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Commit 9d0dc84

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A bunch of JS math snippets
1 parent 65140cc commit 9d0dc84

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+298
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‎public/consolidated/javascript.json‎

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@@ -367,16 +367,109 @@
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{
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"categoryName": "Mathematical Functions",
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"snippets": [
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{
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"title": "Combinations",
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"description": "Calculates the number of combinations (denoted as C(n,r) or \"n choose r\"), which determines how many ways you can select r items from n items without considering the order.",
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"author": "JanluOfficial",
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"tags": [
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"math",
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"number-theory",
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"algebra"
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],
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"contributors": [],
380+
"code": "function combinations(n, r) {\n function factorial(x) {\n if (x === 0 || x === 1) return 1;\n let result = 1;\n for (let i = 2; i <= x; i++) {\n result *= i;\n }\n return result;\n }\n return factorial(n) / (factorial(r) * factorial(n - r));\n}\n\n// Usage:\ncombinations(12,24); // Returns: 7.720248753351544e-16\ncombinations(1,22); // Returns: 8.896791392450574e-22\n"
381+
},
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{
383+
"title": "Cross Product",
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"description": "Computes the cross product of two 3D vectors, which results in a vector perpendicular to both.",
385+
"author": "JanluOfficial",
386+
"tags": [
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"math",
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"vector-algebra"
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],
390+
"contributors": [],
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"code": "function crossProduct(a, b) {\n if (a.length !== 3 || b.length !== 3) {\n throw new Error('Vectors must be 3-dimensional');\n }\n\n return [\n a[1] * b[2] - a[2] * b[1],\n a[2] * b[0] - a[0] * b[2],\n a[0] * b[1] - a[1] * b[0]\n ];\n}\n\n// Usage:\ncrossProduct([1, 2, 3], [4, 5, 6]); // Returns: [-3, 6, -3] \n"
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},
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{
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"title": "Dot Product",
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"description": "Computes the dot product of two vectors, which is the sum of the products of corresponding elements.",
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"author": "JanluOfficial",
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"tags": [
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"math",
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"vector-algebra"
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],
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"contributors": [],
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"code": "function dotProduct(a, b) {\n if (a.length !== b.length) {\n throw new Error('Vectors must be of the same length');\n }\n\n return a.reduce((sum, value, index) => sum + value * b[index], 0);\n}\n\n// Usage:\ndotProduct([1, 2, 3], [4, 5, 6]); // Returns: 32\n"
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},
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{
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"title": "Error function",
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"description": "Computes the error function (erf(x)) for a given input x, which is a mathematical function used frequently in probability, statistics, and partial differential equations.",
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"author": "JanluOfficial",
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"tags": [
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"math"
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],
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"contributors": [],
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"code": "function erf(x) {\n const sign = Math.sign(x);\n const absX = Math.abs(x);\n const t = 1 / (1 + 0.3275911 * absX);\n const a1 = 0.254829592, a2 = -0.284496736, a3 = 1.421413741, a4 = -1.453152027, a5 = 1.061405429;\n const poly = t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5))));\n return sign * (1 - poly * Math.exp(-absX * absX));\n}\n\n// Usage:\nerf(-1); // Returns: -0.8427006897475899\nerf(1); // Returns: 0.8427006897475899\n"
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},
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{
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"title": "Greatest Common Divisor",
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"description": "Calculates the largest positive integer that divides each of the integers without leaving a remainder. Useful for calculating aspect ratios.",
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"author": "JanluOfficial",
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"tags": [
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"math",
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"division"
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"division",
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"number-theory",
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"algebra"
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],
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"contributors": [],
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"code": "function gcd(a, b) {\n while (b !== 0) {\n let temp = b;\n b = a % b;\n a = temp;\n }\n return a;\n}\n\n// Usage:\ngcd(1920, 1080); // Returns: 120\ngcd(1920, 1200); // Returns: 240\ngcd(5,12); // Returns: 1\n"
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},
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{
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"title": "Least common multiple",
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"description": "Computes the least common multiple (LCM) of two numbers a and b. The LCM is the smallest positive integer that is divisible by both a and b.",
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"author": "JanluOfficial",
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"tags": [
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"math",
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"number-theory",
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"algebra"
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],
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"contributors": [],
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"code": "function lcm(a, b) {\n function gcd(x, y) {\n while (y !== 0) {\n const temp = y;\n y = x % y;\n x = temp;\n }\n return Math.abs(x);\n }\n return Math.abs(a * b) / gcd(a, b);\n}\n\n// Usage:\nlcm(12,16); // Returns: 48\nlcm(8,20); // Returns: 40\nlcm(16,17); // Returns: 272\n"
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},
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{
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"title": "Matrix Multiplication",
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"description": "Multiplies two matrices, where the number of columns in the first matrix equals the number of rows in the second.",
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"author": "JanluOfficial",
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"tags": [
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"math",
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"matrix-algebra"
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],
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"contributors": [],
