The Marvelous Mrs Maths

This repo has the vibe from the show The Marvelous Mrs. Maisel

it really does...

Group Theory

Symmetric group

• permutation notations: one-line and disjoint cycle
• composition of permutations
• cyclic subgroup in symmetric group
• parity of a permutation
• generate all possible permutation of n objects (Heap's algorithm)

Small groups

• generate all groups of order n (for small n) using backtracking
• check if two groups are isomorphic to each other

Linear algebra

Basic matrix operations

• addition, scalar multiplication, transpose
• matrix multiplication

Square matrix

• symmetric matrix
• identity matrix
• invertible matrix
• trace
• determinant (leibniz formula)

Gaussian elimination

Number theory

• euclidean algorithm and extended euclidean algorithm
• modular inverse
• linear congruence
• chinese remainder theorem
• fast exponentiation
• miller rabin primality test
• pollard's rho algorithm