「math」の検索結果

Explains DSP math concepts to developers who need the theory behind an algorithm. Use whenever the user asks how a signal-processing concept works, wants intuition behind a formula, or hits a math-shaped bug. Trigger on phrases like "how does a Fourier transform work", "explain z-transforms", "what is convolution", "why does my biquad ring", "what is windowing for", "what causes aliasing", or "how do I convert gain to dB". Also trigger when the user pastes DSP code and asks why it behaves a certain way.

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Verify and write proofs using the Acorn theorem prover for mathematical and cryptographic formalization. Use when working with Acorn proof files (.ac), verifying theorems, formalizing mathematical or cryptographic protocols, or writing proofs in the Acorn language. Triggers on: (1) Creating or editing .ac files, (2) Running acorn verify commands, (3) Formalizing math or crypto proofs, (4) Questions about Acorn syntax or standard library.

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Expert in visualizing and explaining braid theory, knot mathematics, and topological concepts for educational purposes. Use for creating interactive visualizations, explainer cards, step-wise animations, and translating abstract algebra into intuitive understanding. Activate on keywords: braid theory, knot visualization, σ notation, crossing diagrams, Yang-Baxter, topological education. NOT for general math tutoring, pure knot invariant computation, or non-educational knot theory research.

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Performs numerical and symbolic mathematics using NumPy, SciPy, SymPy, and mpmath. Use when the user needs linear algebra, arrays, optimization, integration, ODEs, symbolic expressions, equation solving, or arbitrary-precision arithmetic.

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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

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Trigger when: (1) User mentions "manim" or "Manim Community" or "ManimCE", (2) Code contains `from manim import *`, (3) User runs `manim` CLI commands, (4) Working with Scene, MathTex, Create(), or ManimCE-specific classes. Best practices for Manim Community Edition - the community-maintained Python animation engine. Covers Scene structure, animations, LaTeX/MathTex, 3D with ThreeDScene, camera control, styling, and CLI usage. NOT for ManimGL/3b1b version (which uses `manimlib` imports and `manimgl` CLI).

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Work on one hard mathematics problem in this session yourself, with no sub-agents: reason in stages, record each settled step in a notes file so that nothing written is lost if a response is cut off, and end with a self-contained proof.md. Usage: /math-proof:solo <the problem, stated in full, or the path of a file holding it>.

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Work on one hard mathematics problem in rounds: each round a judge writes a few self-contained questions, independent workers answer them, and the judge keeps a ledger of what is proved, refuted and open, until the judge concludes or the rounds run out, and then a proof.md says plainly what is and is not proved. A run takes hours and dozens of worker runs. Usage: /math-proof:siege [NAME=value settings] <the problem, stated in full, or the path of a file holding it>.

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数学题分步讲解视频的领域知识。适用场景：(1) 用户给出一道数学题并要求做讲解/ 解题视频；(2) 用户说"讲解这道题"、"生成解题视频"、"make a math tutorial"； (3) 需要中文数学教学视频，涉及方程、公式或几何图形。本 skill 只提供领域 知识（题目拆解、讲解节奏、旁白文案规范、版式与 KaTeX 排版风格）；画面、 配音与成片一律用 Creator 原生 Element 与工具从源头构建。

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Use when building a quarterly bookings forecast, ARR projection, pipeline forecast, NRR projection, or commit/best-case/pipe-only board number — especially when the CRO needs to walk the board through funnel math + cohort ARR + per-stage conversion assumptions without the theatre of a single undefended number. Decomposes pipeline into commit, best-case, and pipe-only tiers; projects cohort-level NRR/GRR to surface leaky cohorts before they show up in the consolidated number; scores per-stage funnel confidence so soft-floor stages get treated differently from high-confidence ones. Every output explicitly names the conversion rate used, the data window, and the weighting choice. For Head of Commercial, RevOps, VP Sales, and CRO at quarterly forecast or board prep. NOT financial close (see finance/financial-analysis). NOT strategic CRO hiring/territory (see c-level-advisor/cro-advisor). NOT pricing (see sibling pricing-strategist).

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Pre-built custom directives for json-render — formatting, math, string manipulation, and i18n. Use when working with @json-render/directives, defining custom directives with defineDirective, or adding $format, $math, $concat, $count, $truncate, $pluralize, $join, or $t to specs.

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可重跑的数学计算与反例实验。用于 SymPy 精确代数/微积分/方程/矩阵、NumPy/SciPy 数值方法、mpmath 高精度交叉检查、OEIS 序列识别、有限范围反例搜索和计算证据记录。

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数学形式化与 proof-assistant 验证。用户要求 Lean 4/Mathlib、formal proof、kernel check、无 sorry 编译，或需要把自然语言定理切成可形式化定义和引理时使用。缺少 Lean 工具链时必须 fail-closed。

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Develop and verify a mathematical proof in Lean, continue an incomplete Lean project, or audit whether it proves the original statement. Connect actual inputs to intermediate lemmas, assemble the target theorem, check its transitive axioms, and provide a reproducible handoff. Use when Lean is requested or a specific proof obligation benefits from formal verification; use proof-writer for ordinary mathematical drafting.

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Rigorous mathematical proof verification and fixing workflow. Reads a LaTeX proof, identifies gaps via fresh-agent Codex GPT-6-Astra ultra review, fixes each gap with full derivations, re-reviews, and generates an audit report. Base review is same-family provisional. Use when user says "检查证明", "verify proof", "proof check", "审证明", "check this proof", or wants rigorous mathematical verification of a theory paper.

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Rigorous mathematical proof verification and fixing workflow. Reads a LaTeX proof, identifies gaps via cross-model review (external reviewer backend, ultra reasoning), fixes each gap with full derivations, re-reviews, and generates an audit report. Use when user says "检查证明", "verify proof", "proof check", "审证明", "check this proof", or wants rigorous mathematical verification of a theory paper.

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Calculate and model paid-media CPA, CPL, CPC, CPM, ROAS, MER, break-even targets, contribution margin, LTV:CAC, impression-share opportunity, budgets, forecasts, and experiment economics. Use for PPC math, ad calculator, break-even analysis, ROAS calculator, CPA calculator, budget forecast, LTV CAC, or MER.

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Writes and reviews structured Lean 4 proofs and designs Lean libraries following Mathlib conventions. Use when proving theorems in Lean, formalizing mathematics or specifications in Lean 4, defining new types or definitions in a Lean library, reviewing Lean proofs for readability and maintainability, refactoring long tactic proofs into lemmas, filling in sorry placeholders in a Lean development, setting up CI or linters for a Lean project, diagnosing slow proofs or maxHeartbeats timeouts, or writing custom tactics, macros, or linters.

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数学建模竞赛工作流入口。用于启动完整建模流程：询问用户偏好，生成 plan.md 和 todo.md，并按阶段调用赛题分析、建模、代码与图表、流程图、论文撰写、验证验收等 skills。

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将用户提供的一篇完整数学建模竞赛论文改写为面向 EI 会议投稿的英文研究论文，内置 IEEE conference LaTeX 模板，完成研究主线提炼、结构重组、图表整理、证据核验与源码/PDF 交付。适用于数模论文转会议论文、竞赛论文英文改稿及已有会议稿迭代。

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Develops mathematical understanding through examples, visualization, and analogy

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Routes problems to appropriate mathematical frameworks using expert heuristics

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Unified math capabilities - computation, solving, and explanation. I route to the right tool.

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Guide to the math cognitive stack - what tools exist and when to use each

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