Tuple: Mathematical Tuple

In set6: R6 Mathematical Sets Interface

Description

A general Tuple object for mathematical tuples, inheriting from Set.

Details

Tuples are similar to sets, except that they drop the constraint for elements to be unique, and ordering in a tuple does matter. Tuples are useful for methods including $contains that may require non-unique elements. They are also the return type of the product of sets. See examples.

Super class

set6::Set -> Tuple

Methods

Public methods

• Tuple$equals()

• Tuple$isSubset()

• Tuple$clone()

Inherited methods

• set6::Set$add()

• set6::Set$contains()

• set6::Set$initialize()

• set6::Set$multiplicity()

• set6::Set$print()

• set6::Set$remove()

• set6::Set$strprint()

• set6::Set$summary()

---

Method equals()

Tests if two sets are equal.

Usage

Tuple$equals(x, all = 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.

Details

An object is equal to a Tuple if it contains all the same elements, and in the same order. Infix operators can be used for:

Equal	==
Not equal	!=

Returns

If all is TRUE then returns TRUE if all x are equal to the Set, otherwise FALSE. If all is FALSE then returns a vector of logicals corresponding to each individual element of x.

Examples

Tuple$new(1,2) ==  Tuple$new(1,2)
Tuple$new(1,2) != Tuple$new(1,2)
Tuple$new(1,1) != Set$new(1,1)

---

Method isSubset()

Test if one set is a (proper) subset of another

Usage

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

Arguments

x

any. Object or vector of objects to test.

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.

Details

If using the method directly, and not via one of the operators then the additional boolean argument proper can be used to specify testing of subsets or proper subsets. A Set is a proper subset of another if it is fully contained by the other Set (i.e. not equal to) whereas a Set is a (non-proper) subset if it is fully contained by, or equal to, the other Set.

When calling $isSubset on objects inheriting from Interval, the method treats the interval as if it is a Set, i.e. ordering and class are ignored. Use $isSubinterval to test if one interval is a subinterval of another.

Infix operators can be used for:

Subset	<
Proper Subset	<=
Superset	>
Proper Superset	>=

An object is a (proper) subset of a Tuple if it contains all (some) of the same elements, and in the same order.

Returns

If all is TRUE then returns TRUE if all x are subsets of the Set, otherwise FALSE. If all is FALSE then returns a vector of logicals corresponding to each individual element of x.

Examples

Tuple$new(1,2,3) < Tuple$new(1,2,3,4)
Tuple$new(1,3,2) < Tuple$new(1,2,3,4)

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Tuple$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

See Also

Other sets: ConditionalSet, FuzzyMultiset, FuzzySet, FuzzyTuple, Interval, Multiset, Set

Examples

# Tuple of integers
Tuple$new(1:5)

# Tuple of multiple types
Tuple$new("a", 5, Set$new(1), Tuple$new(2))

# Each Tuple has properties and traits
t <- Tuple$new(1, 2, 3)
t$traits
t$properties

# Elements can be duplicated
Tuple$new(2, 2) != Tuple$new(2)

# Ordering does matter
Tuple$new(1, 2) != Tuple$new(2, 1)

## ------------------------------------------------
## Method `Tuple$equals`
## ------------------------------------------------

Tuple$new(1,2) ==  Tuple$new(1,2)
Tuple$new(1,2) != Tuple$new(1,2)
Tuple$new(1,1) != Set$new(1,1)

## ------------------------------------------------
## Method `Tuple$isSubset`
## ------------------------------------------------

Tuple$new(1,2,3) < Tuple$new(1,2,3,4)
Tuple$new(1,3,2) < Tuple$new(1,2,3,4)

set6 documentation built on Oct. 18, 2021, 5:06 p.m.