API Reference Topology¶

Classes:

Name	Description
`Edge`	The internal representaion of a graph edge.
`Node`	The internal representation of a graph node.
`Topology`	The internal representation of a topology graph.
`TopologyContainer`	The class representing a list of topologies.
`TopologyGenerator`	The main generator class of the topology module.
`TopologyModel`	A model containing only topological information, i.e. the allowed degrees of nodes.
`TopologySelector`	A selector class which determines whether a topology is to be kept or to be discarded. The available critera are

`Edge` ¶

The internal representaion of a graph edge.

Methods:

Name	Description
`momentum`	Get the internal representation of the edge's momentum. The function returns a list of integers, where
`nodes`	Get a list of the ids of the connected nodes.

`momentum() -> list[int]` ¶

Get the internal representation of the edge's momentum. The function returns a list of integers, where the i-th entry is the coefficient of the i-th momentum. The first n_ext momenta are external, the remaining momenta are the n_loops loop momenta.

`nodes() -> list[int]` ¶

Get a list of the ids of the connected nodes.

`Node` ¶

The internal representation of a graph node.

Methods:

Name	Description
`adjacent`	Get a list of the ids of the adjacent nodes.
`degree`	Get the degree of the node.

`adjacent() -> list[int]` ¶

Get a list of the ids of the adjacent nodes.

`degree() -> int` ¶

Get the degree of the node.

`Topology` ¶

The internal representation of a topology graph.

Methods:

Name	Description
`draw_tikz`	Draw the topology in the TikZ format
`edges`	Get a list of all nodes in the topology.
`nodes`	Get a list of all edges in the topology.
`symmetry_factor`	Get the topology's symmetry factor

`draw_tikz(path: str)` ¶

Draw the topology in the TikZ format

`edges() -> list[Edge]` ¶

Get a list of all nodes in the topology.

`nodes() -> list[Node]` ¶

Get a list of all edges in the topology.

`symmetry_factor() -> int` ¶

Get the topology's symmetry factor

`TopologyContainer` ¶

The class representing a list of topologies.

Methods:

Name	Description
`__getitem__`
`__len__`
`draw`	Draw the specified topologies into a large canvas. Returns an SVG string, which can be displayed e.g. in a
`query`	Query whether there is a topology in the container, which would be selected by `selector`.

`getitem(index: int) -> Topology` ¶

`len() -> int` ¶

`draw(topologies: list[int], n_cols: Optional[int] = 4) -> str` ¶

Draw the specified topologies into a large canvas. Returns an SVG string, which can be displayed e.g. in a Jupyter notebook.

Example:

from from IPython.display import SVG
from feyngraph.topology import TopologyGenerator, TopologyModel
topos = TopologyGenerator(4, 0, TopologyModel([3, 4]))
SVG(topos.draw(range(len(topos))))

Parameters:

Name	Type	Description	Default
`topologies`	`list[int]`	list of IDs of topologies to draw	required
`n_cols`	`Optional[int]`	number of topologies to draw in each row	`4`

`query(selector: TopologySelector)` ¶

Query whether there is a topology in the container, which would be selected by selector.

`TopologyGenerator` ¶

The main generator class of the topology module.

Examples:

model = TopologyModel([3, 4])
selector = TopologySelector()
selector.select_opi_components(1)
generator = TopologyGenerator(4, 3, model, selector)
topologies = generator.generate()
assert(len(topologies), 6166)

Methods:

Name	Description
`__new__`	Create a new topology generator.
`count`	Generate the topologies for the given configuration without saving them, only returning the total number.
`generate`	Generate the topologies for the given configuration.

`new(n_external: int, n_loops: int, model: TopologyModel, selector: Optional[TopologySelector] = None) -> TopologyGenerator` ¶

Create a new topology generator.

Parameters:

Name	Type	Description	Default
`selector`	`Optional[TopologySelector]`	the selector choosing whether a given topology is kept or discarded. If no selector is specified, all topologies are kept	`None`

`count() -> int` ¶

Generate the topologies for the given configuration without saving them, only returning the total number.

`generate() -> TopologyContainer` ¶

Generate the topologies for the given configuration.

`TopologyModel` ¶

A model containing only topological information, i.e. the allowed degrees of nodes.

Methods:

Name	Description
`__new__`	Create a new topology model containing nodes with degrees specified in `node_degrees`.

`new(node_degrees: list[int]) -> TopologyModel` ¶

Create a new topology model containing nodes with degrees specified in node_degrees.

