random_events.sigma_algebra

random_events.sigma_algebra#

Attributes#

`EMPTY_SET_SYMBOL`
`SimpleSetContainer`

Classes#

`AbstractSimpleSet`	Abstract class for simple sets.
`AbstractCompositeSet`	Abstract class for composite sets.

Module Contents#

random_events.sigma_algebra.EMPTY_SET_SYMBOL = '∅'#

class random_events.sigma_algebra.AbstractSimpleSet#

Bases: random_events.utils.SubclassJSONSerializer, random_events.utils.CPPWrapper

Abstract class for simple sets.

Simple sets are sets that can be represented as a single object.

This class is a wrapper for the C++ class AbstractSimpleSet.

_cpp_object: random_events_lib.AbstractSimpleSet#: The C++ object that this class wraps.

intersection_with(other: typing_extensions.Self) → typing_extensions.Self#

Form the intersection of this object with another object.

Parameters:: other – The other SimpleSet
Returns:: The intersection of this set with the other set

complement() → SimpleSetContainer#

Returns:: The complement of this set as disjoint set of simple sets.

is_empty() → bool#

Returns:: Rather this set is empty or not.

abstract contains(item) → bool#: Check if this set contains an item. :param item: The item to check :return: Rather if the item is in the set or not

__hash__()#

abstract non_empty_to_string() → str#

Returns:: A string representation of this set if it is not empty.

difference_with(other: typing_extensions.Self) → SimpleSetContainer#

Form the difference of this object with another object.

Parameters:: other – The other SimpleSet
Returns:: The difference as a disjoint set of simple sets.

to_string()#

Returns:: A string representation of this set.

__str__()#

__repr__()#

__lt__(other: typing_extensions.Self)#

__eq__(other)#

abstract as_composite_set() → AbstractCompositeSet#

Convert this simple set to a composite set.

Returns:: The composite set

abstract __deepcopy__()#

class random_events.sigma_algebra.AbstractCompositeSet#

Bases: random_events.utils.SubclassJSONSerializer, random_events.utils.CPPWrapper, abc.ABC

Abstract class for composite sets.

AbstractCompositeSet is a set composed of a union of simple sets. If any operation is called on this, the resulting union will also be disjoint and simplified. A simplified composite set is a set with as few simple sets in it as possible to represent the necessary information.

This class wraps the C++ class AbstractCompositeSet.

_cpp_object: random_events_lib.AbstractCompositeSet#: The C++ object that this class wraps.

simple_set_example: AbstractSimpleSet#: An example of a simple set that is used to create new simple sets. Fields that are python only are read from this instance when reading from cpp.

property simple_sets: SimpleSetContainer#

Returns:: The simple sets contained in the union described by this set.

union_with(other: typing_extensions.Self) → typing_extensions.Self#

Parameters:: other – The other set
Returns:: The union of this set with the other set

__or__(other: typing_extensions.Self) → typing_extensions.Self#

intersection_with(other: typing_extensions.Self) → typing_extensions.Self#

Parameters:: other – The other set
Returns:: The intersection of this set with the other set

__and__(other) → typing_extensions.Self#

difference_with(other: typing_extensions.Self) → typing_extensions.Self#

Parameters:: other – The other set
Returns:: The difference of this set with the other set

__sub__(other) → typing_extensions.Self#

complement() → typing_extensions.Self#

Returns:: The complement of this set

__invert__() → typing_extensions.Self#

is_empty() → bool#

Returns:: If this set is empty or not.

contains(item) → bool#

Parameters:: item – The item to check
Returns:: If the item is in the set or not

__contains__(item) → bool#

to_string() → str#

Returns:: A string representation of this set.

__str__() → str#

__repr__() → str#

is_disjoint() → bool#

Returns:: If the union described by this is disjoint or not.

make_disjoint() → typing_extensions.Self#

Create an equal composite set that contains a disjoint union of simple sets.

Returns:: The disjoint set.

add_simple_set(simple_set: AbstractSimpleSet)#

Add a simple set to this composite set if it is not empty.

Parameters:: simple_set – The simple set to add

simplify() → typing_extensions.Self#

Simplify this set into an equivalent, more compact version.

Returns:: The simplified set

__eq__(other: typing_extensions.Self) → bool#

__hash__() → int#

__iter__() → typing_extensions.Iterable[AbstractSimpleSet]#

__lt__(other: typing_extensions.Self)#

Compare this set with another set. The sets are compared by comparing the simple sets in order. If the pair of simple sets are equal, the next pair is compared. If all pairs are equal, the set with the least amount of simple sets is considered smaller.

..note:: This does not define a total order in the mathematical sense. In the mathematical sense, this defines: a partial order.

Parameters:: other – The other set
Returns:: Rather this set is smaller than the other set

to_json() → Dict[str, Any]#

classmethod _from_json(data: Dict[str, Any]) → typing_extensions.Self#

Create a variable from a json dict. This method is called from the from_json method after the correct subclass is determined and should be overwritten by the respective subclass.

Parameters:: data – The json dict
Returns:: The deserialized object

__deepcopy__()#

random_events.sigma_algebra.SimpleSetContainer#