BMat8¶

Class for fast boolean matrices of dimension up to 8 x 8

The functions for these small matrices over the boolean semiring are more optimised than the generic methods for boolean matrices. Note that all BMat8 are represented internally as an 8 x 8 matrix; any entries not defined by the user are taken to be 0. This does not affect the results of any calculations.

BMat8 objects can be constructed using:

No parameters (uninitialized)
An integer (the binary representation of which corresponds to the matrix)
A list of n lists of truthy or falsy values, each sublist must have length n also.

See the libsemigroups documentation for further details.

class BMat8(*args, **kwargs)¶

Overloaded function.

__init__(self: _libsemigroups_pybind11.BMat8) -> None

Returns an uninitialised BMat8.
__init__(self: _libsemigroups_pybind11.BMat8, arg0: int) -> None
__init__(self: _libsemigroups_pybind11.BMat8, arg0: _libsemigroups_pybind11.BMat8) -> None
__init__(self: _libsemigroups_pybind11.BMat8, arg0: List[List[bool]]) -> None

col_space_basis(self: _libsemigroups_pybind11.BMat8) → _libsemigroups_pybind11.BMat8¶

This method returns a BMat8 whose non-zero columns form a basis for the column space of self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.col_space_basis()
10000000
01000000
00000000
00000000
00000000
00000000
00000000
00000000

column_space_size(self: _libsemigroups_pybind11.BMat8) → int¶

Returns the size of the row space of self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.column_space_size()
4

get(self: _libsemigroups_pybind11.BMat8, i: int, j: int) → bool¶

Returns the entry in the (i, j)th position.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.get(0, 1)
True
>>> x.get(1, 1)
False

is_regular_element(self: _libsemigroups_pybind11.BMat8) → bool¶

Check whether self is a regular element of the full boolean matrix monoid of appropriate dimension.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.is_regular_element()
True

minimum_dim(self: _libsemigroups_pybind11.BMat8) → int¶

This method returns the maximal i such that row i or column i contains a 1.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.minimum_dim()
2

number_of_cols(self: _libsemigroups_pybind11.BMat8) → int¶

Returns the number of non-zero columns in self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.number_of_cols()
2

number_of_rows(self: _libsemigroups_pybind11.BMat8) → int¶

Returns the number of non-zero rows in self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.number_of_rows()
2

one(self: int) → _libsemigroups_pybind11.BMat8¶

This method returns the BMat8 with the first dim entries in the main diagonal equal to 1 and every other value equal to 0.

>>> from libsemigroups_pybind11 import BMat8
>>> BMat8.one(4)
10000000
01000000
00100000
00010000
00000000
00000000
00000000
00000000

static random(*args, **kwargs)¶

Overloaded function.

random() -> _libsemigroups_pybind11.BMat8
random(arg0: int) -> _libsemigroups_pybind11.BMat8

row_space_basis(self: _libsemigroups_pybind11.BMat8) → _libsemigroups_pybind11.BMat8¶

This method returns a BMat8 whose non-zero rows form a basis for the row space of self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.row_space_basis()
10000000
01000000
00000000
00000000
00000000
00000000
00000000
00000000

row_space_size(self: _libsemigroups_pybind11.BMat8) → int¶

Returns the size of the row space of self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.row_space_size()
4

rows(self: _libsemigroups_pybind11.BMat8) → List[int]¶

This method returns a list of integers representing the rows of self. The list will always be of length 8, even if self was constructed with fewer rows.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.rows()
[64, 128, 0, 0, 0, 0, 0, 0]

set(self: _libsemigroups_pybind11.BMat8, i: int, j: int, val: bool) → None¶

Sets the (i, j)th entry to val.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.set(1,1,1)
>>> x
01000000
11000000
00000000
00000000
00000000
00000000
00000000
00000000

swap(self: _libsemigroups_pybind11.BMat8, other: _libsemigroups_pybind11.BMat8) → None¶

Swaps the contents of self and other.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> y = BMat8([[1, 1], [0, 0]])
>>> BMat8.swap(x,y)
>>> x
11000000
00000000
00000000
00000000
00000000
00000000
00000000
00000000

>>> y
01000000
10000000
00000000
00000000
00000000
00000000
00000000
00000000

to_int(self: _libsemigroups_pybind11.BMat8) → int¶

Returns the integer representation of the BMat8, that is an integer obtained by interpreting an 8 x 8 BMat8 as a sequence of 64 bits (reading rows left to right, from top to bottom) and then realising this sequence as an integer.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[0, 1], [1, 0]])
>>> x.to_int()
4647714815446351872

transpose(self: _libsemigroups_pybind11.BMat8) → _libsemigroups_pybind11.BMat8¶

Returns the transpose of self.

>>> from libsemigroups_pybind11 import BMat8
>>> x = BMat8([[1, 0], [1, 0]])
>>> x.transpose()
11000000
00000000
00000000
00000000
00000000
00000000
00000000
00000000