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"code": "function matrixMultiply(A, B) {\n const rowsA = A.length;\n const colsA = A[0].length;\n const rowsB = B.length;\n const colsB = B[0].length;\n\n if (colsA !== rowsB) {\n throw new Error('Number of columns of A must equal the number of rows of B');\n }\n\n let result = Array.from({ length: rowsA }, () => Array(colsB).fill(0));\n\n for (let i = 0; i < rowsA; i++) {\n for (let j = 0; j < colsB; j++) {\n for (let k = 0; k < colsA; k++) {\n result[i][j] += A[i][k] * B[k][j];\n }\n }\n }\n\n return result;\n}\n\n// Usage:\nmatrixMultiply([[1, 2], [3, 4]], [[5, 6], [7, 8]]); // Returns: [[19, 22], [43, 50]]\n"
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},
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{
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"title": "Modular Inverse",
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"description": "Computes the modular multiplicative inverse of a number a under modulo m, which is the integer x such that (a*x) mod m=1.",
453+
"author": "JanluOfficial",
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"tags": [
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"math",
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"number-theory",
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"algebra"
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],
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"contributors": [],
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"code": "function modInverse(a, m) {\n function extendedGCD(a, b) {\n if (b === 0) {\n return { gcd: a, x: 1, y: 0 };\n }\n const { gcd, x: x1, y: y1 } = extendedGCD(b, a % b);\n const x = y1;\n const y = x1 - Math.floor(a / b) * y1;\n return { gcd, x, y };\n }\n\n const { gcd, x } = extendedGCD(a, m);\n\n if (gcd !== 1) {\n return null;\n }\n\n return (x % m + m) % m;\n}\n\n// Usage:\nmodInverse(3, 26); // Returns: 9\nmodInverse(10, 17); // Returns: 12\nmodInverse(6, 9); // Returns: null\n"
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},
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{
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"title": "Prime Number",
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"description": "Calculates the number of combinations (denoted as C(n,r) or \"n choose r\"), which determines how many ways you can select r items from n items without considering the order.",
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"author": "JanluOfficial",
466+
"tags": [
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"math",
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"number-theory",
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"algebra"
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],
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"contributors": [],
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"code": "function isPrime(num) {\n if (num <= 1) return false; // 0 and 1 are not prime numbers\n if (num <= 3) return true; // 2 and 3 are prime numbers\n if (num % 2 === 0 || num % 3 === 0) return false; // Exclude multiples of 2 and 3\n\n // Check divisors from 5 to √num, skipping multiples of 2 and 3\n for (let i = 5; i * i <= num; i += 6) {\n if (num % i === 0 || num % (i + 2) === 0) return false;\n }\n return true;\n}\n\n// Usage:\nisPrime(69); // Returns: false\nisPrime(17); // Returns: true\n"
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}
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]
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},
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---
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title: Combinations
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description: Calculates the number of combinations (denoted as C(n,r) or "n choose r"), which determines how many ways you can select r items from n items without considering the order.
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author: JanluOfficial
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tags: math,number-theory,algebra
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---
7+
8+
```js
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function combinations(n, r) {
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function factorial(x) {
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if (x === 0 || x === 1) return 1;
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let result = 1;
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for (let i = 2; i <= x; i++) {
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result *= i;
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}
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return result;
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}
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return factorial(n) / (factorial(r) * factorial(n - r));
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}
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// Usage:
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combinations(12,24); // Returns: 7.720248753351544e-16
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combinations(1,22); // Returns: 8.896791392450574e-22
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```
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---
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title: Cross Product
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description: Computes the cross product of two 3D vectors, which results in a vector perpendicular to both.
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author: JanluOfficial
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tags: math,vector-algebra
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---
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```js
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function crossProduct(a, b) {
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if (a.length !== 3 || b.length !== 3) {
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throw new Error('Vectors must be 3-dimensional');
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}
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return [
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a[1] * b[2] - a[2] * b[1],
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a[2] * b[0] - a[0] * b[2],
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a[0] * b[1] - a[1] * b[0]
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];
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}
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// Usage:
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crossProduct([1, 2, 3], [4, 5, 6]); // Returns: [-3, 6, -3]
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```
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---
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title: Dot Product
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description: Computes the dot product of two vectors, which is the sum of the products of corresponding elements.
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author: JanluOfficial
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tags: math,vector-algebra
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---
7+
8+
```js
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function dotProduct(a, b) {
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if (a.length !== b.length) {
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throw new Error('Vectors must be of the same length');
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}
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return a.reduce((sum, value, index) => sum + value * b[index], 0);
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}
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// Usage:
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dotProduct([1, 2, 3], [4, 5, 6]); // Returns: 32
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```
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---
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title: Error function
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description: Computes the error function (erf(x)) for a given input x, which is a mathematical function used frequently in probability, statistics, and partial differential equations.
