relations (version 0.1-0)

set: Sets

Description

Creation and manipulation of sets.

Usage

set(...)
as.set(x)
is.set(x)
set_is_empty(x)
set_is_subset(a, b)
set_is_proper_subset(a, b)
set_is_equal(a, b)
set_is_element(e, b)
set_union(...)
set_intersection(...)
set_symdiff(...)
set_complement(a, b)
set_power(x)
set_cartesian(...)
set_combn(x, m)

Arguments

x

For as.set() and is.set(): an Robject. A set object otherwise.

a, b

Set objects.

e

An Robject.

m

Number of elements to choose.

...

For set(): Robjects, and set objects otherwise.

Details

These functions represent basic infrastructure for handling sets of general (R) objects. The set_is_foo() predicates are vectorized. In addition to the methods defined, one can use the following operators: + and | for the union, - for the complement, & for the intersection, %D% for the symmetric difference, * and ^n for the ($n$-fold) cartesian product, 2^ for the power set, %e% for the element-of predicate, < and <=< code=""> for the (proper) subset predicate, > and >= for the (proper) superset predicate, and == and != for (in)equality. The length method for sets gives the cardinality. set_combn returns the set of all subsets of specfied length.

See Also

set_outer, tuple for tuples (vectors), and relation.

Examples

## constructor
s <- set(1,2,3)
s

## a more complex set
set(c,"test",list(1,2,3))

## converter
s2 <- as.set(2:5)
s2

## set of sets
set(set(), set(1))

## cartesian product
s * s2
s * s
s ^ 2 # same as above
s ^ 3

## power set
2 ^ s

## tuples
s3 <- set(tuple(1,2,3), tuple(2,3,4))
s3

## Predicates:

## element
1:2 %e% s
tuple(1,2,3) %e% s3

## subset
s <= s2
s2 >= s # same

## proper subset
s < s

## complement, union, intersection, symmetric difference:
s - 1
s + set("a") # or use: s | set("a")
s & s
s %D% s2
set(1,2,3) - set(1,2)
set_intersection(set(1,2,3), set(2,3,4), set(3,4,5))
set_union(set(1,2,3), set(2,3,4), set(3,4,5))
set_symdiff(set(1,2,3), set(2,3,4), set(3,4,5))

## subsets:
set_combn(as.set(1:3),2)