「math」の検索結果

Use when adding, editing or reviewing skills, role prompts or skill metadata.

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Use when maintaining the skills-only repository or checking whether a change belongs here.

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Use when checking skill metadata, references or repository boundaries, or preparing an explicitly requested skills release.

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Use when starting a modeling task or installing, backing up or maintaining the skills pack.

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Use when planning a modeling solution, selecting the next useful step or briefing a specialist.

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Use when finding literature, datasets, domain facts, citation details or licensed figure references.

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CUMCM 国赛、MCM/ICM 美赛与电工杯数学建模竞赛的端到端协作工作流。Use when a user explicitly works on one of these modeling contests or asks to run/review a modeling-competition paper from problem selection through modeling, solving, robustness, writing, compliance, and final submission review. Provides 10 stages, persistent decision state, competition-specific rules/templates, deterministic scoring helpers, numbered decisions, and Codex/Claude Code handoff. Do not trigger for generic model selection, ordinary data analysis, or non-competition paper review.

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Extract abstract mathematical models from functional code (Haskell, OCaml, F#) for formal reasoning in Isabelle/HOL. Use when users need to: (1) Convert functional programs to Isabelle definitions, (2) Extract high-level algorithm essence from implementation code, (3) Generate formal specifications and properties from code, (4) Create verification-ready models that capture mathematical properties while abstracting away implementation details. Focuses on structural recursion, algebraic data types, higher-order functions, and invariant extraction.

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Generate formal specifications (definitions, predicates, invariants, pre/post-conditions) in Isabelle/HOL or Coq from informal requirements, source code, pseudocode, or mathematical descriptions. Use when users need to: (1) Formalize algorithms or data structures, (2) Create function specifications with contracts, (3) Generate predicates and properties for verification, (4) Translate informal requirements into formal logic, (5) Specify invariants for loops or data structures, or (6) Create formal definitions for mathematical concepts. Supports both Isabelle/HOL and Coq equally.

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Extract abstract mathematical models from imperative code (C, C++, Python, Java, etc.) suitable for formal reasoning in Coq. Use when the user asks to model imperative code in Coq, create Coq specifications from imperative programs, extract mathematical models for verification, or translate imperative algorithms to Coq for formal reasoning and proof.

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Review mathematical agent trajectories for evidence-backed Jacobian improvements; do not resume solving.

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Use Jacobian’s typed operations when exact computation or structural analysis can help solve a mathematical problem.

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Extract reusable Jacobian capabilities from a mathematical solution corpus, rather than one agent trajectory.

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Audit a bounded mathematical slice for missing or unusable Jacobian capabilities, beyond a single-operation review.

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Use Jacobian's MCP operations for nontrivial mathematical computation, finite search, structural analysis, formal checking, probability, or optimization.

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CesiumJS spatial math - Cartesian3, Cartographic, Matrix4, Quaternion, Transforms, Ellipsoid, BoundingSphere, projections, coordinate conversions. Use when converting between coordinate systems, computing positions on the ellipsoid, performing spatial intersection tests, building model matrices, or working with geographic projections.

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Deploy AI models to embedded hardware using MathWorks tools (MATLAB, Simulink, Embedded Coder). Covers two workflow patterns: (1) MathWorks-native or 3P-imported models rebuilt as dlnetwork for lean hardware (Cortex-M, DSP), (2) direct C/C++ code generation from PyTorch and LiteRT models for high-performance hardware (Cortex-A, x86, GPU). Trigger when: user wants to deploy AI to embedded targets; generate C/CUDA from neural networks; compress AI models for MCU/DSP; integrate AI in Simulink for system-level simulation; import PyTorch/ONNX/TensorFlow models for embedded deployment; optimize AI for resource-constrained hardware; or use loadPyTorchExportedProgram, importNetworkFromPyTorch, dlquantizer, exportNetworkToSimulink, or Embedded Coder with AI models.

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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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Create mathematical animations with Manim Community Edition(manimce), with optional TTS voiceover and synced subtitles. Generates distinctive, production-grade animations that avoid generic "AI slop" aesthetics. Use when user wants to animate concepts, equations, illustrate proofs, visualize algorithms, create math explainers, or produce 3Blue1Brown-style videos.

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Family-G proof & derivation integrity forensics: does a THIRD PARTY's written proof/derivation actually establish its theorem, or does it skip an obligation, assume its own conclusion, take an invalid step, drift a symbol's meaning, or smuggle an unstated assumption? Decides from the WRITTEN proof/derivation — verdict-bearing at L1 (the LaTeX source; PDF-extracted math is unreliable, so an L0 PDF-only run surfaces info only) — never asserts 'fabricated', only that the step shown does not hold. A fresh cross-model reviewer reads the theorem/proof + an extraction-only obligation scaffold and proposes per-obligation findings, each span-anchored to the evidence ledger (claims.json); reviewer≠adjudicator. Emits proof-derivation-forensics.findings.json; NEVER computes the verdict. dimension=proof, can be critical. Triggers: "proof forensics", "check this proof", "derivation integrity", "audit the math", "证明审计", "推导有没有漏洞".

