim>* face = ...;
for (const auto& emb : face->embeddings()) { ... }
```
In most cases, the ordering of appearances is arbitrary. The exception
is for codimension 2, where these appearances are ordered in a way
that follows the link around the face (which in codimension 2 is
always a path or a cycle).
Using embeddings() is equivalent to iterating over the face itself. It
generates a tiny amount of extra overhead, but also may be considered
more readable. In particular, the code above is equivalent to both of
the following alternatives:
```
Face<dim, subdim>* face = ...;
for (const auto& emb : *face) { ... }
```
```
Face<dim, subdim>* face = ...;
for (size_t i = 0; i < face->degree(); ++i) {
const auto& emb = face->embedding(i);
...
}
```
Returns:
access to the list of all appearances of this face within a top-
dimensional simplex of the underlying triangulation.
Help on instancemethod in module regina.engine:
vertex(...)
vertex(self: regina.Edge6, arg0: int) -> regina.Vertex6
A dimension-specific alias for face<0>().
This alias is available for all facial dimensions *subdim*.
See face() for further information.
Help on instancemethod in module regina.engine:
triangulation(...)
triangulation(self: regina.BoundaryComponent3) -> regina.Triangulation3
Returns the triangulation to which this boundary component belongs.
Returns:
a reference to the triangulation containing this boundary
component.
Help on instancemethod in module regina.engine:
packet(...)
packet(self: regina.Link) -> regina.PacketOfLink
Returns the packet that holds this data, if there is one.
If this object is being held by a packet *p* of type PacketOf<Held>,
then that packet *p* will be returned. Otherwise, if this is a
"standalone" object of type Held, then this routine will return
``None``.
There is a special case when dealing with a packet *q* that holds a
SnapPea triangulation. Here *q* is of type
PacketOf<SnapPeaTriangulation>, and it holds a Triangulation<3>
"indirectly" in the sense that Packetof<SnapPeaTriangulation> derives
from SnapPeaTriangulation, which in turn derives from
Triangulation<3>. In this scenario:
* calling Triangulation<3>::packet() will return ``None``, since there
is no "direct" PacketOf<Triangulation<3>>;
* calling SnapPeaTriangulation::packet() will return the enclosing
packet *q*, since there is a PacketOf<SnapPeaTriangulation>;
* calling the special routine Triangulation<3>::inAnyPacket() will
also return the "indirect" enclosing packet *q*.
The function inAnyPacket() is specific to Triangulation<3>, and is not
offered for other *Held* types.
Returns:
the packet that holds this data, or ``None`` if this data is not
(directly) held by a packet.
Help on instancemethod in module regina.engine:
__init__(...)
__init__(*args, **kwargs)
Overloaded function.
1. __init__(self: regina.Integer) -> None
Initialises this integer to zero.
2. __init__(self: regina.Integer, arg0: int) -> None
Initialises this integer to the given value.
Python:
In Python, this is the only native-integer constructor available.
Parameter ``value``:
the new value of this integer.
3. __init__(self: regina.Integer, arg0: regina.Integer) -> None
Initialises this integer to the given value.
Parameter ``value``:
the new value of this integer.
4. __init__(self: regina.Integer, arg0: regina.LargeInteger) -> None
Initialises this integer to the given value.
Precondition:
The given integer is not infinite.
Parameter ``value``:
the new value of this integer.
5. __init__(self: regina.Integer, arg0: int) -> None
Initialises this to the given native Python integer.
The argument is of the Python ``int`` type, which Python uses to store
integers of arbitrary magnitude (much like Regina does with its
Integer and LargeInteger classes).
Parameter ``value``:
the new value of this integer.
6. __init__(self: regina.Integer, arg0: float) -> None
Initialises this integer to the truncation of the given real number.
Parameter ``value``:
the real number to be truncated.
7. __init__(self: regina.Integer, arg0: str, base: int = 10) -> None
Initialises this integer to the given value which is represented as a
string of digits in a given base.
If not specified, the base defaults to 10. If the given base is zero,
the base will be automatically determined. If the given string begins
with ``0x`` or ``0X``, the base will be assumed to be 16. Otherwise,
if the string begins with ``0``, the base will be assumed to be 8.
Otherwise it will be taken as base 10.
If the template argument *withInfinity* is ``True``, then any string
beginning with "inf" (after any initial whitesapce) will be
interpreted as infinity.
Whitespace may be present at the beginning or the end of the given
string, and will simply be ignored.
For finer details on how the string parsing works, see strtol() from
the standard C library (on which this method is based).
Precondition:
The given base is zero, or is between 2 and 36 inclusive.
Precondition:
The given string represents an integer in the given base, with
optional whitespace beforehand.
