Set of Powersets

PowersetSet class for symbolic powerset of mathematical sets.

Details

The purpose of this class is to provide a symbolic representation for the powerset of sets that cannot be represented in a simpler class. Whilst this is not an abstract class, it is not recommended to construct this class directly but via the set operation methods.

See also

Set operations: setunion, setproduct, setpower, setcomplement, setsymdiff, powerset, setintersect

Other wrappers: ComplementSet, ExponentSet, ProductSet, UnionSet

Super classes

set6::Set -> set6::SetWrapper -> set6::ProductSet -> PowersetSet

Methods

Public methods

• PowersetSet$new()

• PowersetSet$strprint()

• PowersetSet$contains()

• PowersetSet$isSubset()

• PowersetSet$clone()

Inherited methods

• set6::Set$add()

• set6::Set$multiplicity()

• set6::Set$print()

• set6::Set$remove()

• set6::Set$summary()

• set6::SetWrapper$equals()

---

Method new()

Create a new PowersetSet object. It is not recommended to construct this class directly.

Usage

PowersetSet$new(set)

Arguments

set

Set to wrap.

Returns

A new PowersetSet object.

---

Method strprint()

Creates a printable representation of the object.

Usage

PowersetSet$strprint(n = 2)

Arguments

n

numeric. Number of elements to display on either side of ellipsis when printing.

Returns

A character string representing the object.

---

Method contains()

Tests if elements x are contained in self.

Usage

PowersetSet$contains(x, all = FALSE, bound = NULL)

Arguments

x

Set or vector of Sets.

x

Set or vector of Sets.

all

logical. If FALSE tests each x separately. Otherwise returns TRUE only if all x pass test.

all

logical. If FALSE tests each x separately. Otherwise returns TRUE only if all x pass test.

bound

logical

Returns

If all == TRUE then returns TRUE if all x are contained in self, otherwise FALSE. If all == FALSE returns a vector of logicals corresponding to the length of x, representing if each is contained in self. If bound == TRUE then an element is contained in self if it is on or within the (possibly-open) bounds of self, otherwise TRUE only if the element is within self or the bounds are closed.

---

Method isSubset()

Tests if x is a (proper) subset of self.

Usage

PowersetSet$isSubset(x, proper = FALSE, all = FALSE)

Arguments

x

Set or vector of Sets.

x

Set or vector of Sets.

proper

logical. If TRUE tests for proper subsets.

all

logical. If FALSE tests each x separately. Otherwise returns TRUE only if all x pass test.

all

logical. If FALSE tests each x separately. Otherwise returns TRUE only if all x pass test.

Returns

If all == TRUE then returns TRUE if all x are (proper) subsets of self, otherwise FALSE. If all == FALSE returns a vector of logicals corresponding to the length of x, representing if each is a (proper) subset of self.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

PowersetSet$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.