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Merge pull request #26 from NicklasXYZ/main
Update the combinatorics and sequences module
2 parents 7fd917f + 15f4c0b commit 7fd4d74

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‎README.md

+26-20
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@@ -10,43 +10,49 @@ The library supports both targets: Erlang and JavaScript.
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## Quickstart
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```gleam
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import gleam/float
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import gleam/iterator
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import gleam/option.{Some}
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import gleam_community/maths/arithmetics
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import gleam_community/maths/combinatorics
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import gleam_community/maths/combinatorics.{WithoutRepetitions}
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import gleam_community/maths/elementary
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import gleam_community/maths/piecewise
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import gleam_community/maths/predicates
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import gleam/float
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import gleam/int
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import gleeunit/should
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pub fn main() {
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pub fn example() {
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// Evaluate the sine function
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elementary.sin(elementary.pi())
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// Returns Float: 0.0
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let result = elementary.sin(elementary.pi())
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// Set the relative and absolute tolerance
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let assert Ok(absolute_tol) = elementary.power(10.0, -6.0)
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let relative_tol = 0.0
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// Check that the value is very close to 0.0
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// That is, if 'result' is within +/- 10^(-6)
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predicates.is_close(result, 0.0, relative_tol, absolute_tol)
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|> should.be_true()
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// Find the greatest common divisor
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arithmetics.gcd(54, 24)
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// Returns Int: 6
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|> should.equal(6)
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// Find the minimum and maximum of a list
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piecewise.extrema([10.0, 3.0, 50.0, 20.0, 3.0], float.compare)
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// Returns Tuple: Ok(#(3.0, 50.0))
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// Find the list indices of the smallest value
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piecewise.arg_minimum([10, 3, 50, 20, 3], int.compare)
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// Returns List: Ok([1, 4])
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|> should.equal(Ok(#(3.0, 50.0)))
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// Determine if a number is fractional
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predicates.is_fractional(0.3333)
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// Returns Bool: True
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// Determine if 28 is a power of 3
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predicates.is_power(28, 3)
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// Returns Bool: False
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|> should.equal(True)
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// Generate all k = 1 combinations of [1, 2]
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combinatorics.list_combination([1, 2], 1)
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// Returns List: Ok([[1], [2]])
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// Generate all k = 2 combinations of [1, 2, 3]
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let assert Ok(combinations) =
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combinatorics.list_combination([1, 2, 3], 2, Some(WithoutRepetitions))
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combinations
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|> iterator.to_list()
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|> should.equal([[1, 2], [1, 3], [2, 3]])
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}
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```
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## Installation

