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$new(lower = -Inf + (0+0i), upper = Inf + (0+0i))
lowercomplex. Where to start the set.
uppercomplex. Where to end the set.
A new Complex object.
contains()Tests to see if x is contained in the Set.
Complex$contains(x, all = FALSE, bound = NULL)
xany. Object or vector of objects to test.
alllogical. If FALSE tests each x separately. Otherwise returns TRUE only if all x pass test.
boundlogical.
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)
deepWhether to make a deep clone.
Unlike the other SpecialSets, 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