OrientedPlanarDiagram#

class OrientedPlanarDiagram(incoming_diagram_data=None, **attr)#

Bases: PlanarDiagram

__init__(incoming_diagram_data=None, **attr)#

Initialize a planar diagram.

If no data is provided, an empty diagram is created. Otherwise, the diagram is initialized using the provided data.

Parameters:

incoming_diagram_data (Optional[Any]) – Initial data to construct the diagram (currently not implemented).
attr – Additional attributes such as name, framing, etc.

Methods

`__init__`([incoming_diagram_data])	Initialize a planar diagram.
`add_crossing`(crossing_for_adding, **attr)	Add or update a crossing in the diagram.
`add_crossings_from`(crossings_for_adding, **attr)	Add or update a bunch (iterable) of crossings and update the crossings attributes.
`add_node`(node_for_adding, create_using[, degree])	Add a node to the diagram.
`add_nodes_from`(nodes_for_adding[, create_using])	Add or update a list of nodes to the diagram.
`add_vertex`(vertex_for_adding[, degree])	Add or update a crossing and update the crossing attributes.
`add_vertices_from`(vertices_for_adding, **attr)	Add or update a crossing and update the crossing attributes.
`add_virtual_crossing`(crossing_for_adding, **attr)	Add or update a crossing and update the crossing attributes.
`add_virtual_crossings_from`(...)	Add or update a crossing and update the crossing attributes.
`clear`()	Remove all data from the diagram, resetting it to an empty state.
`convert_node`(node_for_converting, node_type)	Convert node type, e.g. from vertex to crossing.
`convert_nodes`(node_for_converting, node_type)
`copy`([copy_using])	Return a shallow copy of the diagram.
`degree`(node)
`endpoint_from_pair`(endpoint_pair)	Returns the Endpoint instance of the pair (node, position).
`is_framed`()
`is_oriented`()
`permute_node`(node, permutation)	Permute the endpoints of the node of knot k.
`relabel_nodes`(mapping)	Relabels the nodes, can be a partial map
`remove_arc`(arc_for_removing)
`remove_arcs_from`(arcs_for_removing)
`remove_endpoint`(endpoint_for_removal)
`remove_endpoints_from`(endpoints_for_removal)
`remove_node`(node_for_removing[, ...])	Remove the node.
`remove_nodes_from`(nodes_for_removal[, ...])
`set_arc`(arc_for_setting, **attr)	Set the arc (v_endpoint, u_endpoint), which equals setting the two endpoints adj(u_endpoint) = v_endpoint and vice-versa.
`set_arcs_from`(arcs_for_adding, **attr)	Set the list of arcs.
`set_endpoint`(endpoint_for_setting, ...[, ...])	Set the endpoint to the adjacent endpoint and update the endpoint attributes.
`twin`(endpoint)	Return the opposite endpoint (twin) of an endpoint.

Attributes

`arcs`	Return a view of the diagram's arcs, represented as pairs of endpoints.
`crossings`	Return a view of all crossings in the diagram.
`endpoints`	Return a view of the diagram's endpoints.
`faces`	Return a view of the diagram's faces (regions enclosed by arcs), which are given as tuples of endpoints.
`framing`	Blackboard framing number of planar diagram.
`name`	Name identifier of planar diagram.
`nodes`	Return a view of the diagram's nodes, providing adjacency information.
`number_of_arcs`
`number_of_crossings`
`number_of_endpoints`
`number_of_nodes`
`number_of_vertices`
`number_of_virtual_crossings`
`vertices`	Node object holding the adjacencies of each crossing.
`virtual_crossings`	Return a view of all virtual crossings in the diagram.

add_crossing(crossing_for_adding, **attr)#

Add or update a crossing in the diagram.

Parameters:

crossing_for_adding (Hashable) – The crossing to add or update.
attr – Additional attributes for the crossing (color, weight, …)

add_crossings_from(crossings_for_adding, **attr)#: Add or update a bunch (iterable) of crossings and update the crossings attributes. Crossings can be any hashable objects.

add_node(node_for_adding, create_using: type, degree=None, **attr)#

Add a node to the diagram.

Parameters:

node_for_adding (Hashable) – A hashable object representing the node.
create_using (type) – The node type (e.g., Vertex, Crossing).
degree (Optional[int]) – The degree of the node (optional).
attr – Additional attributes to store for the node.

add_nodes_from(nodes_for_adding, create_using=None, **attr)#

Add or update a list of nodes to the diagram.

