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Basic Modular Operations

In this section, we will cover the fundamental operations in modular arithmetic. These operations are essential for performing calculations within a specified modulus.

Functions Overview​

  • modulo(a: number, b: number): number Computes the remainder when a is divided by b.

  • modAdd(a: number, b: number, mod: number): number Adds two numbers modulo mod.

  • modSubtract(a: number, b: number, mod: number): number Subtracts two numbers modulo mod.

  • modMultiply(a: number, b: number, mod: number): number Multiplies two numbers modulo mod.

  • modDivide(a: number, b: number, mod: number): number Divides a by b modulo mod. This operation requires the modular multiplicative inverse of b.

Parameters​

  • a: The first number (or array of numbers) to operate on.
  • b: The second number (or array of numbers) to operate with (if applicable).
  • mod: The modulus to apply for the operation.

Return Value​

Each function returns a number representing the result of the modular operation.

Examples​

modulo​

console.log(modulo(10, 3)); // Output: 1

modAdd​

console.log(modAdd(5, 7, 6)); // Output: 0 (since (5 + 7) % 6 = 0)

modSubtract​

console.log(modSubtract(7, 5, 6)); // Output: 2 (since (7 - 5) % 6 = 2)

modMultiply​

console.log(modMultiply(5, 7, 6)); // Output: 5 (since (5 * 7) % 6 = 5)

modDivide​

console.log(modDivide(4, 3, 5)); // Output: 3 (since 4 * 3^-1 mod 5 = 3)

Error Handling​

  1. Division by Zero: If a division by zero is attempted during modDivide, an error is thrown.
console.log(modDivide(4, 0, 5)); // Throws: "Division by zero is not allowed."
  1. Invalid Inputs: If inputs are not numbers, an error is thrown.
console.log(modAdd("5", 7, 6)); // Throws: "Invalid input: must be a number."

Advanced Use Cases​

Chaining with Other Operations​

You can combine these modular operations with other arithmetic operations for complex calculations.

const result = new Chain(10)
  .add(modulo(10, 3)) // Adds the result of modulo operation
  .subtract(2)
  .getResult();
console.log(result); // Output: 9

Notes​

  • Ensure the modulus (mod) is always positive and non-zero for valid results.
  • For modDivide, ensure that the divisor has a modular multiplicative inverse under the given modulus.