PBR¶

This page contains the documentation for functionality in libsemigroups_pybind11 for PBR. Partitioned binary relations (PBRs) are a generalisation of bipartitions, which were introduced by Martin and Mazorchuk.

`PBR`	Copy constructor.
`PBR.__getitem__`	Returns the nodes adjacent to the given node.
`PBR.__eq__`	Equality comparison.
`PBR.__lt__`	Less than comparison.
`PBR.__mul__`	Right multiply `self` by `that`.
`PBR.degree`	Returns the degree of a PBR.
`PBR.identity`	Returns the identity `PBR` with degree `degree()`.
`PBR.make`	Overloaded function.
`PBR.make_identity`	Returns the identity `PBR` with specified degree.
`PBR.product_inplace`	Multiply two `PBR` objects and store the product in `self`.

class PBR(self: _libsemigroups_pybind11.PBR, that: _libsemigroups_pybind11.PBR)¶

Copy constructor.

Parameters: that (PBR) -- the PBR to copy.

__eq__(self: _libsemigroups_pybind11.PBR, that: _libsemigroups_pybind11.PBR) → bool¶

Equality comparison.

Returns True if self equals that by comparing their image values.

Parameters: that (PBR) -- the PBR for comparison.
Returns: A bool.

__getitem__(self: _libsemigroups_pybind11.PBR, i: int) → List[int]¶

Returns the nodes adjacent to the given node.

Parameters: i (int) -- an integer
Returns: A int.

__lt__(self: _libsemigroups_pybind11.PBR, that: _libsemigroups_pybind11.PBR) → bool¶

Less than comparison.

Returns True if self is less than that.

Parameters: that (PBR) -- the PBR for comparison.
Returns: A bool.

__mul__(self: _libsemigroups_pybind11.PBR, that: _libsemigroups_pybind11.PBR) → _libsemigroups_pybind11.PBR¶

Right multiply self by that.

Parameters: that (PBR) -- the PBR to multiply with.
Returns: A PBR.

degree(self: _libsemigroups_pybind11.PBR) → int¶

Returns the degree of a PBR.

Parameters: None.
Returns: An int.

identity(self: _libsemigroups_pybind11.PBR) → _libsemigroups_pybind11.PBR¶

Returns the identity PBR with degree degree().

Parameters: None.
Returns: A PBR.

static make(*args, **kwargs)¶

Overloaded function.

make(left: List[List[int]], right: List[List[int]]) -> _libsemigroups_pybind11.PBR
Construct and validate.
Parameters
left (List[List[int]]) - the 1st argument to forward to the constructor.

right (List[List[int]]) - the 2nd argument to forward to the constructor.
Returns

A PBR constructed from left and right, and validated.
make(adj: List[List[int]]) -> _libsemigroups_pybind11.PBR
Construct and validate.
Parameters
adj (List[List[int]]) - the list of adjacencies.
Returns

A new PBR.

static make_identity(n: int) → _libsemigroups_pybind11.PBR¶

Returns the identity PBR with specified degree.

Parameters: n (int) - the degree.
Returns: A PBR.

product_inplace(self: _libsemigroups_pybind11.PBR, x: _libsemigroups_pybind11.PBR, y: _libsemigroups_pybind11.PBR, thread_id: int) → None¶

Multiply two PBR objects and store the product in self.

Parameters

x (PBR) -- a PBR.
y (PBR) -- a PBR.
thread_id (int) -- the index of the calling thread (defaults to 0).

Returns

(None)