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调香师与香水 (调香师 / 香水 (Perfumery & Fragrance) — 香水创作与香气调配的职业认知操作系统，从业者/调香师/评香师/学习者视角。覆盖: (a) 第一性张力 — codifiable 理论层 (原料知识/香料化学/嗅觉家族分类/accord 和弦/配方结构 %/挥发度金字塔/IFRA 法规) ⇄ tacit 校准层 (嗅觉记忆/闻香训练/「the nose」/创作直觉/盲嗅识别)，这行的核心矛盾是「可背诵的原料与公式」与「不可言传的嗅觉记忆与品味」之间，嗅觉记忆是极致 tacit 技能; (b) 法系传统 vs 分子/合成派 — 法国 Grasse 天然香料 + haute parfumerie 艺术传统 (天然精油/原精/学徒制) vs 现代分子派 (aroma chemicals 香基/captives 专利分子/headspace 顶空捕香/功能香精)，两套对「香水是什么」的世界观; (c) 培养/传承 — ISIPCA (凡尔赛香水学校) + 四大香精公司内部调香学校 (Givaudan/Firmenich(DSM-Firmenich)/IFF/Symrise) + 学徒制 + 「鼻子」tacit 校准; 角色分工: perfumer(parfumeur 调香师) vs evaluator(评香师) vs flavorist(食用香精师); (d) 行业结构 — 四大香精公司寡头 (Givaudan/DSM-Firmenich/IFF/Symrise) + Mane/Robertet/Takasago，为品牌做 B2B 命题创作 (the brief → creation → mods 模型); vs niche/indie 小众独立香水 (artisanal/直营); 天然 (Grasse/精油) vs 合成 (香基/captives) 的成本与可持续之争; (e) 创作层 — 香调金字塔 (top/heart/base notes 前中后调)、accord 和弦、配方 (酒精中 % 浓度)、浓度分级 (parfum/EDP/EDT/EDC)、调香师的「香风琴」orgue、trials/mods 试样迭代、weighing 称量精度; (f) 法规与安全 — IFRA standards (原料限用)、EU 致敏原标签 (26→80+ allergens)、REACH、橡苔/atranol 限用、经典香水 (Mitsouko/Chanel No.5) 因法规被迫重配 (reformulation) 与创作自由之张力; (g) 评价/批评 — Luca Turin & Tania Sanchez (《Perfumes: The Guide》《The Secret of Scent》气味的科学)、香评人、Fragrantica/Basenotes 社区、vintage vs reformulation 之争、niche vs designer 之争。学派分歧: 法系天然传统派 vs 分子合成派、天然纯粹派 vs 合成实用派、haute parfumerie/niche 艺术派 vs mass designer 商业派、「鼻子=艺术家」vs「调香师=香气工程师/技师」、嗅觉科学之争 (Luca Turin 振动理论 vs 主流形状/受体理论)。不含: 香薰蜡烛/家居香氛纯生产营销、芳香疗法健康宣称 (aromatherapy)、纯化妆品配方学 (超出香精范畴)、DIY 家用香氛套件、精油传销/MLM。) Master OS — automated mastery of 调香师 / 香水 (Perfumery & Fragrance) — 香水创作与香气调配的职业认知操作系统，从业者/调香师/评香师/学习者视角。覆盖: (a) 第一性张力 — codifiable 理论层 (原料知识/香料化学/嗅觉家族分类/accord 和弦/配方结构 %/挥发度金字塔/IFRA 法规) ⇄ tacit 校准层 (嗅觉记忆/闻香训练/「the nose」/创作直觉/盲嗅识别)，这行的核心矛盾是「可背诵的原料与公式」与「不可言传的嗅觉记忆与品味」之间，嗅觉记忆是极致 tacit 技能; (b) 法系传统 vs 分子/合成派 — 法国 Grasse 天然香料 + haute parfumerie 艺术传统 (天然精油/原精/学徒制) vs 现代分子派 (aroma chemicals 香基/captives 专利分子/headspace 顶空捕香/功能香精)，两套对「香水是什么」的世界观; (c) 培养/传承 — ISIPCA (凡尔赛香水学校) + 四大香精公司内部调香学校 (Givaudan/Firmenich(DSM-Firmenich)/IFF/Symrise) + 学徒制 + 「鼻子」tacit 校准; 角色分工: perfumer(parfumeur 调香师) vs evaluator(评香师) vs flavorist(食用香精师); (d) 行业结构 — 四大香精公司寡头 (Givaudan/DSM-Firmenich/IFF/Symrise) + Mane/Robertet/Takasago，为品牌做 B2B 命题创作 (the brief → creation → mods 模型); vs niche/indie 小众独立香水 (artisanal/直营); 天然 (Grasse/精油) vs 合成 (香基/captives) 的成本与可持续之争; (e) 创作层 — 香调金字塔 (top/heart/base notes 前中后调)、accord 和弦、配方 (酒精中 % 浓度)、浓度分级 (parfum/EDP/EDT/EDC)、调香师的「香风琴」orgue、trials/mods 试样迭代、weighing 称量精度; (f) 法规与安全 — IFRA standards (原料限用)、EU 致敏原标签 (26→80+ allergens)、REACH、橡苔/atranol 限用、经典香水 (Mitsouko/Chanel No.5) 因法规被迫重配 (reformulation) 与创作自由之张力; (g) 评价/批评 — Luca Turin & Tania Sanchez (《Perfumes: The Guide》《The Secret of Scent》气味的科学)、香评人、Fragrantica/Basenotes 社区、vintage vs reformulation 之争、niche vs designer 之争。学派分歧: 法系天然传统派 vs 分子合成派、天然纯粹派 vs 合成实用派、haute parfumerie/niche 艺术派 vs mass designer 商业派、「鼻子=艺术家」vs「调香师=香气工程师/技师」、嗅觉科学之争 (Luca Turin 振动理论 vs 主流形状/受体理论)。不含: 香薰蜡烛/家居香氛纯生产营销、芳香疗法健康宣称 (aromatherapy)、纯化妆品配方学 (超出香精范畴)、DIY 家用香氛套件、精油传销/MLM。: top builders' mental models, tool stack, current workflows, jargon, and where to keep up. Trigger this skill when the user works on 调香师 / 香水 (Perfumery & Fragrance) — 香水创作与香气调配的职业认知操作系统，从业者/调香师/评香师/学习者视角。覆盖: (a) 第一性张力 — codifiable 理论层 (原料知识/香料化学/嗅觉家族分类/accord 和弦/配方结构 %/挥发度金字塔/IFRA 法规) ⇄ tacit 校准层 (嗅觉记忆/闻香训练/「the nose」/创作直觉/盲嗅识别)，这行的核心矛盾是「可背诵的原料与公式」与「不可言传的嗅觉记忆与品味」之间，嗅觉记忆是极致 tacit 技能; (b) 法系传统 vs 分子/合成派 — 法国 Grasse 天然香料 + haute parfumerie 艺术传统 (天然精油/原精/学徒制) vs 现代分子派 (aroma chemicals 香基/captives 专利分子/headspace 顶空捕香/功能香精)，两套对「香水是什么」的世界观; (c) 培养/传承 — ISIPCA (凡尔赛香水学校) + 四大香精公司内部调香学校 (Givaudan/Firmenich(DSM-Firmenich)/IFF/Symrise) + 学徒制 + 「鼻子」tacit 校准; 角色分工: perfumer(parfumeur 调香师) vs evaluator(评香师) vs flavorist(食用香精师); (d) 行业结构 — 四大香精公司寡头 (Givaudan/DSM-Firmenich/IFF/Symrise) + Mane/Robertet/Takasago，为品牌做 B2B 命题创作 (the brief → creation → mods 模型); vs niche/indie 小众独立香水 (artisanal/直营); 天然 (Grasse/精油) vs 合成 (香基/captives) 的成本与可持续之争; (e) 创作层 — 香调金字塔 (top/heart/base notes 前中后调)、ac

