Add two numbers together. Pure arithmetic addition operation. (Domain: arithmetic, Category: core)

Subtract the second number from the first number. (Domain: arithmetic, Category: core)

Multiply two numbers together. (Domain: arithmetic, Category: core)

Divide the first number by the second number. (Domain: arithmetic, Category: core)

Raise a number to a power. Handles integer and fractional exponents. (Domain: arithmetic, Category: core)

Calculate the square root of a number. (Domain: arithmetic, Category: core)

Calculate the absolute value of a number. (Domain: arithmetic, Category: core)

Determine the sign of a number. Returns 1, -1, or 0. (Domain: arithmetic, Category: core)

Negate a number (return its additive inverse). (Domain: arithmetic, Category: core)

Round a number to a specified number of decimal places. (Domain: arithmetic, Category: core)

Return the floor of a number (largest integer less than or equal to x). (Domain: arithmetic, Category: core)

Return the ceiling of a number (smallest integer greater than or equal to x). (Domain: arithmetic, Category: core)

Truncate a number towards zero (remove decimal part). (Domain: arithmetic, Category: core)

Round a number up to the nearest multiple of significance. Always rounds away from zero. (Domain: arithmetic, Category: general)

Round a number down to the nearest multiple of significance. Always rounds toward zero. (Domain: arithmetic, Category: general)

Round a number to the nearest multiple of significance. Uses standard rounding rules. (Domain: arithmetic, Category: general)

Calculate the modulo (remainder) of division. Returns a % b. (Domain: arithmetic, Category: core)

Perform division and return both quotient and remainder. Returns (quotient, remainder). (Domain: arithmetic, Category: core)

Calculate modular exponentiation: (base^exponent) mod modulus. Efficient for large numbers. (Domain: arithmetic, Category: core)

Return the integer quotient of division without remainder. Equivalent to a // b. (Domain: arithmetic, Category: general)

Calculate floating-point remainder of division (IEEE remainder operation). (Domain: arithmetic, Category: core)

Calculate floating-point modulo operation. Similar to % but for floats. (Domain: arithmetic, Category: core)

Check if two numbers are exactly equal. For floating-point numbers, consider using approximately_equal instead. (Domain: arithmetic, Category: comparison)

Check if two numbers are not equal. (Domain: arithmetic, Category: comparison)

Check if the first number is less than the second number. (Domain: arithmetic, Category: comparison)

Check if the first number is less than or equal to the second number. (Domain: arithmetic, Category: comparison)

Check if the first number is greater than the second number. (Domain: arithmetic, Category: comparison)

Check if the first number is greater than or equal to the second number. (Domain: arithmetic, Category: comparison)

Check if a number is within a specified range (inclusive by default). (Domain: arithmetic, Category: comparison)

Check if a value is between two bounds (exclusive by default, like mathematical interval notation). (Domain: arithmetic, Category: comparison)

Find the smaller of two numbers. (Domain: arithmetic, Category: comparison)

Find the larger of two numbers. (Domain: arithmetic, Category: comparison)

Clamp a value between a minimum and maximum bound. Ensures the value stays within specified limits. (Domain: arithmetic, Category: comparison)

Sort a list of numbers in ascending or descending order. (Domain: arithmetic, Category: comparison)

Get the rank (1-based position) of each number in a list when sorted. Handles ties appropriately. (Domain: arithmetic, Category: comparison)

Find the minimum value in a list of numbers. (Domain: arithmetic, Category: comparison)

Find the maximum value in a list of numbers. (Domain: arithmetic, Category: comparison)

Check if two floating-point numbers are approximately equal within a tolerance. Handles floating-point precision issues. (Domain: arithmetic, Category: comparison)

Check if a number is close to zero within a tolerance. Useful for floating-point comparisons. (Domain: arithmetic, Category: comparison)

Check if a number is finite (not infinite and not NaN). (Domain: arithmetic, Category: comparison)

Check if a number is NaN (Not a Number). (Domain: arithmetic, Category: comparison)

Check if a number is infinite (positive or negative infinity). (Domain: arithmetic, Category: comparison)

Check if a number is normal (finite, non-zero, and not subnormal). (Domain: arithmetic, Category: comparison)

Relative tolerance comparison using both absolute and relative tolerances. (Domain: arithmetic, Category: comparison)

Check if a number is prime. A prime number is only divisible by 1 and itself. (Domain: arithmetic, Category: number_theory)

Find the next prime number greater than the given number. (Domain: arithmetic, Category: number_theory)

Find the nth prime number (1-indexed). Uses efficient prime generation. (Domain: arithmetic, Category: number_theory)

Find all prime factors of a number. Returns the prime factorization as a list. (Domain: arithmetic, Category: number_theory)

Count the number of prime numbers less than or equal to n (prime counting function π(n)). (Domain: arithmetic, Category: number_theory)

Check if two numbers are coprime (their greatest common divisor is 1). (Domain: arithmetic, Category: number_theory)

Generate the first n prime numbers using the Sieve of Eratosthenes algorithm. (Domain: arithmetic, Category: number_theory)

Calculate the Greatest Common Divisor (GCD) of two integers using Euclidean algorithm. (Domain: arithmetic, Category: number_theory)

