ogposets.GrSet

class rewalt.ogposets.GrSet(*elements)

Bases: object

Class for sets of elements of an oriented graded poset, graded by their dimension.

Objects of the class behave as sets; several methods of the set class are supported. However the data is stored in a way that allows fast access to elements of a given dimension.

Parameters: elements (El) – Any number of elements.

Examples

We create an instance by listing elements; repetitions do not count.

>>> test = GrSet(El(0, 2), El(0, 2), El(0, 3), El(2, 0), El(3, 1))
>>> test
GrSet(El(0, 2), El(0, 3), El(2, 0), El(3, 1))
>>> len(test)
4

We can access the subsets of elements of given dimensions with indexer operators. These support slice syntax.

>>> test[0]
GrSet(El(0, 2), El(0, 3))
>>> test[0:3]
GrSet(El(0, 2), El(0, 3), El(2, 0))

The iterator for graded sets goes through the elements in increasing dimension and, for each dimension, in increasing position.

>>> for x in test:
...     print(x)
...
El(0, 2)
El(0, 3)
El(2, 0)
El(3, 1)

We can add and remove elements.

>>> test.remove(El(0, 3))
>>> test
GrSet(El(0, 2), El(2, 0), El(3, 1))
>>> test.add(El(1, 1))
>>> test
GrSet(El(0, 2), El(1, 1), El(2, 0), El(3, 1))

Set methods such as union, difference, and intersection are available with the same syntax.

Methods

`add`(element)	Adds a single element.
`copy`()	Returns a copy of the graded set.
`difference`(other)	Returns the difference of the graded set with another graded set.
`intersection`(*others)	Returns the intersection of the graded set with other graded sets.
`isdisjoint`(other)	Returns whether the graded set is disjoint from another.
`issubset`(other)	Returns whether the graded set is a subset of another.
`remove`(element)	Removes a single element.
`union`(*others)	Returns the union of the graded set with other graded sets.

Attributes

`as_list`	Returns the list of elements in increasing dimension, and, dimensionwise, in increasing position.
`as_set`	Returns a Python set containing the same elements.
`dim`	Returns the maximal dimension in which the graded set is not empty, or -1 if it is empty.
`grades`	Returns the list of dimensions in which the graded set is not empty.

property grades

Returns the list of dimensions in which the graded set is not empty.

Returns: grades – The list of dimensions in which the graded set is not empty.
Return type: list[int]

property dim

Returns the maximal dimension in which the graded set is not empty, or -1 if it is empty.

Returns: dim – The maximal dimension in which the graded set is not empty.
Return type: int

property as_set

Returns a Python set containing the same elements.

Returns: as_set – A Python set containing the same elements.
Return type: set[El]

property as_list

Returns the list of elements in increasing dimension, and, dimensionwise, in increasing position.

Returns: as_list – A list containing the same elements.
Return type: list[El]

add(element)

Adds a single element.

Parameters: element (El) – The element to add.

remove(element)

Removes a single element.

Parameters: element (El) – The element to remove.

union(*others)

Returns the union of the graded set with other graded sets.

Parameters: *others (GrSet) – Any number of graded sets.
Returns: union – The union of the graded set with all the given others.
Return type: GrSet

intersection(*others)

Returns the intersection of the graded set with other graded sets.

Parameters: *others (GrSet) – Any number of graded sets.
Returns: intersection – The intersection of the graded set with all the given others.
Return type: GrSet

difference(other)

Returns the difference of the graded set with another graded set.

Parameters: other (GrSet) – Another graded set.
Returns: difference – The difference between the two graded sets.
Return type: GrSet

issubset(other)

Returns whether the graded set is a subset of another.

Parameters: other (GrSet) – Another graded set.
Returns: issubset – True if and only self is a subset of other.
Return type: bool

isdisjoint(other)

Returns whether the graded set is disjoint from another.

Parameters: other (GrSet) – Another graded set.
Returns: isdisjoint – True if and only self and other are disjoint.
Return type: bool

copy()

Returns a copy of the graded set.

Returns: copy – A copy of the graded set.
Return type: GrSet