`TopologySelector` ¶

A selector class which determines whether a topology is to be kept or to be discarded. The available critera are

node degrees: select only topologies for which the number of nodes with a specified degree matches any of the given counts
node partition: select only topologies matching any of the given node partitions, i.e. a topology for which the number of nodes of each degree exactly matches the count specified in the partition.
opi components: select only topologies for which the number of one-particle-irreducible components matches any of the given counts
custom functions: select only topologies for which any of the given custom functions return true

Methods:

Name	Description
`add_custom_function`	Add a constraint to only select topologies for which the given function returns `true`. The function receives
`clear`	Clear all criteria.
`select_node_degree`	Add a constraint to only select topologies which contain `selection` nodes of degree `degree`.
`select_node_degree_range`	Add a constraint to only select topologies which contain between `start` and `end` nodes of degree `degree`.
`select_node_partition`	Add a constraint to only select topologies for which the number of nodes of all given degree exactly matches
`select_on_shell`	Select only topologies with no self-energy insertions on external legs. This implementation considers internal
`select_opi_components`	Add a constraints to only select topologies with `opi_count` one-particle-irreducible components.
`select_self_loops`	Select only topologies containing exactly `n` self-loops.

`add_custom_function(py_function: Callable[[Topology], bool])` ¶

Add a constraint to only select topologies for which the given function returns true. The function receives a single topology as input and should return a boolean.

Examples:

def no_self_loop(topo: feyngraph.topology.Topology) -> bool:
    return any(edge.get_nodes()[0] == edge.get_nodes()[1] for edge in topo.get_edges())

selector = feyngraph.topology.TopologySelector()
selector.add_custom_function(no_self_loop)

`clear()` ¶

Clear all criteria.

`select_node_degree(degree: int, selection: int)` ¶

Add a constraint to only select topologies which contain selection nodes of degree degree.

`select_node_degree_range(degree: int, start: int, end: int)` ¶

Add a constraint to only select topologies which contain between start and end nodes of degree degree.

`select_node_partition(partition: list[tuple[int, int]])` ¶

Add a constraint to only select topologies for which the number of nodes of all given degree exactly matches he specified count.

Examples:

selector = TopologySelector()
# Select only topologies containing exactly four nodes of degree 3 and one node of degree 4
selector.select_node_partition([(3, 4), (4, 1)])

`select_on_shell()` ¶

Select only topologies with no self-energy insertions on external legs. This implementation considers internal edges carrying a single external momentum and no loop momentum, which is equivalent to a self-energy insertion on an external edge.

`select_opi_components(opi_count: int)` ¶

Add a constraints to only select topologies with opi_count one-particle-irreducible components.

`select_self_loops(n: int)` ¶

Select only topologies containing exactly n self-loops.

API Reference Topology¶

Edge ¶

momentum() -> list[int] ¶

nodes() -> list[int] ¶

Node ¶

adjacent() -> list[int] ¶

degree() -> int ¶

Topology ¶

draw_tikz(path: str) ¶

edges() -> list[Edge] ¶

nodes() -> list[Node] ¶

symmetry_factor() -> int ¶

TopologyContainer ¶

__getitem__(index: int) -> Topology ¶

__len__() -> int ¶

draw(topologies: list[int], n_cols: Optional[int] = 4) -> str ¶

query(selector: TopologySelector) ¶

TopologyGenerator ¶

__new__(n_external: int, n_loops: int, model: TopologyModel, selector: Optional[TopologySelector] = None) -> TopologyGenerator ¶

count() -> int ¶

generate() -> TopologyContainer ¶

TopologyModel ¶

__new__(node_degrees: list[int]) -> TopologyModel ¶

TopologySelector ¶

add_custom_function(py_function: Callable[[Topology], bool]) ¶

clear() ¶

select_node_degree(degree: int, selection: int) ¶

select_node_degree_range(degree: int, start: int, end: int) ¶

select_node_partition(partition: list[tuple[int, int]]) ¶

select_on_shell() ¶

select_opi_components(opi_count: int) ¶

select_self_loops(n: int) ¶

`Edge` ¶

`momentum() -> list[int]` ¶

`nodes() -> list[int]` ¶

`Node` ¶

`adjacent() -> list[int]` ¶

`degree() -> int` ¶

`Topology` ¶

`draw_tikz(path: str)` ¶

`edges() -> list[Edge]` ¶

`nodes() -> list[Node]` ¶

`symmetry_factor() -> int` ¶

`TopologyContainer` ¶

`getitem(index: int) -> Topology` ¶

`len() -> int` ¶

`draw(topologies: list[int], n_cols: Optional[int] = 4) -> str` ¶

`query(selector: TopologySelector)` ¶

`TopologyGenerator` ¶

`new(n_external: int, n_loops: int, model: TopologyModel, selector: Optional[TopologySelector] = None) -> TopologyGenerator` ¶

`count() -> int` ¶

`generate() -> TopologyContainer` ¶

`TopologyModel` ¶

`new(node_degrees: list[int]) -> TopologyModel` ¶

`TopologySelector` ¶

`add_custom_function(py_function: Callable[[Topology], bool])` ¶

`clear()` ¶

`select_node_degree(degree: int, selection: int)` ¶

`select_node_degree_range(degree: int, start: int, end: int)` ¶

`select_node_partition(partition: list[tuple[int, int]])` ¶

`select_on_shell()` ¶

`select_opi_components(opi_count: int)` ¶

`select_self_loops(n: int)` ¶