‎src/gleam_community/maths/arithmetics.gleam

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////<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.css" integrity="sha384-wcIxkf4k558AjM3Yz3BBFQUbk/zgIYC2R0QpeeYb+TwlBVMrlgLqwRjRtGZiK7ww" crossorigin="anonymous">
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////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/katex.min.js" integrity="sha384-hIoBPJpTUs74ddyc4bFZSM1TVlQDA60VBbJS0oA934VSz82sBx1X7kSx2ATBDIyd" crossorigin="anonymous"></script>
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////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
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////<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.css" integrity="sha384-nB0miv6/jRmo5UMMR1wu3Gz6NLsoTkbqJghGIsx//Rlm+ZU03BU6SQNC66uf4l5+" crossorigin="anonymous">
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////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/katex.min.js" integrity="sha384-7zkQWkzuo3B5mTepMUcHkMB5jZaolc2xDwL6VFqjFALcbeS9Ggm/Yr2r3Dy4lfFg" crossorigin="anonymous"></script>
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////<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.11/dist/contrib/auto-render.min.js" integrity="sha384-43gviWU0YVjaDtb/GhzOouOXtZMP/7XUzwPTstBeZFe/+rCMvRwr4yROQP43s0Xk" crossorigin="anonymous"></script>
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////<script>
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//// document.addEventListener("DOMContentLoaded", function() {
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//// renderMathInElement(document.body, {
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//// // customised options
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//// // • auto-render specific keys, e.g.:
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//// delimiters: [
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//// {left: '$$', right: '$$', display: false},
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//// // {left: '$', right: '$', display: false},
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//// // {left: '\\(', right: '\\)', display: false},
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//// {left: '$', right: '$', display: false},
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//// {left: '\\(', right: '\\)', display: false},
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//// {left: '\\[', right: '\\]', display: true}
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//// ],
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//// // • rendering keys, e.g.:
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//// throwOnError : false
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//// throwOnError : true
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//// });
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//// });
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////</script>
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/// </div>
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///
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/// The function calculates the greatest common divisor of two integers
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/// $$x, y \in \mathbb{Z}$$. The greatest common divisor is the largest positive
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/// integer that is divisible by both $$x$$ and $$y$$.
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/// \\(x, y \in \mathbb{Z}\\). The greatest common divisor is the largest positive
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/// integer that is divisible by both \\(x\\) and \\(y\\).
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///
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/// <details>
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/// <summary>Example:</summary>
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/// </div>
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///
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///
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/// Given two integers, $$x$$ (dividend) and $$y$$ (divisor), the Euclidean modulo
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/// of $$x$$ by $$y$$, denoted as $$x \mod y$$, is the remainder $$r$$ of the
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/// division of $$x$$ by $$y$$, such that:
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/// Given two integers, \\(x\\) (dividend) and \\(y\\) (divisor), the Euclidean modulo
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/// of \\(x\\) by \\(y\\), denoted as \\(x \mod y\\), is the remainder \\(r\\) of the
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/// division of \\(x\\) by \\(y\\), such that:
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///
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/// \\[
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/// x = q \cdot y + r \quad \text{and} \quad 0 \leq r < |y|,
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/// \\]
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///
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/// where $$q$$ is an integer that represents the quotient of the division.
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/// where \\(q\\) is an integer that represents the quotient of the division.
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///
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/// The Euclidean modulo function of two numbers, is the remainder operation most
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/// commonly utilized in mathematics. This differs from the standard truncating
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/// </div>
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///
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/// The function calculates the least common multiple of two integers
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/// $$x, y \in \mathbb{Z}$$. The least common multiple is the smallest positive
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/// integer that has both $$x$$ and $$y$$ as factors.
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/// \\(x, y \in \mathbb{Z}\\). The least common multiple is the smallest positive
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/// integer that has both \\(x\\) and \\(y\\) as factors.
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///
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/// <details>
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/// <summary>Example:</summary>
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/// \sum_{i=1}^n w_i x_i
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/// \\]
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///
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/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$ is
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/// the value in the input list indexed by $$i$$, while the $$w_i \in \mathbb{R}$$
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/// are corresponding weights ($$w_i = 1.0\\;\forall i=1...n$$ by default).
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/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{R}\\) is
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/// the value in the input list indexed by \\(i\\), while the \\(w_i \in \mathbb{R}\\)
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/// are corresponding weights (\\(w_i = 1.0\\;\forall i=1...n\\) by default).
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///
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/// <details>
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/// <summary>Example:</summary>
