Borelian sets are formed by enumerable union, intersection or complement, of intervals.
Borel enables performing regular operations on intervals of any comparable class.
Borel borrows many of the ideas (and code) from the Intervals gem. However it differs from Intervals in which it's aim is not on numerical precision and calculation, but on ease of use and solving some general interval related problems.
You may install it traditionally, tipically for interactive sessions:
$ gem install borel
Or just put this somewhere on your application's
An Interval can be initialized with an empty, one or two sized array
(respectively for an empty, degenerate or
Simple interval), or
an array of one or two sized arrays (for a
Interval Interval Interval[0,1] Interval[[0,1],[2,3],]
Another way to initialize an Interval is by using the
#to_interval method extension.
nil.to_interval # -> Interval 1.to_interval # -> Interval (1..2).to_interval # -> Interval[1,2] (1...3).to_interval # -> Interval[1,2] [1,2].to_interval # -> Interval[1,2]
Infinity constant is available for specifying intervals
with no upper or lower boundary.
Interval[-Infinity, 0] Interval[1, Infinity] Interval[-Infinity, Infinity]
Some natural properties of intervals:
Interval[1,2].inf # -> 1 Interval[1,2].sup # -> 2 Interval.degenerate? # -> true Interval[[0,1],[2,3]].simple? # -> false Interval.empty? # -> true Interval[1,5].include?(3.4) # -> true
~Interval[0,5] # -> Interval[[-Infinity, 0], [5, Infinity]]
Interval[0,5] | Interval[-1,3] # -> Interval[-1,5]
Interval[0,5] ^ Interval[-1,3] # -> Interval[0,3]
Interval[0,5] - Interval[-1,3] # -> Interval[3,5]
You may use any Comparable class:
Interval['a','c'] ^ Interval['b','d'] # -> Interval['b','c'] Interval['a','c'] | Interval['b','d'] # -> Interval['a','d']
def t(seconds) Time.now + seconds end Interval[t(1),t(5)] ^ Interval[t(3),t(7)] # -> Interval[t(3),t(5)] Interval[t(1),t(2)] | Interval[t(3),t(4)] # -> Interval[[t(1),t(2)],[t(3),t(4)]]
borel/math_extensions you are provided with some natural
math-related interval methods:
require 'borel/math_extensions' Interval[1,5].rand # -> Random.new.rand 1..5 Interval[1,5].width # -> 5-1, only for simple intervals
It's supported only for
Comparable and arithmetic supported classes
- There is no distinction between open and closed intervals
minusoperations, and also Math Extensions have limited support for non numeric-comparable classes
(The MIT License)
Copyright (c) 2012 Amadeus Folego
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