[Snippets] Added several new mathematical snippets for JavaScript.

public/consolidated/javascript.json

@@ -400,16 +400,109 @@
     {
         "name": "Mathematical Functions",
         "snippets": [
+            {
+                "title": "Combinations",
+                "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.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "number-theory",
+                    "algebra"
+                ],
+                "contributors": [],
+                "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"
+            },
+            {
+                "title": "Cross Product",
+                "description": "Computes the cross product of two 3D vectors, which results in a vector perpendicular to both.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "vector-algebra"
+                ],
+                "contributors": [],
+                "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"
+            },
+            {
+                "title": "Dot Product",
+                "description": "Computes the dot product of two vectors, which is the sum of the products of corresponding elements.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "vector-algebra"
+                ],
+                "contributors": [],
+                "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"
+            },
+            {
+                "title": "Error function",
+                "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.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math"
+                ],
+                "contributors": [],
+                "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"
+            },
             {
                 "title": "Greatest Common Divisor",
                 "description": "Calculates the largest positive integer that divides each of the integers without leaving a remainder. Useful for calculating aspect ratios.",
                 "author": "JanluOfficial",
                 "tags": [
                     "math",
-                    "division"
+                    "division",
+                    "number-theory",
+                    "algebra"
                 ],
                 "contributors": [],
                 "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"
+            },
+            {
+                "title": "Least common multiple",
+                "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.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "number-theory",
+                    "algebra"
+                ],
+                "contributors": [],
+                "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"
+            },
+            {
+                "title": "Matrix Multiplication",
+                "description": "Multiplies two matrices, where the number of columns in the first matrix equals the number of rows in the second.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "matrix-algebra"
+                ],
+                "contributors": [],
+                "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"
+            },
+            {
+                "title": "Modular Inverse",
+                "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.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "number-theory",
+                    "algebra"
+                ],
+                "contributors": [],
+                "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"
+            },
+            {
+                "title": "Prime Number",
+                "description": "Checks if a number is a prime number or not.",
+                "author": "JanluOfficial",
+                "tags": [
+                    "math",
+                    "number-theory",
+                    "algebra"
+                ],
+                "contributors": [],
+                "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"
             }
         ]
     },

snippets/javascript/mathematical-functions/combinations.md

@@ -0,0 +1,31 @@
+---
+title: Combinations
+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.
+author: JanluOfficial
+tags: math,number-theory,algebra
+---
+
+```js
+function combinations(n, r) {
+    if (n < 0 || r < 0 || n < r) {
+        throw new Error('Invalid input: n and r must be non-negative and n must be greater than or equal to r.');
+    }
+
+    function factorial(x) {
+        if (x === 0 || x === 1) return 1;
+        let result = 1;
+        for (let i = 2; i <= x; i++) {
+            result *= i;
+        }
+        return result;
+    }
+
+    const numerator = factorial(n);
+    const denominator = factorial(r) * factorial(n - r);
+    return numerator / denominator;
+}
+
+// Usage:
+combinations(24,22); // Returns:    276
+combinations(5,3);   // Returns:     10
+```

snippets/javascript/mathematical-functions/cross-product.md

@@ -0,0 +1,23 @@
+---
+title: Cross Product
+description: Computes the cross product of two 3D vectors, which results in a vector perpendicular to both.
+author: JanluOfficial
+tags: math,vector-algebra
+---
+
+```js
+function crossProduct(a, b) {
+    if (a.length !== 3 || b.length !== 3) {
+        throw new Error('Vectors must be 3-dimensional');
+    }
+
+    return [
+        a[1] * b[2] - a[2] * b[1],
+        a[2] * b[0] - a[0] * b[2],
+        a[0] * b[1] - a[1] * b[0]
+    ];
+}
+
+// Usage:
+crossProduct([1, 2, 3], [4, 5, 6]); // Returns: [-3, 6, -3] 
+```

snippets/javascript/mathematical-functions/dot-product.md

@@ -0,0 +1,19 @@
+---
+title: Dot Product
+description: Computes the dot product of two vectors, which is the sum of the products of corresponding elements.
+author: JanluOfficial
+tags: math,vector-algebra
+---
+
+```js
+function dotProduct(a, b) {
+    if (a.length !== b.length) {
+        throw new Error('Vectors must be of the same length');
+    }
+
+    return a.reduce((sum, value, index) => sum + value * b[index], 0);
+}
+
+// Usage:
+dotProduct([1, 2, 3], [4, 5, 6]); // Returns: 32
+```

snippets/javascript/mathematical-functions/error-function.md

@@ -0,0 +1,21 @@
+---
+title: Error function
+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.
+author: JanluOfficial
+tags: math
+---
+
+```js
+function erf(x) {
+    const sign = Math.sign(x);
+    const absX = Math.abs(x);
+    const t = 1 / (1 + 0.3275911 * absX);
+    const a1 = 0.254829592, a2 = -0.284496736, a3 = 1.421413741, a4 = -1.453152027, a5 = 1.061405429;
+    const poly = t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5))));
+    return sign * (1 - poly * Math.exp(-absX * absX));
+}
+
+// Usage:
+erf(-1); // Returns:    -0.8427006897475899
+erf(1);  // Returns:     0.8427006897475899
+```

