Sets

Constraining Order contains DataStructures to represent sets of discrete elements and real numbers.

A DiscreteSet is a wrapper around pythons builtin frozenset. The main difference is that a DiscreteSet can represent a set of all possible elements.

In addition, there are data structures to represent sets of real numbers, in form of connected Intervals and collections of such intervals, called IntervalSet.

DiscreteSet

class constrainingorder.sets.DiscreteSet(elements)

A set data structure for hashable elements

This is a wrapper around pythons set type, which additionally provides the possibility to express the set of everything (which only makes sense sometimes).

__contains__(element)

Check membership of the element.

Parameters:element – Element to check membership of Return type:bool

__init__(elements)

Create a new DiscreteSet

Parameters:elements (sequence) – The elements of the newly created set

difference(other)

Return a new DiscreteSet with the difference of the two sets, i.e. all elements that are in self but not in other.

Parameters:other (DiscreteSet) – Set to subtract Return type:DiscreteSet Raises ValueError:  if self is a set of everything

classmethod everything()

Create a new set of everything.

One can not iterate over the elements of this set, but many operations are actually well defined and useful.

intersection(other)

Return a new DiscreteSet with the intersection of the two sets, i.e. all elements that are in both self and other.

Parameters:other (DiscreteSet) – Set to intersect with Return type:DiscreteSet

is_discrete()

Check whether the set is discrete, i.e. if iter_members() can be used.

Return type:bool

is_empty()

Check whether the set is empty

Return type:bool

iter_members()

Iterate over all elements of the set.

Raises ValueError:  if self is a set of everything

union(other)

Return a new DiscreteSet with the union of the two sets, i.e. all elements that are in self or in other.

Parameters:other (DiscreteSet) – Set to unite with Return type:DiscreteSet

Interval

class constrainingorder.sets.Interval(bounds, included)

An interval on the real axis.

__contains__(x)

Check membership of the element.

Parameters:x (float) – Element to check membership of Return type:bool

__init__(bounds, included)

Create a new Interval with bounds. If the right bound is larger than the left bound, the interval is assumed to be empty.

Parameters:

• bounds (sequence) – left and right bounds
• included (sequence) – bools indicating whether the bounds are included in the interval.

classmethod closed(a, b)

Create a new closed Interval.

Parameters:

• a (float) – Left bound
• b (float) – Right bound

classmethod everything()

Create a new Interval representing the full real axis

classmethod from_value(value)

Create a new Interval representing a single real number.

Parameters:value (float) – The member of the Interval

get_point()

Return the number contained in this interval.

Return type:float Raises ValueError:  if Interval contains more than exactly one number.

intersection(other)

Return a new Interval with the intersection of the two intervals, i.e. all elements that are in both self and other.

Parameters:other (Interval) – Interval to intersect with Return type:Interval

is_discrete()

Check whether this interval contains exactly one number

Return type:bool

is_disjoint(other)

Check whether two Intervals are disjoint.

Parameters:other (Interval) – The Interval to check disjointedness with.

is_empty()

Check whether this interval is empty.

Return type:bool

classmethod leftopen(a, b)

Create a new halfopen Interval (left bound is excluded, right bound included).

Parameters:

• a (float) – Left bound
• b (float) – Right bound

classmethod open(a, b)

Create a new open Interval.

Parameters:

• a (float) – Left bound
• b (float) – Right bound

classmethod rightopen(a, b)

Create a new halfopen Interval (right bound is excluded, left bound included).

Parameters:

• a (float) – Left bound
• b (float) – Right bound

IntervalSet

class constrainingorder.sets.IntervalSet(ints)

A set of intervals to represent quite general sets in R

__contains__(x)

Check membership of the element.

Parameters:element – Element to check membership of Return type:bool

__init__(ints)

Create a new IntervalSet.

Parameters:ints (sequence) – Intervals for this IntervalSet

difference(other)

Return a new IntervalSet with the difference of the two sets, i.e. all elements that are in self but not in other.

Parameters:other (IntervalSet) – Set to subtract Return type:IntervalSet

classmethod everything()

Create a new IntervalSet representing the full real axis.

classmethod from_values(values)

Create a new IntervalSet representing a set of isolated real numbers.

Parameters:values (sequence) – The values for this IntervalSet

intersection(other)

Return a new IntervalSet with the intersection of the two sets, i.e. all elements that are both in self and other.

Parameters:other (IntervalSet) – Set to intersect with Return type:IntervalSet

is_discrete()

Check whether this IntervalSet contains only isolated numbers.

Return type:bool

is_empty()

Check whether this IntervalSet is empty.

Return type:bool

iter_members()

Iterate over all elements of the set.

Raises ValueError:  if self is a set of everything

union(other)

Return a new IntervalSet with the union of the two sets, i.e. all elements that are in self or other.

Parameters:other (IntervalSet) – Set to intersect with Return type:IntervalSet