polynomials-and-fft

What problem does it solve?

Polynomial multiplication is expensive in coefficient form; converting to a point-value representation via DFT/FFT enables fast convolution, provided padding, root-of-unity structure, and exactness considerations are properly managed.

Core Features & Use Cases

• Efficient polynomial multiplication using the FFT pipeline: padding to an appropriate transform length, forward DFT, pointwise multiplication, inverse DFT, and result trimming.
• Two representations: switch between coefficient form and a point-value form with evaluation points, ensuring consistent ordering of points.
• Guidance on degree-bounds, root-of-unity requirements, and when exact vs floating-point accuracy is appropriate.
• Use case examples: multiplying two degree-n polynomials, performing many-labeled convolutions, and reasoning about interpolation from roots of unity.

Quick Start

Multiply polynomials using FFT with proper padding and root-of-unity handling.