The mathematical set of complex numbers, defined as the the set of reals with possibly imaginary components. i.e. $$\\{a + bi \\ : \\ a,b \in R\\}$$ where \(R\) is the set of reals.
set6::Set
-> set6::Interval
-> set6::SpecialSet
-> Complex
new()
Create a new Complex
object.
Complex$new(lower = -Inf + (0+0i), upper = Inf + (0+0i))
lower
complex. Where to start the set.
upper
complex. Where to end the set.
A new Complex
object.
contains()
Tests to see if x
is contained in the Set.
Complex$contains(x, all = FALSE, bound = NULL)
x
any. Object or vector of objects to test.
all
logical. If FALSE
tests each x
separately. Otherwise returns TRUE
only if all x
pass test.
bound
logical.
x
can be of any type, including a Set itself. x
should be a tuple if
checking to see if it lies within a set of dimension greater than one. To test for multiple x
at the same time, then provide these as a list.
If all = TRUE
then returns TRUE
if all x
are contained in the Set
, otherwise
returns a vector of logicals. For Intervals, bound
is used to specify if elements lying on the
(possibly open) boundary of the interval are considered contained (bound = TRUE
) or not (bound = FALSE
).
If all
is TRUE
then returns TRUE
if all elements of x
are contained in the Set
, otherwise
FALSE.
If all
is FALSE
then returns a vector of logicals corresponding to each individual
element of x
.
The infix operator %inset%
is available to test if x
is an element in the Set
,
see examples.
clone()
The objects of this class are cloneable with this method.
Complex$clone(deep = FALSE)
deep
Whether to make a deep clone.
Unlike the other SpecialSet
s, Complex
can be used to define an Interval
. In this
case where values can be complex, as opposed to reals or integers in Interval.
Other special sets:
ExtendedReals
,
Integers
,
Naturals
,
NegIntegers
,
NegRationals
,
NegReals
,
PosIntegers
,
PosNaturals
,
PosRationals
,
PosReals
,
Rationals
,
Reals