sets (version 0.1-1)

set: Sets

Description

Creation and manipulation of sets.

Usage

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

Arguments

x

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

y

A set object.

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: | for the union, - for the difference (or 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. The Summary methods do also work if defined for the set elements. The mean and median methods try to convert the object to a numeric vector before calling the default methods.

Because set elements are unordered, it is not sensible to use indexing (except using labels). However, it is possible to iterate over all elements using for and lapply/sapply.

Note that set_union, set_intersection, and set_symdiff accept any number of arguments. The $n$-ary symmetric difference of sets contains just elements which are in an odd number of the sets.

set_contains_element is vectorized in e, that is, if e is an atomic vector or list, the is-element operation is performed element-wise, and a logical vector returned. Note that, however, objects of class "tuple" are taken as atomic objects to correctly handle sets of tuples.

See Also

set_outer, gset for generalized sets, and tuple for tuples (vectors).

Examples

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

## named elements
snamed <- set(one = 1, 2, three = 3)
snamed

## named elements can directly be accessed
snamed[["one"]]

## 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)

## iterators:
sapply(s, sqrt)
for (i in s) print(i)

## Summary methods
sum(s)
range(s)

## mean / median
mean(s)
median(s)