Exception ``InvalidArgument``:
The given string was not a valid large integer representation.
Parameter ``value``:
the new value of this integer, represented as a string of digits
in base *base*.
Parameter ``base``:
the base in which *value* is given.
Help on instancemethod in module regina.engine:
__init__(...)
__init__(*args, **kwargs)
Overloaded function.
1. __init__(self: regina.LargeInteger) -> None
Initialises this integer to zero.
2. __init__(self: regina.LargeInteger, arg0: int) -> None
Initialises this integer to the given value.
Python:
In Python, this is the only native-integer constructor available.
Parameter ``value``:
the new value of this integer.
3. __init__(self: regina.LargeInteger, arg0: regina.LargeInteger) -> None
Initialises this integer to the given value.
Parameter ``value``:
the new value of this integer.
4. __init__(self: regina.LargeInteger, arg0: regina.Integer) -> None
Initialises this integer to the given value.
Precondition:
The given integer is not infinite.
Parameter ``value``:
the new value of this integer.
5. __init__(self: regina.LargeInteger, arg0: int) -> None
Initialises this to the given native Python integer.
The argument is of the Python ``int`` type, which Python uses to store
integers of arbitrary magnitude (much like Regina does with its
Integer and LargeInteger classes).
Parameter ``value``:
the new value of this integer.
6. __init__(self: regina.LargeInteger, arg0: float) -> None
Initialises this integer to the truncation of the given real number.
Parameter ``value``:
the real number to be truncated.
7. __init__(self: regina.LargeInteger, arg0: str, base: int = 10) -> None
Initialises this integer to the given value which is represented as a
string of digits in a given base.
If not specified, the base defaults to 10. If the given base is zero,
the base will be automatically determined. If the given string begins
with ``0x`` or ``0X``, the base will be assumed to be 16. Otherwise,
if the string begins with ``0``, the base will be assumed to be 8.
Otherwise it will be taken as base 10.
If the template argument *withInfinity* is ``True``, then any string
beginning with "inf" (after any initial whitesapce) will be
interpreted as infinity.
Whitespace may be present at the beginning or the end of the given
string, and will simply be ignored.
For finer details on how the string parsing works, see strtol() from
the standard C library (on which this method is based).
Precondition:
The given base is zero, or is between 2 and 36 inclusive.
Precondition:
The given string represents an integer in the given base, with
optional whitespace beforehand.
Exception ``InvalidArgument``:
The given string was not a valid large integer representation.
Parameter ``value``:
the new value of this integer, represented as a string of digits
in base *base*.
Parameter ``base``:
the base in which *value* is given.
Help on ListView_Triangulation3_vertices in module regina.engine.internal object:
class ListView_Triangulation3_vertices(pybind11_builtins.pybind11_object)
| A lightweight object that can be used for iteration and random access
| to all elements of a given list.
|
| This access is read-only, in the sense that both the list itself and
| the list elements are read-only. (Of course, if the list elements are
| non-const pointers then this means that the _pointers_ cannot be
| reassigned to point to different objects, but the objects they _point_
| to can still be modified.)
|
| Typically a ListView would be returned from a class member function to
| grant the user some basic read-only access to a much richer private
| data structure, in a way that allows the internal data structure to
| change at some later date without affecting the public API.
|
| The ListView class supports several different ways of representing a
| list:
|
| * If your list is stored using a container class (e.g., std::vector or
| regina::MarkedVector), then you can create a ListView directly from
| the container using the syntax ``ListView(container)``. This uses
| the generic ListView<Container> class template. There is no need to
| explicitly specify the ListView template arguments.
|
| * If your list is stored using a C-style array whose size is not known
| at compile-time, you can create a ListView using either the syntax
| ``ListView(array, size)`` or ``ListView(begin, end)``. Here *array*
| is a pointer to the beginning of the array, and *begin* and *end*
| behave as an iterator pair (so ``begin == array`` and ``end == array
| + size``). This syntax uses the specialised ListView<Element*> class
| template. Again, there is no need to explicitly specify the ListView
| template arguments.
|
| * If your list is stored using a C-style array whose size is fixed at
| compile-time (i.e., the type is ``Element[n]`` for some constant
| *n*), you can create a ListView using the syntax
| ``ListView(array)``. Once again, there is no need to explicitly
| specify the ListView template arguments.
|
| End users should always store ListView objects using ``auto``, not by
| explicitly writing out the full ListView type. One reason for this is
| that, now that Regina has moved to C++20, the ListView class will most
| likely be removed completely (in favour of the new C++20 ranges
| library).
|
| ListView objects are small enough to pass by value and swap with
| std::swap(), with no need for any specialised move operations or swap
| functions.