日本語の概要は準備中です。原文の説明を表示しています。

Applies the Neoplatonic and mathematical reasoning of Hypatia of Alexandria. Use this skill whenever the user is grappling with the pursuit of truth, foundational logic, the hierarchy of knowledge, or the distraction of superficial and physical desires versus deeper intellectual pursuits. Trigger this when discussing mathematics as a foundation for higher understanding, astronomy, overcoming base impulses, or seeking the ultimate source of truth. It is highly relevant for questions about rigorous intellectual discipline, esoteric philosophy, and elevating one's mind above material distractions.

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Proof writing and verification techniques for mathematical reasoning. Covers 13 proof strategies with canonical worked examples — direct, contrapositive, contradiction, cases, WLOG, vacuous/trivial, biconditional, counterexample, existence (constructive and non-constructive), uniqueness, induction (weak, strong, structural), pigeonhole/double-counting, and diagonal argument/invariants. Use when writing, verifying, or selecting proof strategies for any mathematical claim.

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Conjecture generation, sequence analysis, and experimental mathematics for mathematical discovery. Covers sequence analysis (OEIS lookups, recurrence relations, generating functions), pattern detection methods (finite differences, ratio analysis, modular patterns), conjecture generation workflow, classical integer sequences (Fibonacci, Catalan, partition numbers, Bernoulli numbers), combinatorial identities, the probabilistic method (Erdos, expected value arguments, Lovasz Local Lemma), AI-assisted discovery (FunSearch, Ramanujan Machine), and confidence calibration with cautionary tales (Mertens conjecture, Polya conjecture). Use when discovering patterns, analyzing sequences, generating conjectures, or working with combinatorial identities.

日本語の概要は準備中です。原文の説明を表示しています。