Results for “equation-solving”

Provides guidance for using SymPy for exact symbolic mathematics in Python, covering algebra, calculus, equation solving, linear algebra, physics, and code generation.

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...

Strategic patterns for solving intractable problems through cascading approximation, self-improvement, and heterogeneous evaluation from DeepMind's AlphaGo system

Advanced Logic Testing Skill

Algebra Based Analysis Skill

Universal transformation λ(ο,K).τ with recursive self-improvement. USE WHEN routing reasoning, validating knowledge graphs, preparing CICM/ANZCA examinations, or when self-improvement of reasoning/architecture/context is required. Routes queries through R0-R3 complexity pipelines, validates topology (η≥target) and governance (KROG), emits per style (Φ), and compounds learnings into knowledge K. Triggers on complexity assessment, multi-step reasoning, examination mode, or /λ invocation.

Applied Logic Modeling Skill

Algebra Based Estimation Skill

当意识到自己处于长期迷茫、缺乏动力阶段，需要系统性方法走出困境时

Applied Logic Testing Skill

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

Calculus Based Analysis Skill

Advanced Algebra Testing Skill

Harness Compound

Balance game systems including difficulty curves, stat tuning, economy rates, matchmaking fairness, and player power progression. Use when tuning numbers and systems for fair, engaging gameplay. Also trigger for "game balance", "difficulty tuning", "stat balancing", "nerf", "buff", "power curve", or "difficulty curve".

Applies TRIZ cross-domain analogical reasoning to find solutions from adjacent fields. Use when stuck on a problem and needing inventive perspectives.

Advanced Logic Debugging Skill

Socratic coach for breaking down problems to fundamental truths. Use when users want to think through a problem deeply, challenge assumptions, or find innovative solutions. Triggers on requests like "help me think through this", "let's break this down", "what are my blind spots", "I'm stuck on a problem", "challenge my assumptions", or explicit requests for first-principles thinking.

Algebra Modeling Expert Skill

Calculus Design Expert Skill

当遇到令人情绪激动或陷入僵局的情境，需要跳出固有反应模式以做出更优决策时

Solve Advent of Code puzzles and algorithm challenges with a TDD workflow, algorithm selection guidance, and input parsing patterns.

Algebra Debugging Expert Skill

Advanced Optics Design Skill

实现问题分析和技能调用的完整思考链路，支持AI快速识别和调用合适的技能。

Use when writing, solving, or debugging MATLAB optimization code — formulating problems (optimproblem, optimvar, fcn2optimexpr), selecting and configuring solvers (fmincon, linprog, quadprog, intlinprog, lsqnonlin, ga, surrogateopt, optimoptions), or validating results (exitflag, convergence, constraint violations). Covers problem-based and solver-based approaches, solver tuning, and solution verification.

Analyze complex systems through stocks, flows, and feedback loops to find high-leverage interventions. For organizational, environmental, social, and technical systems exhibiting circular causality. NOT for linear problems or simple cause-effect chains.

Understand through recursive decomposition and modular reconstruction of simple operations to reproduce emergent complexity. Use this skill whenever reasoning is required. Framework for [[#parse|parsing]], [[#branch|branching]], [[#reduce|reducing]], [[#ground|grounding]] and [[#emit|emitting]]. Employs metacognitive reasoning epistemology, leveraging first principles through recursive decomposition[^1]. Self-referential and scale-invariant.

SONA self-optimizing neural architecture with ReasoningBank trajectory learning, EWC++ anti-forgetting, and reinforcement learning feedback loops.

当需要在写作中与读者建立情感连接、放大问题严重性，并引出后续解决方案时