|
| Python:
| The ListView classes are deliberately difficult to access: they
| live within their own private Python namespaces, and are all give
| the same class name (*ListView*). You would typically only
| interact with a ListView when it is returned from a function
| (e.g., ``Link.crossings()``), and in most cases you would simply
| iterate over this resulting ListView without ever knowing its
| exact type.
|
| Template parameter ``Container``:
| the internal type of the list that this object grants access to.
| This type must support at least the same operations as this class
| itself, except for the copy semantics. In particular, both
| std::vector and regina::MarkedVector types (as well as many other
| standard container types) are suitable.
|
| Method resolution order:
| ListView_Triangulation3_vertices
| pybind11_builtins.pybind11_object
| builtins.object
|
| Methods defined here:
|
| __eq__(...)
| __eq__(*args, **kwargs)
| Overloaded function.
|
| 1. __eq__(self: <internal>.ListView[regina.Vertex3], arg0: <internal>.ListView[regina.Vertex3]) -> bool
|
| Determines whether this and the given list view are accessing the same
| underlying container.
|
| Here the containers are compared by _reference_ (i.e., they must be
| the same container object at the same location in memory; it is not
| enough to be two containers with identical contents).
|
| Returns:
| ``True`` if and only if this and the given list use the same
| underlying container.
|
| 2. __eq__(self: <internal>.ListView[regina.Vertex3], arg0: None) -> bool
|
| Always returns ``False``, since an object of this type is never equal
| to ``None``.
|
| __getitem__(...)
| __getitem__(self: <internal>.ListView[regina.Vertex3], arg0: int) -> regina.Vertex3
|
| Returns the requested element of this list.
|
| Parameter ``index``:
| indicates which element to return; this must be between 0 and
| size()-1 inclusive.
|
| Returns:
| the (*index*)th element in this list.
|
| __init__(...)
| __init__(self: regina.internal.ListView_Triangulation3_vertices, arg0: <internal>.ListView[regina.Vertex3]) -> None
|
| Creates a new copy of the given list view.
|
| __iter__(...)
| __iter__(self: <internal>.ListView[regina.Vertex3]) -> Iterator[regina.Vertex3]
|
| Returns a Python iterator over the elements of this list.
|
| Returns:
| an iterator over the elements of this list.
|
| __len__(...)
| __len__(self: <internal>.ListView[regina.Vertex3]) -> int
|
| Returns the number of elements in this list.
|
| Python:
| This is also used to implement the Python special method
| __len__().
|
| Returns:
| the number of elements.
|
| __ne__(...)
| __ne__(*args, **kwargs)
| Overloaded function.
|
| 1. __ne__(self: <internal>.ListView[regina.Vertex3], arg0: <internal>.ListView[regina.Vertex3]) -> bool
|
| Determines whether this and the given object have different values.
| This operator ``x != y`` is generated automatically, as the negation
| of ``x == y``.
|
| This test compares the _contents_ of the two objects (i.e., it
| compares by value, not by reference). See the documentation for the
| corresponding equality test (i.e., the member function ``__eq__``)
| for full details on how objects of this type will be compared.
|
| 2. __ne__(self: <internal>.ListView[regina.Vertex3], arg0: None) -> bool
|
| Always returns ``True``, since an object of this type is never equal
| to ``None``.
|
| __repr__(...)
| __repr__(self: <internal>.ListView[regina.Vertex3]) -> str
|
| __str__(...)
| __str__(self: <internal>.ListView[regina.Vertex3]) -> str
|
| back(...)
| back(self: <internal>.ListView[regina.Vertex3]) -> regina.Vertex3
|
| Returns the last element of this list.
|
| Precondition:
| This list is not empty.
|
| Returns:
| the last element in this list.
|
| empty(...)
| empty(self: <internal>.ListView[regina.Vertex3]) -> bool
|
| Determines if this list is empty.
|
| Returns:
| ``True`` if and only if this list is empty.
|
| front(...)
| front(self: <internal>.ListView[regina.Vertex3]) -> regina.Vertex3
|
| Returns the first element of this list.
|
| Precondition:
| This list is not empty.
|
| Returns:
| the first element in this list.
|
| size(...)
| size(self: <internal>.ListView[regina.Vertex3]) -> int
|
| Returns the number of elements in this list.
|
| Python:
| This is also used to implement the Python special method
| __len__().
|
| Returns:
| the number of elements.
|
| ----------------------------------------------------------------------
| Data and other attributes defined here:
|
| __hash__ = None
|
| equalityType = <EqualityType.BY_VALUE: 1>
|
| ----------------------------------------------------------------------
| Static methods inherited from pybind11_builtins.pybind11_object:
|
| __new__(*args, **kwargs) from pybind11_builtins.pybind11_type
| Create and return a new object. See help(type) for accurate signature.
|