Concepts4
∑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
⚙️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