Set of Complements

ComplementSet class for symbolic complement of mathematical sets.

Details

The purpose of this class is to provide a symbolic representation for the complement 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: ExponentSet, PowersetSet, ProductSet, UnionSet

Super classes

set6::Set -> set6::SetWrapper -> ComplementSet

Active bindings

elements

Returns the elements in the object.

length

Returns the number of elements in the object.

addedSet

For the ComplementSet wrapper, X-Y, returns the set X.

subtractedSet

For the ComplementSet wrapper, X-Y, returns the set Y.

Methods

Public methods

• ComplementSet$new()

• ComplementSet$strprint()

• ComplementSet$contains()

• ComplementSet$clone()

Inherited methods

• set6::Set$add()

• set6::Set$multiplicity()

• set6::Set$print()

• set6::Set$remove()

• set6::Set$summary()

• set6::SetWrapper$equals()

• set6::SetWrapper$isSubset()

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Method new()

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

Usage

ComplementSet$new(addset, subtractset, lower = NULL, upper = NULL, type = NULL)

Arguments

addset

Set to be subtracted from.

subtractset

Set to subtract.

lower

lower bound of new object.

upper

upper bound of new object.

type

closure type of new object.

Returns

A new ComplementSet object.

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Method strprint()

Creates a printable representation of the object.

Usage

ComplementSet$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.

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Method contains()

Tests if elements x are contained in self.

Usage

ComplementSet$contains(x, all = FALSE, bound = FALSE)

Arguments

x

Set or vector of Sets.

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.

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Method clone()

The objects of this class are cloneable with this method.

Usage

ComplementSet$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.