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author: JanluOfficial
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tags: math
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---
7+
8+
```js
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function erf(x) {
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const sign = Math.sign(x);
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const absX = Math.abs(x);
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const t = 1 / (1 + 0.3275911 * absX);
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const a1 = 0.254829592, a2 = -0.284496736, a3 = 1.421413741, a4 = -1.453152027, a5 = 1.061405429;
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const poly = t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5))));
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return sign * (1 - poly * Math.exp(-absX * absX));
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}
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// Usage:
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erf(-1); // Returns: -0.8427006897475899
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erf(1); // Returns: 0.8427006897475899
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```

‎snippets/javascript/mathematical-functions/greatest-common-divisor.md‎

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title: Greatest Common Divisor
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description: Calculates the largest positive integer that divides each of the integers without leaving a remainder. Useful for calculating aspect ratios.
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author: JanluOfficial
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tags: math,division
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tags: math,division,number-theory,algebra
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---
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```js
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---
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title: Least common multiple
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description: Computes the least common multiple (LCM) of two numbers a and b. The LCM is the smallest positive integer that is divisible by both a and b.
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author: JanluOfficial
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tags: math,number-theory,algebra
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---
7+
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```js
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function lcm(a, b) {
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function gcd(x, y) {
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while (y !== 0) {
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const temp = y;
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y = x % y;
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x = temp;
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}
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return Math.abs(x);
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}
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return Math.abs(a * b) / gcd(a, b);
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}
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// Usage:
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lcm(12,16); // Returns: 48
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lcm(8,20); // Returns: 40
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lcm(16,17); // Returns: 272
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```
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---
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title: Matrix Multiplication
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description: Multiplies two matrices, where the number of columns in the first matrix equals the number of rows in the second.
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author: JanluOfficial
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tags: math,matrix-algebra
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---
7+
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```js
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function matrixMultiply(A, B) {
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const rowsA = A.length;
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const colsA = A[0].length;
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const rowsB = B.length;
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const colsB = B[0].length;
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if (colsA !== rowsB) {
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throw new Error('Number of columns of A must equal the number of rows of B');
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}
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let result = Array.from({ length: rowsA }, () => Array(colsB).fill(0));
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for (let i = 0; i < rowsA; i++) {
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for (let j = 0; j < colsB; j++) {
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for (let k = 0; k < colsA; k++) {
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result[i][j] += A[i][k] * B[k][j];
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}
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}
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}
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return result;
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}
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// Usage:
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matrixMultiply([[1, 2], [3, 4]], [[5, 6], [7, 8]]); // Returns: [[19, 22], [43, 50]]
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```
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---
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title: Modular Inverse
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description: Computes the modular multiplicative inverse of a number a under modulo m, which is the integer x such that (a*x) mod m=1.
4+
author: JanluOfficial
5+
tags: math,number-theory,algebra
6+
---
7+
8+
```js
9+
function modInverse(a, m) {
10+
function extendedGCD(a, b) {
11+
if (b === 0) {
12+
return { gcd: a, x: 1, y: 0 };
13+
}
14+
const { gcd, x: x1, y: y1 } = extendedGCD(b, a % b);
15+
const x = y1;
16+
const y = x1 - Math.floor(a / b) * y1;
17+
return { gcd, x, y };
18+
}
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const { gcd, x } = extendedGCD(a, m);
21+
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if (gcd !== 1) {
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return null;
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}
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return (x % m + m) % m;
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}
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// Usage:
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modInverse(3, 26); // Returns: 9
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modInverse(10, 17); // Returns: 12
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modInverse(6, 9); // Returns: null
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```
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---
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title: Prime Number
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description: Calculates the number of combinations (denoted as C(n,r) or "n choose r"), which determines how many ways you can select r items from n items without considering the order.
4+
author: JanluOfficial
5+
tags: math,number-theory,algebra
6+
---
7+
8+
```js
9+
function isPrime(num) {
10+
if (num <= 1) return false; // 0 and 1 are not prime numbers
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if (num <= 3) return true; // 2 and 3 are prime numbers
12+
if (num % 2 === 0 || num % 3 === 0) return false; // Exclude multiples of 2 and 3
13+
14+
// Check divisors from 5 to √num, skipping multiples of 2 and 3
15+
for (let i = 5; i * i <= num; i += 6) {
16+
if (num % i === 0 || num % (i + 2) === 0) return false;
17+
}
18+
return true;
19+
}
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// Usage:
22+
isPrime(69); // Returns: false
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isPrime(17); // Returns: true
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```

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