Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add Arcadi4/nerdy --skill polynomials-and-fftgit clone --depth 1 https://github.com/Arcadi4/nerdyWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/arcadi4/nerdy/polynomials-and-fft)<a href="https://agentmods.dev/skills/arcadi4/nerdy/polynomials-and-fft"><img src="https://agentmods.dev/badge/skills/arcadi4/nerdy/polynomials-and-fft.svg" alt="Measured on agentmods" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00042 | $0.03401 |
| Opus 5 | $0.00021 | $0.01700 |
| Sonnet 5 | $0.00008 | $0.00680 |
| Haiku 4.5 | $0.00004 | $0.00340 |
Grade A, and why
polynomials-and-fft scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 341 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Polynomials and the FFT
Overview
The FFT chapter is about changing representation at the right points. Polynomial multiplication is expensive in coefficient form, cheap in point-value form, and fast overall only when the evaluation and interpolation points have roots-of-unity structure.
Core principle: never treat FFT as a magic multiplication primitive. State the representation, degree-bound, evaluation length, root system, inverse transform, and exactness model before giving an algorithm or bound.
Shared CLRS Conventions
Follow the parent clrs skill for mathematical formatting, formula-free headings, direct polished answers, and CLRS-wide answer style. Keep formulas in display blocks, including degree-bounds, roots of unity, DFT definitions, recurrence equations, and convolution identities.
When to Use
- A prompt asks for polynomial multiplication, convolution, coefficient representation, point-value representation, interpolation, or evaluation at many points.
- A prompt mentions DFT, inverse DFT, FFT, roots of unity, twiddle factors, butterflies, bit reversal, or FFT circuits.
- A prompt tries to multiply degree-bounded polynomials using too few point-value pairs.
- A prompt asks whether textbook complex FFT is safe for exact integer answers.
- A prompt asks for proof moves involving cancellation, halving, summation over roots of unity, or Vandermonde uniqueness.
Do not use this skill for general signal-processing design unless the algorithmic question is the discrete transform, convolution, or roots-of-unity structure.
First Decision: Which Representation Is the Work In?
| Workload | Representation to prefer | Watch for |
|---|---|---|
| Add two polynomials already in coefficient form | Coefficients | Add coordinatewise; multiplication is the hard operation |
| Evaluate one polynomial at one point | Coefficients with Horner's rule | This is linear, not FFT-worthy |
| Multiply many coefficients directly | Convert through point values | Degree-bound must grow before interpolation |
| Add or multiply values at the same evaluation points | Point values | The points must match between inputs |
| Recover coefficients from arbitrary points | Interpolation | General interpolation is slower and numerically fragile |
| Recover coefficients from roots of unity | Inverse DFT | Divide by the transform length after using inverse roots |
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 7d ago First seen · 341 lines · 42 tokens per session scan A bcfdae99d7ce
polynomials-and-fft is a skill published in the GitHub repository Arcadi4/nerdy (7 stars, last pushed 4mo ago), licensed MIT. It adds 42 tokens to every session and 3,401 once invoked, about $0.0002 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.
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