The PBR class

Class for representing PBRs.

Partitioned binary relations (PBRs) are a generalisation of a bipartitions, and were introduced by Martin and Mazorchuk in [MM11].

Contents

`PBR`	Class for representing PBRs.
`PBR.copy`(…)	Copy a `PBR` object.
`PBR.degree`(…)	Returns the degree of a `PBR`.
`PBR.number_of_points`(…)	Returns the number of points of a `PBR`.
`PBR.product_inplace`(…)	Multiply two PBR objects and store the product in self.

Full API

class PBR

__init__(*args, **kwargs)

Overloaded function.

__init__(self: PBR, n: int) → None

Construct empty PBR of given degree.

Parameters:: n (int) – the degree

__init__(self: PBR, left: list[list[int]], right: list[list[int]]) → None

Construct from adjacencies 1 to n and -1 to -n.

Construct from adjacencies 1 to n and -1 to -n. The parameters left and right should be containers of n lists of integer values, so that the list in position i of left is the list of points adjacent to i in the PBR, and the list in position i of right is the list of points adjacent to n + i in the PBR. A negative value i corresponds to n - i.

Parameters:

left (list[list[int]]) – container of adjacencies of 1 to n
right (list[list[int]]) – container of adjacencies of n + 1 to 2n.

Raises:

LibsemigroupsError –

if the resultant PBR:

would not describe a binary relation on an even number of points; or
would have a point related to a point that is greater than PBR.degree;

__init__(self: PBR, x: list[list[int]]) → None

Construct from adjacencies 0 to 2n - 1.

Construct from adjacencies 0 to 2n - 1. The parameter x must be a container of lists of int with size 2n for some integer n, and the list in position i is the list of points adjacent to i in the PBR constructed.

Parameters:

x (list[list[int]]) – the container of lists of adjacencies.

Raises:

LibsemigroupsError –

if the resultant PBR:

would not describe a binary relation on an even number of points; or
would have a point related to a point that is greater than PBR.degree;
x contains a list of points related to a point that is not sorted.

copy(self: PBR) → PBR

Copy a PBR object.

Returns:: A copy.
Return type:: PBR

degree(self: PBR) → int

Returns the degree of a PBR.

Returns the degree of a PBR, where the degree of a PBR is half the number of points in the PBR.

Returns:: The degree of the PBR.
Return type:: int
Complexity:: Constant.

number_of_points(self: PBR) → int

Returns the number of points of a PBR.

Returns:: A value of type int.
Return type:: int
Complexity:: Constant.

product_inplace(self: PBR, x: PBR, y: PBR, thread_id: int) → None

Multiply two PBR objects and store the product in self.

The parameter thread_id is required since some temporary storage is required to find the product of x and y. Note that if different threads call this member function with the same value of thread_id then bad things will happen.

Parameters:

x (PBR) – the left multiplicand.
y (PBR) – the right multiplicand.
thread_id (int) – the index of the calling thread (defaults to 0).

Raises:

LibsemigroupsError – if: * the PBR.degree of x is not the same as the PBR.degree of y; * the PBR.degree of self is not the same as the PBR.degree of x; or * either x or y is the same object as self.