Parameters:

nodes_for_adding (List[Hashable]) – A list/set/tuple of hashable objects representing the nodes.
create_using (type) – The node type (e.g., Vertex, Crossing).
attr – Additional attributes to store for the node.

add_vertex(vertex_for_adding, degree=None, **attr)#: Add or update a crossing and update the crossing attributes. A crossing can be any hashable object.

add_vertices_from(vertices_for_adding, **attr)#: Add or update a crossing and update the crossing attributes. A crossing can be any hashable object.

add_virtual_crossing(crossing_for_adding, **attr)#: Add or update a crossing and update the crossing attributes. A crossing can be any hashable object.

add_virtual_crossings_from(crossings_for_adding, **attr)#: Add or update a crossing and update the crossing attributes. A crossing can be any hashable object.

property arcs#: Return a view of the diagram’s arcs, represented as pairs of endpoints.

clear()#: Remove all data from the diagram, resetting it to an empty state.

convert_node(node_for_converting, node_type: type)#: Convert node type, e.g. from vertex to crossing

copy(copy_using=None, **attr)#

Return a shallow copy of the diagram.

Parameters:: copy_using – The class type of the new diagram (defaults to the same type as self).

Serves for converting e.g. oriented to unoriented diagrams. :type copy_using: Optional[type] :return: A new instance of the planar diagram with the same structure and attributes (shallow copy). :rtype: PlanarDiagram

property crossings#

Return a view of all crossings in the diagram.

Returns:: A filtered node view containing only crossings.
Return type:: FilteredNodeView

endpoint_from_pair(endpoint_pair)#

Returns the Endpoint instance of the pair (node, position).

Parameters:: endpoint_pair – a pair (node, position)
Returns:: Endpoint instance

property endpoints#: Return a view of the diagram’s endpoints.

property faces#: Return a view of the diagram’s faces (regions enclosed by arcs), which are given as tuples of endpoints.

property framing#: Blackboard framing number of planar diagram.

property name#: Name identifier of planar diagram.

property nodes#: Return a view of the diagram’s nodes, providing adjacency information.

permute_node(node, permutation)#: Permute the endpoints of the node of knot k. For example, if p = {0: 0, 1: 2, 2: 3, 3: 1} (or p = [0,2,2,1]), and if node has endpoints [a, b, c, d] (ccw) then the new endpoints will be [a, d, b, c]. :param node: node of which we permute its endpoints :param permutation: permutation given as a dict or list/tuple :return: TODO: are there problems regarding endpoint attributes? TODO: check if it works for loops (probably does not)

relabel_nodes(mapping)#: Relabels the nodes, can be a partial map

remove_node(node_for_removing, remove_incident_endpoints=True)#: Remove the node. :param node_for_removing: :param remove_incident_endpoints: use with care, if False, it breaks the planar structure :return: planar diagram without node

set_arc(arc_for_setting, **attr)#: Set the arc (v_endpoint, u_endpoint), which equals setting the two endpoints adj(u_endpoint) = v_endpoint and vice-versa.

set_arcs_from(arcs_for_adding, **attr)#

Set the list of arcs. Can also add arcs as a string, e.g. “a0b1,a1b0” in this case also vertices are added if the nodes do not yet exist.

Parameters:: arcs_for_adding – a iterable of tuples (v_endpoint, u_endpoint) or a string like “a1b4,c2d3”.
Returns:: None

set_endpoint(endpoint_for_setting, adjacent_endpoint, create_using=<class 'knotpy.classes.endpoint.Endpoint'>, **attr)#

Set the endpoint to the adjacent endpoint and update the endpoint attributes.

Parameters:

endpoint_for_setting – Endpoint object or tuple (crossing name, position)
adjacent_endpoint – overwrite the endpoint with adjacent_endpoint (Endpoint object or tuple (crossing name, position))
create_using – if the type is not Endpoint (or IngoingEndpoint or OutgoingEndpoint), the class should be given, be default Endpoint is assumed if endpoint_for_setting is given as a tuple. If an Endpoint instance is given instead of a class, the instance type is used with attributes copied.
attr – additional attributes of the (adjacent) endpoint

Returns:

None

twin(endpoint) → Endpoint#

Return the opposite endpoint (twin) of an endpoint. Both endpoints form an arc.

Parameters:: endpoint – Endpoint instance or pair (node, position)
Returns:: twin endpoint instance

property vertices#: Node object holding the adjacencies of each crossing.

property virtual_crossings#

Return a view of all virtual crossings in the diagram.

Returns:: A filtered node view containing only virtual crossings.
Return type:: FilteredNodeView