Bipartition¶

This page contains the documentation for functionality in libsemigroups_pybind11 for bipartitions.

`Bipartition`	A bipartition is a partition of the set \(\{0, ..., 2n - 1\}\) for some non-negative integer \(n\) see the Semigroups package for GAP documentation for more details.
`Bipartition.__getitem__`	Returns the index of the block containing a value.
`Bipartition.__eq__`	Equality comparison.
`Bipartition.__lt__`	Less than comparison.
`Bipartition.__mul__`	Right multiply `self` by `that`.
`Bipartition.degree`	Returns the degree of the `Bipartition`.
`Bipartition.identity`	Returns an identity bipartition.
`Bipartition.left_blocks`	Returns an iterator pointing to the index of the first left
`Bipartition.make`	Validates the arguments, constructs a bipartition and validates it.
`Bipartition.make_identity`	Returns an identity bipartition.
`Bipartition.product_inplace`	Modify the current bipartition in-place to contain the product of two bipartitions.
`Bipartition.rank`	Returns the number of transverse blocks.
`Bipartition.right_blocks`	Returns an iterator pointing to the index of the first right block.

class Bipartition(self: _libsemigroups_pybind11.Bipartition, arg0: _libsemigroups_pybind11.Bipartition)¶

A bipartition is a partition of the set \(\{0, ..., 2n - 1\}\) for some non-negative integer \(n\) see the Semigroups package for GAP documentation for more details.

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

Equality comparison.

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

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

__getitem__(self: _libsemigroups_pybind11.Bipartition, i: int) → int¶

Returns the index of the block containing a value.

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

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

Less than comparison.

Returns True if self is less than that.

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

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

Right multiply self by that.

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

degree(self: _libsemigroups_pybind11.Bipartition) → int¶

Returns the degree of the Bipartition.

Parameters: None.
Returns: An int.

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

Returns an identity bipartition.

Returns: A newly constructed Bipartition.

is_transverse_block(self: _libsemigroups_pybind11.Bipartition, index: int) → bool¶

Check if a block is a transverse block.

Parameters: index (int) -- the index of a block
Returns: A bool.

left_blocks(self: _libsemigroups_pybind11.Bipartition) → Iterator¶

Returns an iterator pointing to the index of the first left block.

Parameters: None.
Returns: An iterator.

lookup(self: _libsemigroups_pybind11.Bipartition) → List[bool]¶

Returns a list whose i-th entry indicates whether or not the block with index i is transverse or not.

Parameters: None.
Returns: A list.

static make(arg0: List[int]) → _libsemigroups_pybind11.Bipartition¶: Validates the arguments, constructs a bipartition and validates it.

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

Returns an identity bipartition.

Parameters: n (int) - the degree of the identity to be returned.
Returns: A newly constructed Bipartition.

number_of_blocks(self: _libsemigroups_pybind11.Bipartition) → int¶

Returns the number of blocks in a Bipartition.

Parameters: None.
Returns: An int.

number_of_left_blocks(self: _libsemigroups_pybind11.Bipartition) → int¶

Returns the number of blocks containing a positive integer.

Parameters: None.
Returns: An int.

number_of_right_blocks(self: _libsemigroups_pybind11.Bipartition) → int¶

Returns the number of blocks containing a negative integer.

Parameters: None.
Returns: An int.

product_inplace(self: _libsemigroups_pybind11.Bipartition, x: _libsemigroups_pybind11.Bipartition, y: _libsemigroups_pybind11.Bipartition, thread_id: int = 0) → None¶

Modify the current bipartition in-place to contain the product of two bipartitions.

Parameters

x (Bipartition) -- the first bipartition to multiply
y (Bipartition) -- the second bipartition to multiply
thread_id (int) -- the index of the calling thread (defaults to 0)

Returns

(None)

rank(self: _libsemigroups_pybind11.Bipartition) → int¶

Returns the number of transverse blocks.

Parameters: None.
Returns: An int

right_blocks(self: _libsemigroups_pybind11.Bipartition) → Iterator¶

Returns an iterator pointing to the index of the first right block.

Parameters: None.
Returns: An iterator.