Research, academic papers, education, and exam prep (4.4K skills)
Helps solve contour integral problems by choosing suitable paths, locating singularities, and applying the residue theorem, which relates an integral to values around poles. Includes Sympy commands for finding poles, calculating residues, and checking definite integrals.
Choose numerical methods for approximating integrals based on the interval, function behavior, and number of dimensions. The skill guides SciPy calculations, error tolerance settings, and accuracy checks against known solutions or repeated calculations with tighter tolerances.
Solve complex analysis problems by choosing residue calculations for different singularities, points where a function is not analytic. The skill covers limits, derivatives, Laurent series, and contour integrals using the residue theorem, with Sympy and Z3 command examples.
Analyze propositional formulas and arguments using truth tables, deduction rules, and branching proof trees. Classify formulas as always true, always false, or dependent on their inputs, and check whether an argument follows from its premises.
Choose a mathematical approach for a problem you do not yet know how to model. Guided questions clarify change, uncertainty, optimization goals, and required precision, leading to a recommended framework, starting equations, tools, and related skills.
Review progress while solving a math problem by organizing previous attempts, checking intermediate results, and assessing growing complexity. The skill recommends whether to continue, adjust the approach, switch strategies, or tackle a smaller problem first.
Work through abstract algebra problems about fields, number systems supporting addition, subtraction, multiplication, and division by nonzero elements. Follow a decision tree covering field axioms, extensions, characteristic, and algebraic elements, with commands for polynomial calculations.
Work through graduate-level problems using Rudin's Real and Complex Analysis. The skill guides theorem selection for measure theory, integration, and complex analysis, with commands for textbook searches, symbolic calculations, and verification.
Work through information theory problems about channel capacity, the maximum information a channel can carry. Organize channel models, calculate mutual information, and choose formulas or iterative methods to examine capacity and input distributions.
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.
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.
Researches library documentation, implementation practices, and specific web pages using Nia, Perplexity, and Firecrawl through MCP tools. Produces a handoff document with findings, available code examples, recommendations, pitfalls, and source links for another agent.
Use Pint to convert measurements, calculate with units, and check whether units describe compatible physical quantities. It also breaks quantities into values and units, simplifies compound units, and returns calculation results as JSON.
Research library usage, recommended approaches, and general topics using external documentation and web sources. Choose a brief or thorough investigation, then organize examples, pitfalls, comparisons, and source links into a research document or implementation handoff.
Retrieve web page content from a URL or search query through Firecrawl MCP. Export it as Markdown, HTML, or plain text, with support for extracting structured data from pages.
Turn math requests into specific command-line instructions using pattern-based routing. It covers calculus, equations, unit conversion, geometry, logical proofs, and plotting, returning a command for the agent to execute with the corresponding math script.
Find the right tool for equations, calculus, numerical calculations, proof checks, or math practice. The guide connects tasks to commands for computing results, verifying steps, requesting hints, and plotting functions.
Handle equations, calculus, matrices, unit conversions, and mathematical explanations through one entry point. The skill selects a suitable calculation tool or topic guide, including symbolic math tools that work directly with expressions.
Investigate where or when a photo was taken using visible clues, metadata, reverse image search, maps, and image comparisons. Results include coordinates, an error radius, evidence images, and confidence levels that distinguish verified findings from uncertain candidates.
Search Wayback Machine archives for deleted GitHub files, issues, pull requests, and wiki pages. Recover available text and repository details from saved web pages to investigate a project's past state.
Prepares Claude Code or OpenAI Codex for in-depth research with hyperresearch, then hands the request to a structured workflow for research reports, literature reviews, and analysis using multiple sources with verified citations.
Investigate firsthand sources before making a judgment or recommendation. Separate verified facts, reasoned inferences, and unknowns, document their sources, and produce a conclusion that explains the current situation, constraints, and remaining uncertainty.
Retrieve pages blocked by web access filters, read Chinese and social platforms through dedicated tools, and inspect archived copies with their dates. Escalate to browser interaction when simpler extraction methods cannot provide the needed content.
Investigate a topic with cooperating agents assigned to distinct questions. Track sources, conflicting evidence, and unresolved claims, then assemble a cited deliverable with verification records and quality checks suited to the requested format.