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/// \sum_{i=1}^n x_i
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/// \\]
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///
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/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{Z}$$ is
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/// the value in the input list indexed by $$i$$.
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/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{Z}\\) is
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/// the value in the input list indexed by \\(i\\).
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///
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/// <details>
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/// <summary>Example:</summary>
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/// \prod_{i=1}^n x_i^{w_i}
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/// \\]
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///
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/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$ is
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/// the value in the input list indexed by $$i$$, while the $$w_i \in \mathbb{R}$$
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/// are corresponding weights ($$w_i = 1.0\\;\forall i=1...n$$ by default).
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/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{R}\\) is
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/// the value in the input list indexed by \\(i\\), while the \\(w_i \in \mathbb{R}\\)
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/// are corresponding weights (\\(w_i = 1.0\\;\forall i=1...n\\) by default).
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///
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/// <details>
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/// <summary>Example:</summary>
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/// \prod_{i=1}^n x_i
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/// \\]
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///
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/// In the formula, $$n$$ is the length of the list and $$x_i \in \mathbb{Z}$$ is
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/// the value in the input list indexed by $$i$$.
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/// In the formula, \\(n\\) is the length of the list and \\(x_i \in \mathbb{Z}\\) is
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/// the value in the input list indexed by \\(i\\).
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///
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/// <details>
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/// <summary>Example:</summary>
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/// v_j = \sum_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
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/// \\]
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///
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/// In the formula, $$v_j$$ is the $$j$$'th element in the cumulative sum of $$n$$
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/// elements. That is, $$n$$ is the length of the list and $$x_i \in \mathbb{R}$$
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/// is the value in the input list indexed by $$i$$. The value $$v_j$$ is thus the
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/// sum of the $$1$$ to $$j$$ first elements in the given list.
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/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative sum of \\(n\\)
539+
/// elements. That is, \\(n\\) is the length of the list and \\(x_i \in \mathbb{R}\\)
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/// is the value in the input list indexed by \\(i\\). The value \\(v_j\\) is thus the
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/// sum of the \\(1\\) to \\(j\\) first elements in the given list.
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///
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/// <details>
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/// <summary>Example:</summary>
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/// v_j = \sum_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
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/// \\]
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///
588-
/// In the formula, $$v_j$$ is the $$j$$'th element in the cumulative sum of $$n$$
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/// elements. That is, $$n$$ is the length of the list and $$x_i \in \mathbb{Z}$$
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/// is the value in the input list indexed by $$i$$. The value $$v_j$$ is thus the
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/// sum of the $$1$$ to $$j$$ first elements in the given list.
588+
/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative sum of \\(n\\)
589+
/// elements. That is, \\(n\\) is the length of the list and \\(x_i \in \mathbb{Z}\\)
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/// is the value in the input list indexed by \\(i\\). The value \\(v_j\\) is thus the
591+
/// sum of the \\(1\\) to \\(j\\) first elements in the given list.
592592
///
593593
/// <details>
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/// <summary>Example:</summary>
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635635
/// v_j = \prod_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
636636
/// \\]
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///
638-
/// In the formula, $$v_j$$ is the $$j$$'th element in the cumulative product of
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/// $$n$$ elements. That is, $$n$$ is the length of the list and
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/// $$x_i \in \mathbb{R}$$ is the value in the input list indexed by $$i$$. The
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/// value $$v_j$$ is thus the sum of the $$1$$ to $$j$$ first elements in the
638+
/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative product of
639+
/// \\(n\\) elements. That is, \\(n\\) is the length of the list and
640+
/// \\(x_i \in \mathbb{R}\\) is the value in the input list indexed by \\(i\\). The
641+
/// value \\(v_j\\) is thus the sum of the \\(1\\) to \\(j\\) first elements in the
642642
/// given list.
643643
///
644644
/// <details>
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/// v_j = \prod_{i=1}^j x_i \\;\\; \forall j = 1,\dots, n
688688
/// \\]
689689
///
690-
/// In the formula, $$v_j$$ is the $$j$$'th element in the cumulative product of
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/// $$n$$ elements. That is, $$n$$ is the length of the list and
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/// $$x_i \in \mathbb{Z}$$ is the value in the input list indexed by $$i$$. The
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/// value $$v_j$$ is thus the product of the $$1$$ to $$j$$ first elements in the
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/// In the formula, \\(v_j\\) is the \\(j\\)'th element in the cumulative product of
691+
/// \\(n\\) elements. That is, \\(n\\) is the length of the list and
692+
/// \\(x_i \in \mathbb{Z}\\) is the value in the input list indexed by \\(i\\). The
693+
/// value \\(v_j\\) is thus the product of the \\(1\\) to \\(j\\) first elements in the
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/// given list.
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///
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/// <details>

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