Singleton [class]

The class splinekit.interval.Singleton is the concrete class that handles the degenerate intervals that contains only one real number.

This concrete class honors Interval and Degenerate; it handles intervals made of just one finite real number.

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class splinekit.interval.singleton.Singleton(value: float)

Bases: Interval, Degenerate

The degenerate interval \(\{x\in{\mathbb{R}}|x=x_{0}\}=[x_{0},x_{0}].\)

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property infimum: float

self.value

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property supremum: float

self.value

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property isleftopen: bool

False

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property isrightopen: bool

False

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property isopen: bool

False

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property ishalfopen: bool

False

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property isclosed: bool

True

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property isleftbounded: bool

True

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property isrightbounded: bool

True

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property ishalfbounded: bool

False

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property isbounded: bool

True

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property isdegenerate: bool

True

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property isproper: bool

False

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property interior: Self

Empty()

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property closure: Self

Singleton(self.value)

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property diameter: float

0.0

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property midpoint: float

self.value

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sortorder() → float

self.value

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__contains__(x: float) → bool

Tests if the number \(x\) is contained in this interval \(U,\) as in \(\left(x\in U\right).\)

Parameters:

x (float) – Real number whose membership is queried.

Returns:

• False if x is not a member of this interval.

• True if x is a member of this interval.

Return type:

bool

Examples

Load the library.

>>> import splinekit.interval as ivl

0.0 is in Singleton(0.0).

>>> 0.0 in ivl.Singleton(0.0)
True

float("inf") is not in RR().

>>> float("inf") in ivl.RR()
False

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static __new__(cls, value: float) → Self

Creates the degenerate interval \(\{x\in{\mathbb{R}}|x=x_{0}\}=[x_{0},x_{0}]\) that contains exactly one number.

Parameters:

value – The number contained by this degenerate interval.

Returns:

A Singleton interval if value is a finite number; an Empty interval otherwise.

Return type:

Interval