Calculate the Least Common Multiple (LCM) of two integers. (Domain: arithmetic, Category: number_theory)

Find all positive divisors of a number in sorted order. (Domain: arithmetic, Category: number_theory)

Check if the first number is divisible by the second number (remainder is zero). (Domain: arithmetic, Category: number_theory)

Check if a number is even (divisible by 2). (Domain: arithmetic, Category: number_theory)

Check if a number is odd (not divisible by 2). (Domain: arithmetic, Category: number_theory)

Extended Euclidean algorithm. Returns gcd(a,b) and coefficients x,y such that ax + by = gcd(a,b). (Domain: arithmetic, Category: number_theory)

Count the number of positive divisors of a number (divisor function τ(n)). (Domain: arithmetic, Category: number_theory)

Calculate the sum of all positive divisors of a number (divisor function σ(n)). (Domain: arithmetic, Category: number_theory)

Check if a number is a perfect square. (Domain: arithmetic, Category: basic_sequences)

Generate the first n perfect squares. (Domain: arithmetic, Category: basic_sequences)

Get the nth perfect square (0-indexed). (Domain: arithmetic, Category: basic_sequences)

Check if a number is a power of two. (Domain: arithmetic, Category: basic_sequences)

Generate the first n powers of two. (Domain: arithmetic, Category: basic_sequences)

Get the nth power of two (0-indexed). (Domain: arithmetic, Category: basic_sequences)

Calculate the nth Fibonacci number using efficient matrix exponentiation. (Domain: arithmetic, Category: basic_sequences)

Generate the first n Fibonacci numbers. (Domain: arithmetic, Category: basic_sequences)

Check if a number is a Fibonacci number. (Domain: arithmetic, Category: basic_sequences)

Calculate factorial n! = n × (n-1) × ... × 2 × 1. (Domain: arithmetic, Category: basic_sequences)

Calculate the double factorial of a number. n!! = n × (n-2) × (n-4) × ... × 2 or 1. (Domain: arithmetic, Category: general)

Calculate subfactorial !n (derangements of n items). (Domain: arithmetic, Category: basic_sequences)

Calculate the nth triangular number T_n = n(n+1)/2. (Domain: arithmetic, Category: basic_sequences)

Check if a number is a triangular number. (Domain: arithmetic, Category: basic_sequences)

Generate the first n triangular numbers. (Domain: arithmetic, Category: basic_sequences)

Calculate the nth pentagonal number P_n = n(3n-1)/2. (Domain: arithmetic, Category: basic_sequences)

Check if a number is a pentagonal number. (Domain: arithmetic, Category: basic_sequences)

Generate the first n pentagonal numbers. (Domain: arithmetic, Category: basic_sequences)

Calculate the nth square pyramidal number. (Domain: arithmetic, Category: figurate_numbers)

Calculate the nth tetrahedral number (sum of first n triangular numbers). (Domain: arithmetic, Category: basic_sequences)

Calculate the nth Catalan number C_n = (2n)!/(n+1)!n!. (Domain: arithmetic, Category: combinatorial_numbers)

Check if a number is a Mersenne prime (prime of form 2^p - 1 where p is prime). (Domain: arithmetic, Category: special_primes)

Get known Mersenne prime exponents up to a limit. (Domain: arithmetic, Category: special_primes)

Perform Lucas-Lehmer primality test for Mersenne numbers. (Domain: arithmetic, Category: special_primes)

Generate Mersenne numbers 2^p - 1 for prime exponents up to limit. (Domain: arithmetic, Category: special_primes)

Check if a number is a Fermat prime (prime of form 2^(2^n) + 1). (Domain: arithmetic, Category: special_primes)

Generate Fermat numbers F_n = 2^(2^n) + 1 up to index limit. (Domain: arithmetic, Category: special_primes)

Get the five known Fermat primes. (Domain: arithmetic, Category: special_primes)

Check if a prime p is a Sophie Germain prime (2p + 1 is also prime). (Domain: arithmetic, Category: special_primes)

Check if a prime q is a safe prime (q = 2p + 1 where p is prime). (Domain: arithmetic, Category: special_primes)

Find Sophie Germain and safe prime pairs up to limit. (Domain: arithmetic, Category: special_primes)

Check if a number is part of a twin prime pair (p, p+2). (Domain: arithmetic, Category: special_primes)

Find twin prime pairs up to limit. (Domain: arithmetic, Category: special_primes)

Find all cousin prime pairs (primes differing by 4) up to limit. (Domain: arithmetic, Category: prime_patterns)

Find all sexy prime pairs (primes differing by 6) up to limit. (Domain: arithmetic, Category: prime_patterns)

Check Wilson's theorem: p is prime iff (p-1)! ≡ -1 (mod p). (Domain: arithmetic, Category: primality_tests)

Calculate k! mod m efficiently for Wilson's theorem. (Domain: arithmetic, Category: primality_tests)

Check if n is a Fermat pseudoprime to base a. (Domain: arithmetic, Category: pseudoprimes)

Perform Fermat primality check for base a. (Domain: arithmetic, Category: primality_tests)

Check if n is a Carmichael number (absolute Fermat pseudoprime). (Domain: arithmetic, Category: pseudoprimes)