The submodule Symbols

IntervalArithmetic includes the submodule Symbols to make coding a bit simpler with respect to the use of some functions of the library. Some examples are provided here.

julia> using IntervalArithmetic, IntervalArithmetic.Symbolsjulia> a = 0 .. 2Interval{Float64}(0.0, 2.0, com, true)julia> b = 1 ± 0.5Interval{Float64}(0.5, 1.5, com, true)julia> a ≛ atruejulia> b ⊑ atruejulia> b ⋤ atruejulia> ∅ ⪽ ℝtrue

The following table summarizes the functions, the usage with the corresponding (unicode) symbols, how to obtain the symbol in Julia, and a brief description of the function.

Function	Symbol	Julia syntax	Description
`interval(a, b; format=:infsup)`	`..(a,b)`		Create interval `[a, b]` using bounds
`interval(m, r; format=:midpoint)`	`±(m, r)`	`\pm<tab>`	Create interval `[m - r, m + r]` using midpoint-radius form
`isequal_interval(x, y)`	`≛(x, y)`	`\starequal<tab>`	Check interval equality
`issubset_interval(x, y)`	`⊑(x, y)`	`\sqsubseteq<tab>`	Check if `x` is a (non-strict) subset of `y`
`isstrictsubset(x, y)`	`⋤(x, y)`	`\sqsubsetneq<tab>`	Check if `x` is a strict subset of `y`
`isinterior(x, y)`	`⪽(x, y)`	`\subsetdot<tab>`	Check if `x` is in the interior of `y`
`precedes(x, y)`	`⪯(x, y)`	`\preceq<tab>`	Precedes relation
`strictprecedes(x, y)`	`≺(x, y)`	`\prec<tab>`	Strictly precedes relation
`hull(x, y)`	`⊔(x, y)`	`\sqcup<tab>`	Interval hull of `x` and `y`
`intersect_interval(x, y)`	`⊓(x, y)`	`\sqcap<tab>`	Intersection of intervals
`emptyinterval()`	`∅`	`\emptyset<tab>`	Empty interval
`entireinterval()`	`ℝ`	`\bbR<tab>`	Entire real line

IntervalArithmetic.Symbols.ℝ — Constant

ℝ

Unicode alias of entireinterval() representing an entire interval of default flavor and default bound type.

See also: emptyinterval.

source

IntervalArithmetic.Symbols.:.. — Method

..(a, b)
a .. b

Create the interval $[a, b]$ according to the IEEE Standard 1788-2015. This is semantically equivalent to interval(a, b).

Danger

Nothing is done to compensate for the fact that floating point literals are rounded to the nearest when parsed (e.g. 0.1). In such cases, parse the string containing the desired value to ensure its tight enclosure.

See also: interval, ± and @I_str.

Examples

julia> using IntervalArithmeticjulia> using IntervalArithmetic.Symbolsjulia> setdisplay(:full);julia> (1//1)..πInterval{Rational{Int64}}(1//1, 85563208//27235615, com, true)julia> 0.1..0.3Interval{Float64}(0.1, 0.3, com, true)

source

IntervalArithmetic.Symbols.:± — Method

±(m, r)
m ± r

Create the interval $[m - r, m + r]$ according to the IEEE Standard 1788-2015. Despite using the midpoint-radius notation, the returned interval is still an Interval represented by its bounds.

Danger

See also: interval, .. and @I_str.

Examples

julia> using IntervalArithmeticjulia> using IntervalArithmetic.Symbolsjulia> setdisplay(:full);julia> 0 ± πInterval{Float64}(-3.1415926535897936, 3.1415926535897936, com, true)julia> 0//1 ± πInterval{Rational{Int64}}(-85563208//27235615, 85563208//27235615, com, true)

source

IntervalArithmetic.Symbols.:≛ — Function

≛(x, y)
x ≛ y

Unicode alias of isequal_interval.

source

IntervalArithmetic.Symbols.:≺ — Function

≺(x, y)
x ≺ y

Unicode alias of strictprecedes.

source

IntervalArithmetic.Symbols.:⊑ — Function

⊑(x, y)
x ⊑ y

Unicode alias of issubset_interval.

source

IntervalArithmetic.Symbols.:⊓ — Function

⊓(x, y)
x ⊓ y

Unicode alias of intersect_interval.

source

IntervalArithmetic.Symbols.:⊔ — Function

⊔(x, y)
x ⊔ y

Unicode alias of hull.

source

IntervalArithmetic.Symbols.:⋤ — Function

⋤(x, y)
x ⋤ y

Unicode alias of isstrictsubset.

source

IntervalArithmetic.Symbols.:⪯ — Function

⪯(x, y)
x ⪯ y

Unicode alias of precedes.

source

IntervalArithmetic.Symbols.:⪽ — Function

⪽(x, y)
x ⪽ y

Unicode alias of isinterior.

source