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

@@ -2,7 +2,7 @@
 title: Greatest Common Divisor
 description: Calculates the largest positive integer that divides each of the integers without leaving a remainder. Useful for calculating aspect ratios.
 author: JanluOfficial
-tags: math,division
+tags: math,division,number-theory,algebra
 ---
 
 ```js

snippets/javascript/mathematical-functions/least-common-multiple.md

@@ -0,0 +1,25 @@
+---
+title: Least common multiple
+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.
+author: JanluOfficial
+tags: math,number-theory,algebra
+---
+
+```js
+function lcm(a, b) {
+    function gcd(x, y) {
+        while (y !== 0) {
+            const temp = y;
+            y = x % y;
+            x = temp;
+        }
+        return Math.abs(x);
+    }
+    return Math.abs(a * b) / gcd(a, b);
+}
+
+// Usage:
+lcm(12,16); // Returns:    48
+lcm(8,20);  // Returns:    40
+lcm(16,17); // Returns:   272
+```

snippets/javascript/mathematical-functions/matrix-multiplication.md

@@ -0,0 +1,34 @@
+---
+title: Matrix Multiplication
+description: Multiplies two matrices, where the number of columns in the first matrix equals the number of rows in the second.
+author: JanluOfficial
+tags: math,matrix-algebra
+---
+
+```js
+function matrixMultiply(A, B) {
+    const rowsA = A.length;
+    const colsA = A[0].length;
+    const rowsB = B.length;
+    const colsB = B[0].length;
+
+    if (colsA !== rowsB) {
+        throw new Error('Number of columns of A must equal the number of rows of B');
+    }
+
+    let result = Array.from({ length: rowsA }, () => Array(colsB).fill(0));
+
+    for (let i = 0; i < rowsA; i++) {
+        for (let j = 0; j < colsB; j++) {
+            for (let k = 0; k < colsA; k++) {
+                result[i][j] += A[i][k] * B[k][j];
+            }
+        }
+    }
+
+    return result;
+}
+
+// Usage:
+matrixMultiply([[1, 2], [3, 4]], [[5, 6], [7, 8]]); // Returns: [[19, 22], [43, 50]]
+```

snippets/javascript/mathematical-functions/modular-inverse.md

@@ -0,0 +1,33 @@
+---
+title: Modular Inverse
+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.
+author: JanluOfficial
+tags: math,number-theory,algebra
+---
+
+```js
+function modInverse(a, m) {
+    function extendedGCD(a, b) {
+        if (b === 0) {
+            return { gcd: a, x: 1, y: 0 };
+        }
+        const { gcd, x: x1, y: y1 } = extendedGCD(b, a % b);
+        const x = y1;
+        const y = x1 - Math.floor(a / b) * y1;
+        return { gcd, x, y };
+    }
+
+    const { gcd, x } = extendedGCD(a, m);
+
+    if (gcd !== 1) {
+        return null;
+    }
+
+    return (x % m + m) % m;
+}
+
+// Usage:
+modInverse(3, 26);  // Returns: 9
+modInverse(10, 17); // Returns: 12
+modInverse(6, 9);   // Returns: null
+```

snippets/javascript/mathematical-functions/prime-number.md

@@ -0,0 +1,24 @@
+---
+title: Prime Number
+description: Checks if a number is a prime number or not.
+author: JanluOfficial
+tags: math,number-theory,algebra
+---
+
+```js
+function isPrime(num) {
+    if (num <= 1) return false; // 0 and 1 are not prime numbers
+    if (num <= 3) return true;  // 2 and 3 are prime numbers
+    if (num % 2 === 0 || num % 3 === 0) return false; // Exclude multiples of 2 and 3
+
+    // Check divisors from 5 to √num, skipping multiples of 2 and 3
+    for (let i = 5; i * i <= num; i += 6) {
+        if (num % i === 0 || num % (i + 2) === 0) return false;
+    }
+    return true;
+}
+
+// Usage:
+isPrime(69); // Returns:  false
+isPrime(17); // Returns:  true
+```