Work through linear algebra problems involving vector spaces, from checking subspaces and linear independence to finding bases, dimensions, and coordinate changes. The skill connects each task to symbolic calculation or proof scripts for checking the results.
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Work through optimization problems using gradients, which indicate how a function changes. The skill guides method selection, step size choices, and convergence checks, with SciPy examples for conjugate gradient and BFGS methods.
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Choose an approach for second-order ordinary differential equations based on their coefficients and forcing terms. Work through characteristic equations and particular solutions, or use numerical methods for problems defined by initial values or boundary conditions.
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Work through integration problems in measure theory by matching the problem's conditions to suitable theorems. The skill covers simple functions, exchanging limits and integrals, lower bounds, and changing integration order, with commands for symbolic calculations and proof tools.
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Work through abstract algebra problems about rings by checking their defining rules and properties. The skill organizes questions about ideals and structure-preserving maps, with Z3 and Sympy command examples for proof checks and symbolic calculations.
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Build understanding of mathematical ideas before calculating. The skill guides you through concrete examples, diagrams, simpler cases, and analogies, then summarizes the intuition and suggests a next step with a check.
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Work through measure theory problems involving sigma algebras, collections of sets closed under complements and countable unions. The skill outlines approaches to checking axioms, generating these collections, testing measurability, and studying products, with supporting tool commands.
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Apply consistent rules when creating or editing Claude Code skills. It covers concise instructions, usage conditions, trigger registration, and tool permissions, with additional guidance for skills that call scripts for MCP operations.
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Create Claude Code skills from reusable scripts or workflows that connect external tools. It guides the structure of SKILL.md, supporting files, execution instructions, and optional rules that suggest when a skill should be used.
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Choose a code search tool based on whether you need symbols, structural patterns, conceptual answers, or exact text. The rules guide agents toward relevant files before reading full contents, helping limit unnecessary search output.
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Choose code search tools based on the question: AST-grep for code structure, LEANN for meaning, and Grep for exact names. Read complete files after locating relevant matches to limit unnecessary output and token use.
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Organize agent skills around domain routers that map requests to specific commands. It guides router selection, automatic activation alongside related skills, and the separation between broad activation rules and precise command matching.
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Review code changes from several perspectives using parallel specialist agents. It combines findings on code quality, design alignment, and change risks into a final verdict, prioritized actions, and a distinction between blocking and non-blocking issues.
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Restructure an existing SKILL.md into v5 Hybrid format. Four agents use indexed reference books to identify workflow states, actions, decision rules, constraints, and completion conditions, then combine their findings into an upgraded skill and validation report.
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Resume work from a handoff document by reviewing linked materials and checking the current code against recorded changes. The skill proposes next steps, creates a prioritized task list, and assigns approved work to specialist agents.
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Investigate how an existing codebase works and document its components, connections, and file references. Combine current code findings with historical notes to produce a research document grounded in specific paths and line numbers.
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Investigate an unfamiliar codebase and create a handoff document covering its structure, technologies, implementation patterns, and contribution rules. Findings include source file references, issue and pull request templates, testing requirements, and practical points to check before contributing.
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Prepare software releases through security checks, end-to-end tests that cover the full system, and final review. After approval, coordinate version updates, a changelog, and release notes, with blocking issues stopping the workflow.
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Search stored learnings from past sessions by meaning or keywords. Retrieve relevant entries in full, along with their type, confidence, and session context, to revisit earlier findings about development patterns, installation, or errors.
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Search previous work records to recover useful decisions, successful approaches, and failed attempts. Find context in handoffs, plans, and build or test histories, then use those findings when tackling similar tasks or recurring errors.
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Check code quality with qlty CLI, a command-line tool for multiple languages. Review changed or selected files, automatically fix supported issues, format code, and measure complexity and duplication to identify areas that need attention.
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Turn mathematical claims into Lean4 proofs, checked by a theorem prover. A five-phase workflow researches existing results, designs the proof, tests candidate lemmas, implements it, and reports remaining proof gaps and any custom axioms.
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Turn feature requests and conversation context into an implementation plan and handoff document. Review existing code, clarify complex requirements, and organize concrete tasks, affected files, verification steps, assumptions, and risks for review before implementation.
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Use Perplexity to find web sources, get cited research summaries, explore complex decisions, or investigate a topic in depth. Separate modes support quick questions, ranked search results, combined answers, and comprehensive research.
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