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∑MathAdvanced

Generating Functions - OGF

An ordinary generating function (OGF) encodes a sequence (a_n) as a formal power series A(x) = \sum_{n \ge 0} a_n x^n.

#ordinary generating function#ogf#coefficient extraction+12
∑MathAdvanced

Primitive Roots

A primitive root modulo n is a number g that cycles through all units modulo n when you repeatedly multiply by g, so its multiplicative order equals \(\varphi(n)\).

#primitive root
Advanced
Filtering by:
#ntt
#multiplicative order
#euler totient
+10
⚙️AlgorithmAdvanced

Polynomial Operations

Fast polynomial operations treat coefficients like numbers but use FFT/NTT to multiply in O(n \log n) time instead of O(n^2).

#polynomial#ntt#fft+12
⚙️AlgorithmAdvanced

Convolution Applications

Convolution turns local pairwise combinations (like matching characters or adding two dice) into a single fast transform–multiply–inverse pipeline.

#convolution#fft#ntt+12
⚙️AlgorithmAdvanced

NTT (Number Theoretic Transform)

The Number Theoretic Transform (NTT) is an FFT-like algorithm that performs discrete convolutions exactly using modular arithmetic instead of floating-point numbers.

#ntt#number theoretic transform#polynomial multiplication+11
⚙️AlgorithmAdvanced

FFT (Fast Fourier Transform)

FFT converts a polynomial from coefficients to values at the n-th roots of unity in O(n log n) time, enabling fast multiplication via pointwise products.

#fft#polynomial multiplication#convolution+11